diff --git a/changelog b/changelog index 160ae63..c4acf60 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,4 @@ +20081122 tpd src/axiom-website put website under change control 20081122 tpd zips/gcl-2.6.8pre3.unixport.makefile.patch added 20081122 tpd zips/gcl-2.6.8pre3.unixport.init_gcl.lsp.in.patch added 20081122 tpd zips/gcl-2.6.8pre3.cmpnew.gcl_cmpflet.lsp.patch added diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html new file mode 100644 index 0000000..b74f1c8 --- /dev/null +++ b/src/axiom-website/CATS/index.html @@ -0,0 +1,128 @@ + + + + (CATS) Computer Algebra Test Suite + + + +This work is part of the Computer Algebra Test Suite (CATS). +These files show the results that Axiom computes given the +set of integrals listed in +
+  Spiegel, Murray R. 
+  Mathematical Handbook of Formulas and Tables
+  Schaum's Outline Series McGraw-Hill 1968 
+
+

+Each integral is computed by Axiom and compared against the +published result. +

+Each Axiom result is differenced from the published result +and reduced to a constant (usually 0). +

+ + + Schaums 14.59-14.83  + source + pdf
+ Schaums 14.84-14.104  + source + pdf
+ Schaums 14.104-14.112  + source + pdf
+ Schaums 14.113-.119  + source + pdf
+ Schaums 14.120-14.124  + source + pdf
+ Schaums 14.125-14.143  + source + pdf
+ Schaums 14.144-14.162  + source + pdf
+ Schaums 14.163-14.181  + source + pdf
+ Schaums 14.182-14.209  + source + pdf
+ Schaums 14.210-14.236  + source + pdf
+ Schaums 14.237-14.264  + source + pdf
+ Schaums 14.265-14.279  + source + pdf
+ Schaums 14.280-14.298  + source + pdf
+ Schaums 14.299-14.310  + source + pdf
+ Schaums 14.311-14.324  + source + pdf
+ Schaums 14.325-14.338  + source + pdf
+ Schaums 14.339-14.368  + source + pdf
+ Schaums 14.369-14.398  + source + pdf
+ Schaums 14.399-14.428  + source + pdf
+ Schaums 14.429-14.439  + source + pdf
+ Schaums 14.440-14.450  + source + pdf
+ Schaums 14.451-14.460  + source + pdf
+ Schaums 14.461-14.470  + source + pdf
+ Schaums 14.471-14.508  + source + pdf
+ Schaums 14.509-14.524  + source + pdf
+ Schaums 14.525-14.539  + source + pdf
+ Schaums 14.540-14.561  + source + pdf
+ Schaums 14.562-14.589  + source + pdf
+ Schaums 14.590-14.603  + source + pdf
+ Schaums 14.604-14.614  + source + pdf
+ Schaums 14.615-14.625  + source + pdf
+ Schaums 14.626-14.635  + source + pdf
+ Schaums 14.636-14.645  + source + pdf
+ Schaums 14.646-14.677  + source + pdf
+ + \ No newline at end of file diff --git a/src/axiom-website/CATS/schaum1.input.pamphlet b/src/axiom-website/CATS/schaum1.input.pamphlet new file mode 100644 index 0000000..615d907 --- /dev/null +++ b/src/axiom-website/CATS/schaum1.input.pamphlet @@ -0,0 +1,1430 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/input schaum1.input} +\author{Timothy Daly} +\maketitle +\eject +\tableofcontents +\eject +\section{\cite{1}:14.59~~~~~$\displaystyle +\int{\frac{dx}{ax+b}}$} +$$\int{\frac{1}{ax+b}}= +\frac{1}{a}~\ln(ax+b) +$$ +<<*>>= +)spool schaum1.output +)set message test on +)set message auto off +)clear all + +--S 1 +aa:=integrate(1/(a*x+b),x) +--R +--R log(a x + b) +--R (1) ------------ +--R a +--R Type: Union(Expression Integer,...) +--E 1 + +--S 2 +bb:=1/a*log(a*x+b) +--R +--R log(a x + b) +--R (2) ------------ +--R a +--R Type: Expression Integer +--E + +--S 3 14:59 Schaums and Axiom agree +cc:=bb-aa +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.60~~~~~$\displaystyle +\int{\frac{x~dx}{ax+b}}$} +$$\int{\frac{x}{ax+b}}= +\frac{x}{a}-\frac{b}{a^2}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 4 +aa:=integrate(x/(a*x+b),x) +--R +--R +--R - b log(a x + b) + a x +--R (1) ---------------------- +--R 2 +--R a +--R Type: Union(Expression Integer,...) +--E + +--S 5 +bb:=x/a-b/a^2*log(a*x+b) +--R +--R - b log(a x + b) + a x +--R (2) ---------------------- +--R 2 +--R a +--R Type: Expression Integer +--E + +--S 6 14:60 Schaums and Axiom agree +cc:=bb-aa +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.61~~~~~$\displaystyle +\int{\frac{x^2~dx}{ax+b}}$} +$$\int{\frac{x^2}{ax+b}}= +\frac{(ax+b)^2}{2a^3}-\frac{2b(ax+b)}{a^3}+\frac{b^2}{a^3}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 7 +aa:=integrate(x^2/(a*x+b),x) +--R +--R 2 2 2 +--R 2b log(a x + b) + a x - 2a b x +--R (1) ------------------------------- +--R 3 +--R 2a +--R Type: Union(Expression Integer,...) +--E + +--S 8 +bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b) +--R +--R 2 2 2 2 +--R 2b log(a x + b) + a x - 2a b x - 3b +--R (2) ------------------------------------- +--R 3 +--R 2a +--R Type: Expression Integer +--E + +--S 9 +cc:=bb-aa +--R +--R 2 +--R 3b +--R (3) - --- +--R 3 +--R 2a +--R Type: Expression Integer +--E +@ +This factor is constant with respect to $x$ as shown by taking the +derivative. It is a constant of integration. +<<*>>= +--S 10 14:61 Schaums and Axiom differ by a constant +differentiate(cc,x) +--R +--R (4) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.62~~~~~$\displaystyle +\int{\frac{x^3~dx}{ax+b}}$} +$$\int{\frac{x^3}{ax+b}}= +\frac{(ax+b)^3}{3a^4}-\frac{3b(ax+b)^2}{2a^4}+ +\frac{3b^2(ax+b)}{a^4}-\frac{b^3}{a^4}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 11 +aa:=integrate(x^3/(a*x+b),x) +--R +--R 3 3 3 2 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (1) -------------------------------------------- +--R 4 +--R 6a +--R Type: Union(Expression Integer,...) +--E +@ +and the book expression is: +<<*>>= +--S 12 +bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b) +--R +--R 3 3 3 2 2 2 3 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x + 11b +--R (2) --------------------------------------------------- +--R 4 +--R 6a +--R Type: Expression Integer +--E +@ + +The difference is a constant with respect to x: +<<*>>= +--S 13 +cc:=aa-bb +--R +--R 3 +--R 11b +--R (3) - ---- +--R 4 +--R 6a +--R Type: Expression Integer +--E +@ + +If we differentiate each expression we see that this is the integration +constant. +<<*>>= +--S 14 14:62 Schaums and Axiom differ by a constant +dd:=D(cc,x) +--R +--R (4) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.63~~~~~$\displaystyle +\int{\frac{dx}{x~(ax+b)}}$} +$$\int{\frac{1}{x~(ax+b)}}= +\frac{1}{b}~\ln\left(\frac{x}{ax+b}\right) +$$ +<<*>>= +)clear all + +--S 15 +aa:=integrate(1/(x*(a*x+b)),x) +--R +--R - log(a x + b) + log(x) +--R (1) ----------------------- +--R b +--R Type: Union(Expression Integer,...) +--E + +--S 16 +bb:=1/b*log(x/(a*x+b)) +--R +--R x +--R log(-------) +--R a x + b +--R (2) ------------ +--R b +--R Type: Expression Integer +--E + +--S 17 +cc:=aa-bb +--R +--R x +--R - log(a x + b) + log(x) - log(-------) +--R a x + b +--R (3) -------------------------------------- +--R b +--R Type: Expression Integer +--E +@ +but we know that $$\log(a)-\log(b)=\log(\frac{a}{b})$$ + +We can express this fact as a rule: +<<*>>= +--S 18 +logdiv:=rule(log(a)-log(b) == log(a/b)) +--R +--R a +--I (4) - log(b) + log(a) + %I == log(-) + %I +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E +@ +and use this rule to rewrite the logs into divisions: +<<*>>= +--S 19 14:63 Schaums and Axiom agree +dd:=logdiv cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ +so we can see the equivalence directly. + +\section{\cite{1}:14.64~~~~~$\displaystyle +\int{\frac{dx}{x^2~(ax+b)}}$} +$$\int{\frac{1}{x^2~(ax+b)}}= +-\frac{1}{bx}+\frac{a}{b^2}~\ln\left(\frac{ax+b}{x}\right) +$$ +<<*>>= +)clear all + +--S 20 +aa:=integrate(1/(x^2*(a*x+b)),x) +--R +--R a x log(a x + b) - a x log(x) - b +--R (1) --------------------------------- +--R 2 +--R b x +--R Type: Union(Expression Integer,...) +--E +@ + +The original form given in the book expands to: +<<*>>= +--S 21 +bb:=-1/(b*x)+a/b^2*log((a*x+b)/x) +--R +--R a x + b +--R a x log(-------) - b +--R x +--R (2) -------------------- +--R 2 +--R b x +--R Type: Expression Integer +--E + +--S 22 +cc:=aa-bb +--R +--R a x + b +--R a log(a x + b) - a log(x) - a log(-------) +--R x +--R (3) ------------------------------------------ +--R 2 +--R b +--R Type: Expression Integer +--E +@ + +We can define the following rule to expand log forms: +<<*>>= +--S 23 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E +@ +and apply it to the difference +<<*>>= +--S 24 14:64 Schaums and Axiom agree +divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.65~~~~~$\displaystyle +\int{\frac{dx}{x^3~(ax+b)}}$} +$$\int{\frac{1}{x^3~(ax+b)}}= +\frac{2ax-b}{2b^2x^2}+\frac{a^2}{b^3}~\ln\left(\frac{x}{ax+b}\right) +$$ +<<*>>= +)clear all +--S 25 +aa:=integrate(1/(x^3*(a*x+b)),x) +--R +--R 2 2 2 2 2 +--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b +--R (1) ----------------------------------------------- +--R 3 2 +--R 2b x +--R Type: Union(Expression Integer,...) +--E + +--S 26 +bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b)) +--R +--R 2 2 x 2 +--R 2a x log(-------) + 2a b x - b +--R a x + b +--R (2) ------------------------------- +--R 3 2 +--R 2b x +--R Type: Expression Integer +--E + +--S 27 +cc:=aa-bb +--R +--R 2 2 2 x +--R - a log(a x + b) + a log(x) - a log(-------) +--R a x + b +--R (3) -------------------------------------------- +--R 3 +--R b +--R Type: Expression Integer +--E + +--S 28 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 29 14:65 Schaums and Axiom agree +dd:=divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.66~~~~~$\displaystyle +\int{\frac{dx}{(ax+b)^2}}$} +$$\int{\frac{1}{(ax+b)^2}}= +\frac{-1}{a~(ax+b)} +$$ +<<*>>= +)clear all + +--S 30 +aa:=integrate(1/(a*x+b)^2,x) +--R +--R 1 +--R (1) - --------- +--R 2 +--R a x + a b +--R Type: Union(Expression Integer,...) +--E + +--S 31 +bb:=-1/(a*(a*x+b)) +--R +--R 1 +--R (2) - --------- +--R 2 +--R a x + a b +--R Type: Fraction Polynomial Integer +--E + +--S 32 14:66 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.67~~~~~$\displaystyle +\int{\frac{x~dx}{(ax+b)^2}}$} +$$\int{\frac{x}{(ax+b)^2}}= +\frac{b}{a^2~(ax+b)}+\frac{1}{a^2}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 33 +aa:=integrate(x/(a*x+b)^2,x) +--R +--R (a x + b)log(a x + b) + b +--R (1) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Union(Expression Integer,...) +--E + +--S 34 +bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b) +--R +--R (a x + b)log(a x + b) + b +--R (2) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Expression Integer +--E + +--S 35 14:67 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.68~~~~~$\displaystyle +\int{\frac{x^2~dx}{(ax+b)^2}}$} +$$\int{\frac{x^2}{(ax+b)^2}}= +\frac{ax+b}{a^3}-\frac{b^2}{a^3~(ax+b)} +-\frac{2b}{a^3}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 36 +aa:=integrate(x^2/(a*x+b)^2,x) +--R +--R 2 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (1) ------------------------------------------------ +--R 4 3 +--R a x + a b +--R Type: Union(Expression Integer,...) +--E +@ +and the book expression expands into +<<*>>= +--S 37 +bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b) +--R +--R 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + 2a b x +--R (2) -------------------------------------------- +--R 4 3 +--R a x + a b +--R Type: Expression Integer +--E +@ + +These two expressions differ by the constant +<<*>>= +--S 38 +cc:=aa-bb +--R +--R b +--R (3) - -- +--R 3 +--R a +--R Type: Expression Integer +--E +@ + +That this expression is constant can be shown by differentiation: +<<*>>= +--S 39 14:68 Schaums and Axiom differ by a constant +D(cc,x) +--R +--R (4) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.69~~~~~$\displaystyle +\int{\frac{x^3~dx}{(ax+b)^2}}$} +$$\int{\frac{x^3}{(ax+b)^2}}= +\frac{(ax+b)^2}{2a^4}-\frac{3b(ax+b)}{a^4}+\frac{b^3}{a^4(ax+b)} ++\frac{3b^2}{a^4}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 40 +aa:=integrate(x^3/(a*x+b)^2,x) +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (1) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Union(Expression Integer,...) +--E + +--S 41 +bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b) +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 9a b x - 3b +--R (2) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Expression Integer +--E + +--S 42 +cc:=aa-bb +--R +--R 2 +--R 5b +--R (3) --- +--R 4 +--R 2a +--R Type: Expression Integer +--E + +--S 43 14:69 Schaums and Axiom differ by a constant +dd:=D(cc,x) +--R +--R (4) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.70~~~~~$\displaystyle +\int{\frac{dx}{x~(ax+b)^2}}$} +$$\int{\frac{1}{x~(ax+b)^2}}= +\frac{1}{b~(ax+b)}+\frac{1}{b^2}~\ln\left(\frac{x}{ax+b}\right) +$$ +<<*>>= +)clear all + +--S 44 +aa:=integrate(1/(x*(a*x+b)^2),x) +--R +--R (- a x - b)log(a x + b) + (a x + b)log(x) + b +--R (1) --------------------------------------------- +--R 2 3 +--R a b x + b +--R Type: Union(Expression Integer,...) +--E +@ +and the book says: +<<*>>= +--S 45 +bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b))) +--R +--R x +--R (a x + b)log(-------) + b +--R a x + b +--R (2) ------------------------- +--R 2 3 +--R a b x + b +--R Type: Expression Integer +--E + +--S 46 +cc:=aa-bb +--R +--R x +--R - log(a x + b) + log(x) - log(-------) +--R a x + b +--R (3) -------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E +@ +So we look at the divlog rule again: +<<*>>= +--S 47 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E +@ + +we apply it: +<<*>>= +--S 48 14:70 Schaums and Axiom agree +dd:=divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.71~~~~~$\displaystyle +\int{\frac{dx}{x^2~(ax+b)^2}}$} +$$\int{\frac{1}{x^2~(ax+b)^2}}= +\frac{-a}{b^2~(ax+b)}-\frac{1}{b^2~x}+ +\frac{2a}{b^3}~\ln\left(\frac{ax+b}{x}\right) +$$ +<<*>>= +)clear all + +--S 49 +aa:=integrate(1/(x^2*(a*x+b)^2),x) +--R +--R 2 2 2 2 2 +--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b +--R (1) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + b x +--R Type: Union(Expression Integer,...) +--E +@ +and the book says: +<<*>>= +--S 50 +bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x) +--R +--R 2 2 a x + b 2 +--R (2a x + 2a b x)log(-------) - 2a b x - b +--R x +--R (2) ------------------------------------------ +--R 3 2 4 +--R a b x + b x +--R Type: Expression Integer +--E + +--S 51 +cc:=aa-bb +--R +--R a x + b +--R 2a log(a x + b) - 2a log(x) - 2a log(-------) +--R x +--R (3) --------------------------------------------- +--R 3 +--R b +--R Type: Expression Integer +--E +@ +which calls for our divlog rule: +<<*>>= +--S 52 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E +@ +which we use to transform the result: +<<*>>= +--S 53 14:71 Schaums and Axiom agree +dd:=divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.72~~~~~$\displaystyle +\int{\frac{dx}{x^3~(ax+b)^2}}$} +$$\int{\frac{1}{x^3~(ax+b)^2}}= +-\frac{(ax+b)^2}{2b^4x^2}+\frac{3a(ax+b)}{b^4x}- +\frac{a^3x}{b^4(ax+b)}-\frac{3a^2}{b^4}~\ln\left(\frac{ax+b}{x}\right) +$$ +<<*>>= +)clear all + +--S 54 +aa:=integrate(1/(x^3*(a*x+b)^2),x) +--R +--R (1) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - b +--R / +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Union(Expression Integer,...) +--E + +--S 55 +bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x) +--R +--R 3 3 2 2 a x + b 3 3 2 2 2 3 +--R (- 6a x - 6a b x )log(-------) + 3a x + 9a b x + 3a b x - b +--R x +--R (2) --------------------------------------------------------------- +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Expression Integer +--E + +--S 56 +cc:=aa-bb +--R +--R 2 2 2 a x + b 2 +--R - 6a log(a x + b) + 6a log(x) + 6a log(-------) - 3a +--R x +--R (3) ----------------------------------------------------- +--R 4 +--R 2b +--R Type: Expression Integer +--E + +--S 57 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 58 +dd:=divlog cc +--R +--R 2 +--R 3a +--R (5) - --- +--R 4 +--R 2b +--R Type: Expression Integer +--E + +--S 59 14:72 Schaums and Axiom differ by a constant +ee:=D(dd,x) +--R +--R (6) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.73~~~~~$\displaystyle +\int{\frac{dx}{(ax+b)^3}}$} +$$\int{\frac{1}{(ax+b)^3}}= +\frac{-1}{2a(ax+b)^2} +$$ +<<*>>= +)clear all + +--S 60 +aa:=integrate(1/(a*x+b)^3,x) +--R +--R 1 +--R (1) - ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression Integer,...) +--E + +--S 61 +bb:=-1/(2*(a*x+b)^2) +--R +--R 1 +--R (2) - -------------------- +--R 2 2 2 +--R 2a x + 4a b x + 2b +--R Type: Fraction Polynomial Integer +--E + +--S 62 +cc:=aa-bb +--R +--R a - 1 +--R (3) ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression Integer +--E + +--S 63 +dd:=aa/bb +--R +--R 1 +--R (4) - +--R a +--R Type: Expression Integer +--E + +--S 64 14:73 Schaums and Axiom differ by a constant +ee:=D(dd,x) +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.74~~~~~$\displaystyle +\int{\frac{x~dx}{(ax+b)^3}}$} +$$\int{\frac{x}{(ax+b)^3}}= +\frac{-1}{a^2(ax+b)}+\frac{b}{2a^2(ax+b)^2} +$$ +<<*>>= +)clear all + +--S 65 +aa:=integrate(x/(a*x+b)^3,x) +--R +--R - 2a x - b +--R (1) ---------------------- +--R 4 2 3 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression Integer,...) +--E + +--S 66 +bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2) +--R +--R - 2a x - b +--R (2) ---------------------- +--R 4 2 3 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Fraction Polynomial Integer +--E + +--S 67 14:74 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.75~~~~~$\displaystyle +\int{\frac{x^2~dx}{(ax+b)^3}}$} +$$\int{\frac{x^2}{(ax+b)^3}}= +\frac{2b}{a^3(ax+b)}-\frac{b^2}{2a^3(ax+b)^2}+ +\frac{1}{a^3}~\ln(ax+b) +$$ +<<*>>= +)clear all + +--S 68 +aa:=integrate(x^2/(a*x+b)^3,x) +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (1) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression Integer,...) +--E + +--S 69 +bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b) +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (2) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression Integer +--E + +--S 70 14:75 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.76~~~~~$\displaystyle +\int{\frac{x^3~dx}{(ax+b)^3}}$} +$$\int{\frac{x^3}{(ax+b)^3}}= +\frac{x}{a^3}-\frac{3b^2}{a^4(ax+b)}+\frac{b^3}{2a^4(ax+b)^2}- +\frac{3b}{a^4}~\ln(ax+b) +$$ +<<*>>= +)clear all +--S 71 +aa:=integrate(x^3/(a*x+b)^3,x) +--R +--R (1) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression Integer,...) +--E + +--S 72 +bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b) +--R +--R (2) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression Integer +--E + +--S 73 14:76 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.77~~~~~$\displaystyle +\int{\frac{dx}{x(ax+b)^3}}$} +$$\int{\frac{1}{x(ax+b)^3}}= +\frac{3}{2b(ax+b)^2}+\frac{2ax}{2b^2(ax+b)^2}- +\frac{1}{b^3}*\ln\left(\frac{ax+b}{x}\right) +$$ + +<<*>>= +)clear all + +--S 74 +aa:=integrate(1/(x*(a*x+b)^3),x) +--R +--R (1) +--R 2 2 2 2 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x) +--R + +--R 2 +--R 2a b x + 3b +--R / +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Union(Expression Integer,...) +--E + +--S 75 +bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x) +--R +--R 2 2 2 a x + b 2 2 +--R (- 2a x - 4a b x - 2b )log(-------) - 3a x - 4a b x +--R x +--R (2) ----------------------------------------------------- +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Expression Integer +--E + +--S 76 +cc:=aa-bb +--R +--R a x + b +--R - 2log(a x + b) + 2log(x) + 2log(-------) + 3 +--R x +--R (3) --------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E + +--S 77 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 78 +dd:=divlog cc +--R +--R 3 +--R (5) --- +--R 3 +--R 2b +--R Type: Expression Integer +--E + +--S 79 14:77 Schaums and Axiom differ by a constant +ee:=D(dd,x) +--R +--R (6) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.78~~~~~$\displaystyle +\int{\frac{dx}{x^2(ax+b)^3}}$} +$$\int{\frac{1}{x^2(ax+b)^3}}= +\frac{-a}{2b^2(ax+b)^2}-\frac{2a}{b^3(ax+b)}- +\frac{1}{b^3x}+\frac{3a}{b^4}~\ln\left(\frac{ax+b}{x}\right) +$$ +<<*>>= +)clear all + +--S 80 +aa:=integrate(1/(x^2*(a*x+b)^3),x) +--R +--R (1) +--R 3 3 2 2 2 +--R (6a x + 12a b x + 6a b x)log(a x + b) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression Integer,...) +--E + +--S 81 +bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x) +--R +--R 3 3 2 2 2 a x + b 2 2 2 3 +--R (6a x + 12a b x + 6a b x)log(-------) - 6a b x - 9a b x - 2b +--R x +--R (2) ---------------------------------------------------------------- +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Expression Integer +--E + +--S 82 +cc:=aa-bb +--R +--R a x + b +--R 3a log(a x + b) - 3a log(x) - 3a log(-------) +--R x +--R (3) --------------------------------------------- +--R 4 +--R b +--R Type: Expression Integer +--E + +--S 83 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 84 14:78 Schaums and Axiom agree +dd:=divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.79~~~~~$\displaystyle +\int{\frac{dx}{x^3(ax+b)^3}}$} +$$\int{\frac{1}{x^3(ax+b)^3}}= +-\frac{1}{2bx^2(ax+b)^2}+ +\frac{2a}{b^2x(ax+b)^2}+ +\frac{9a^2}{b^3(ax+b)^2}+ +\frac{6a^3x}{b^4(ax+b)^2}- +\frac{6a^2}{b^5}~\ln\left(\frac{ax+b}{x}\right)$$ + +<<*>>= +)clear all + +--S 85 +aa:=integrate(1/(x^3*(a*x+b)^3),x) +--R +--R (1) +--R 4 4 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression Integer,...) +--E + +--S 86 +bb:=-1/(2*b*x^2*(a*x+b)^2)_ + +(2*a)/(b^2*x*(a*x+b)^2)_ + +(9*a^2)/(b^3*(a*x+b)^2)_ + +(6*a^3*x)/(b^4*(a*x+b)^2)_ + +(-6*a^2)/b^5*log((a*x+b)/x) +--R +--R (2) +--R 4 4 3 3 2 2 2 a x + b 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(-------) + 12a b x + 18a b x +--R x +--R + +--R 3 4 +--R 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Expression Integer +--E + +--S 87 +cc:=aa-bb +--R +--R 2 2 2 a x + b +--R - 6a log(a x + b) + 6a log(x) + 6a log(-------) +--R x +--R (3) ----------------------------------------------- +--R 5 +--R b +--R Type: Expression Integer +--E + +--S 88 +divlog:=rule(log(a/b) == log(a) - log(b)) +--R +--R a +--R (4) log(-) == - log(b) + log(a) +--R b +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 89 14:79 Schaums and Axiom agree +dd:=divlog cc +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.80~~~~~$\displaystyle +\int{(ax+b)^n~dx}$} +$$\int{(ax+b)^n}= +\frac{(ax+b)^{n+1}}{(n+1)a}{\rm\ provided\ }n \ne -1 +$$ +<<*>>= +)clear all +--S 90 +aa:=integrate((a*x+b)^n,x) +--R +--R n log(a x + b) +--R (a x + b)%e +--R (1) ------------------------- +--R a n + a +--R Type: Union(Expression Integer,...) +--E + +--S 91 +bb:=(a*x+b)^(n+1)/((n+1)*a) +--R +--R n + 1 +--R (a x + b) +--R (2) -------------- +--R a n + a +--R Type: Expression Integer +--E + +--S 92 +cc:=aa-bb +--R +--R n log(a x + b) n + 1 +--R (a x + b)%e - (a x + b) +--R (3) ------------------------------------------ +--R a n + a +--R Type: Expression Integer +--E +@ +This messy formula can be simplified using the explog rule: +<<*>>= +--S 93 +explog:=rule(%e^(n*log(x)) == x^n) +--R +--R n log(x) n +--R (4) %e == x +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 94 +dd:=explog cc +--R +--R n + 1 n +--R - (a x + b) + (a x + b)(a x + b) +--R (5) -------------------------------------- +--R a n + a +--R Type: Expression Integer +--E + +--S 95 14:80 Schaums and Axiom agree +ee:=complexNormalize dd +--R +--R (6) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.81~~~~~$\displaystyle +\int{x(ax+b)^n~dx}$} +$$\int{x(ax+b)^n}= +\frac{(ax+b)^{n+2}}{(n+2)a^2}-\frac{b(ax+b)^{n+1}}{(n+1)a^2} +{\rm\ provided\ }n \ne -1,-2 +$$ +<<*>>= +)clear all +--S 96 +aa:=integrate(x*(a*x+b)^n,x) +--R +--R 2 2 2 2 n log(a x + b) +--R ((a n + a )x + a b n x - b )%e +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Union(Expression Integer,...) +--E + +--S 97 +bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2) +--R +--R n + 2 n + 1 +--R (n + 1)(a x + b) + (- b n - 2b)(a x + b) +--R (2) -------------------------------------------------- +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression Integer +--E + +--S 98 +cc:=aa-bb +--R +--R (3) +--R 2 2 2 2 n log(a x + b) n + 2 +--R ((a n + a )x + a b n x - b )%e + (- n - 1)(a x + b) +--R + +--R n + 1 +--R (b n + 2b)(a x + b) +--R / +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression Integer +--E + +--S 99 +explog:=rule(%e^(n*log(x)) == x^n) +--R +--R n log(x) n +--R (4) %e == x +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 100 +dd:=explog cc +--R +--R (5) +--R n + 2 n + 1 +--R (- n - 1)(a x + b) + (b n + 2b)(a x + b) +--R + +--R 2 2 2 2 n +--R ((a n + a )x + a b n x - b )(a x + b) +--R / +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression Integer +--E + +--S 101 +ee:=complexNormalize dd +--R +--R (6) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.82~~~~~$\displaystyle +\int{x^2(ax+b)^n~dx}$} +$$\int{x^2(ax+b)^n}= +\frac{(ax+b)^{n+2}}{(n+3)a^3}- +\frac{2b(ax+b)^{n+2}}{(n+2)a^3}+ +\frac{b^2(ax+b)^{n+1}}{(n+1)a^3} +{\rm\ provided\ }n \ne -1,-2,-3 +$$ + +<<*>>= +)clear all +--S 102 +aa:=integrate(x^2*(a*x+b)^n,x) +--R +--R (1) +--R 3 2 3 3 3 2 2 2 2 2 3 n log(a x + b) +--R ((a n + 3a n + 2a )x + (a b n + a b n)x - 2a b n x + 2b )%e +--R ----------------------------------------------------------------------------- +--R 3 3 3 2 3 3 +--R a n + 6a n + 11a n + 6a +--R Type: Union(Expression Integer,...) +--E + +--S 103 +bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3) +--R +--R (2) +--R 2 n + 3 2 n + 2 +--R (n + 3n + 2)(a x + b) + (- 2b n - 8b n - 6b)(a x + b) +--R + +--R 2 2 2 2 n + 1 +--R (b n + 5b n + 6b )(a x + b) +--R / +--R 3 3 3 2 3 3 +--R a n + 6a n + 11a n + 6a +--R Type: Expression Integer +--E + +--S 104 +cc:=aa-bb +--R +--R (3) +--R 3 2 3 3 3 2 2 2 2 2 3 +--R ((a n + 3a n + 2a )x + (a b n + a b n)x - 2a b n x + 2b ) +--R * +--R n log(a x + b) +--R %e +--R + +--R 2 n + 3 2 n + 2 +--R (- n - 3n - 2)(a x + b) + (2b n + 8b n + 6b)(a x + b) +--R + +--R 2 2 2 2 n + 1 +--R (- b n - 5b n - 6b )(a x + b) +--R / +--R 3 3 3 2 3 3 +--R a n + 6a n + 11a n + 6a +--R Type: Expression Integer +--E + +--S 105 +explog:=rule(%e^(n*log(x)) == x^n) +--R +--R n log(x) n +--R (4) %e == x +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 106 +dd:=explog cc +--R +--R (5) +--R 2 n + 3 2 n + 2 +--R (- n - 3n - 2)(a x + b) + (2b n + 8b n + 6b)(a x + b) +--R + +--R 2 2 2 2 n + 1 +--R (- b n - 5b n - 6b )(a x + b) +--R + +--R 3 2 3 3 3 2 2 2 2 2 3 n +--R ((a n + 3a n + 2a )x + (a b n + a b n)x - 2a b n x + 2b )(a x + b) +--R / +--R 3 3 3 2 3 3 +--R a n + 6a n + 11a n + 6a +--R Type: Expression Integer +--E + +--S 107 14:82 Schaums and Axiom agree +ee:=complexNormalize dd +--R +--R (6) 0 +--R Type: Expression Integer +--E +@ +\section{\cite{1}:14.83~~~~~$\displaystyle +\int{x^m(ax+b)^n}~dx$} +$$\int{x^m(ax+b)^n} +\left\{ +\begin{array}{l} +\displaystyle +\frac{x^{m+1}(ax+b)^n}{m+n+1} ++\frac{nb}{m+n+1}\int{x^m(ax+b)^{n-1}}\\ +\\ +\displaystyle +\frac{x^{m+1}(ax+b)^{n+1}}{(m+n+1)a} +-\frac{mb}{(m+n+1)a}\int{x^{m-1}(ax+b)^n}\\ +\\ +\displaystyle +\frac{-x^{m+1}(ax+b)^{n+1}}{(n+1)b} ++\frac{m+n+2}{(n+1)b}\int{x^m(ax+b)^{n+1}}\\ +\end{array} +\right. +$$ + +<<*>>= +--S 108 14:83 Axiom cannot do this integration +aa:=integrate(x^m*(a*x+b)^n,x) +--R +--R x +--R ++ m n +--I (1) | %U (b + %U a) d%U +--R ++ +--R Type: Union(Expression Integer,...) +--E + +)spool +)lisp (bye) +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} Spiegel, Murray R. +{\sl Mathematical Handbook of Formulas and Tables}\\ +Schaum's Outline Series McGraw-Hill 1968 pp60-61 +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/schaum1.input.pdf b/src/axiom-website/CATS/schaum1.input.pdf new file mode 100644 index 0000000..1c316b5 --- /dev/null +++ b/src/axiom-website/CATS/schaum1.input.pdf @@ -0,0 +1,3029 @@ +%PDF-1.2 +7 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +10 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F1 +/FontDescriptor 9 0 R +/BaseFont/FPGSSG+CMR17 +/FirstChar 33 +/LastChar 196 +/Widths[249.6 458.6 772.1 458.6 772.1 719.8 249.6 354.1 354.1 458.6 719.8 249.6 301.9 +249.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 249.6 249.6 +249.6 719.8 432.5 432.5 719.8 693.3 654.3 667.6 706.6 628.2 602.1 726.3 693.3 327.6 +471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 +693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 +458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 +510.9 484.7 667.6 484.7 484.7 406.4 458.6 917.2 458.6 458.6 458.6 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 576 772.1 719.8 641.1 615.3 693.3 +667.6 719.8 667.6 719.8 0 0 667.6 525.4 499.3 499.3 748.9 748.9 249.6 275.8 458.6 +458.6 458.6 458.6 458.6 693.3 406.4 458.6 667.6 719.8 458.6 837.2 941.7 719.8 249.6 +458.6] +>> +endobj +13 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F2 +/FontDescriptor 12 0 R +/BaseFont/ZTNFWY+CMR12 +/FirstChar 33 +/LastChar 196 +/Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 +462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 +734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 +272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 +544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 +489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 +761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 +299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 +761.6 272 489.6] +>> +endobj +16 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F3 +/FontDescriptor 15 0 R +/BaseFont/KHZWRY+CMR10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +18 0 obj +<< +/Filter[/FlateDecode] +/Length 179 +>> +stream +x%@ wÑHwĄی1*$& Ԧ/h^ >) "'ԁ/j{9G֩}wX4=T5盯t1e!oDl4;fӂͯb +jK$Sօvk@y4㌙̢Q46 +endstream +endobj +20 0 obj +<< +/F1 10 0 R +/F2 13 0 R +/F3 16 0 R +>> +endobj +6 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 20 0 R +>> +endobj +25 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F4 +/FontDescriptor 24 0 R +/BaseFont/DKLHRG+CMBX12 +/FirstChar 33 +/LastChar 196 +/Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 +562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 +875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 +675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 +687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 +343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 +593.7 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 +656.2 625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 +812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] +>> +endobj +28 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F5 +/FontDescriptor 27 0 R +/BaseFont/OOVPHA+CMBX10 +/FirstChar 33 +/LastChar 196 +/Widths[350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 +575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 +869.4 818.1 830.6 881.9 755.6 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 +863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 +319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 +319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 +511.1 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 691.7 958.3 894.4 805.6 766.7 900 830.6 894.4 830.6 894.4 0 0 830.6 670.8 +638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 +575 1041.7 1169.4 894.4 319.4 575] +>> +endobj +31 0 obj +<< +/Type/Font +/Subtype/Type1 +/Name/F6 +/FontDescriptor 30 0 R +/BaseFont/IORQIL+CMEX10 +/FirstChar 33 +/LastChar 196 +/Widths[791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 +1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 +888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 +1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 +833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 +1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 +1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 458.3 458.3 416.7 416.7 +472.2 472.2 472.2 472.2 583.3 583.3 0 0 472.2 472.2 333.3 555.6 577.8 577.8 597.2 +597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 +791.7 777.8] +>> +endobj +32 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/omega/epsilon/theta1/pi1/rho1/sigma1/phi1/arrowlefttophalf/arrowleftbothalf/arrowrighttophalf/arrowrightbothalf/arrowhookleft/arrowhookright/triangleright/triangleleft/zerooldstyle/oneoldstyle/twooldstyle/threeoldstyle/fouroldstyle/fiveoldstyle/sixoldstyle/sevenoldstyle/eightoldstyle/nineoldstyle/period/comma/less/slash/greater/star/partialdiff/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/flat/natural/sharp/slurbelow/slurabove/lscript/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/dotlessi/dotlessj/weierstrass/vector/tie/psi +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/tie] +>> +endobj +35 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F7 +/FontDescriptor 34 0 R +/BaseFont/ZHEONB+CMMI10 +/FirstChar 33 +/LastChar 196 +/Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 +750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 +762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 +388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 +298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 +465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 +639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 +570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] +>> +endobj +38 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F8 +/FontDescriptor 37 0 R +/BaseFont/OZINXB+CMR7 +/FirstChar 33 +/LastChar 196 +/Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 +323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 +323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 +874 706.4 1027.8 843.3 877 767.9 877 829.4 631 815.5 843.3 843.3 1150.8 843.3 843.3 +692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 +323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 +600.2 600.2 507.9 569.4 1138.9 569.4 569.4 569.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 +877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 +843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] +>> +endobj +39 0 obj +<< +/Filter[/FlateDecode] +/Length 824 +>> +stream +xݘK0 +Bxc@<.,@b>~$inJPrbObJʗ(4Fm?)DueٷƋfJT`ZudbMH.I|l`'A!1Ã.E8]~yN*tx^ 5@<.N>>ng}DDT!>wPyr? 6McCW N,BRVĕ|`o/pJ=hnjaG YMYBW pȫoh[ifՏ'4zs\AVgÛ|N=CpÑ9M=x4 N=ڃ]!E ɃÏ CEdx"*FLwˀNkc| +%q #7 >MIE|i8@JΎ|2 u$%zDף@ }4x+ ƌ YcX Bcpv3$};c}c#lKnH0V`W}Cs҇Rl?wç-T-8ھ+$ 홗+DmEzVEDI,ԜZQRa(EѬ(EʇILNr?C'X&WfO2;2HgmfI= F +endstream +endobj +40 0 obj +<< +/F4 25 0 R +/F5 28 0 R +/F6 31 0 R +/F7 35 0 R +/F3 16 0 R +/F8 38 0 R +>> +endobj +22 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 40 0 R +>> +endobj +45 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F9 +/FontDescriptor 44 0 R +/BaseFont/NBNZIE+CMMI7 +/FirstChar 33 +/LastChar 196 +/Widths[719.7 539.7 689.9 950 592.7 439.2 751.4 1138.9 1138.9 1138.9 1138.9 339.3 +339.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 339.3 +339.3 892.9 585.3 892.9 585.3 610.1 859.1 863.2 819.4 934.1 838.7 724.5 889.4 935.6 +506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 +1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 +594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 +530.4 539.2 431.6 675.4 571.4 826.4 647.8 579.4 545.8 398.6 442 730.1 585.3 339.3 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 693.8 954.4 868.9 +797.6 844.5 935.6 886.3 677.6 769.8 716.9 0 0 880 742.7 647.8 600.1 519.2 476.1 519.8 +588.6 544.1 422.8 668.8 677.6 694.6 572.8 519.8 668 592.7 662 526.8 632.9 686.9 713.8 +756 339.3] +>> +endobj +46 0 obj +<< +/Filter[/FlateDecode] +/Length 643 +>> +stream +xՖMs0@ +acő2Õh{(Ӂ J~>+q,v0Ҟ {~䌮mSxPZ]NЅ@W}_tb}ő/t+j_fwZ'Ov2? ?)SK% q8(r2glkAV7MeYMade)1/A&NNEZM؊JK/j7xR(H)iHD"hp@~wd_(\.(9c;wi5ڎ&lŇ u\.Eczh] [)}YϏ?Mת|?W>OsEOewvӒj{ x{C +endstream +endobj +47 0 obj +<< +/F5 28 0 R +/F6 31 0 R +/F7 35 0 R +/F3 16 0 R +/F8 38 0 R +/F9 45 0 R +>> +endobj +42 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 47 0 R +>> +endobj +52 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F10 +/FontDescriptor 51 0 R +/BaseFont/FYUDNE+CMMI12 +/FirstChar 33 +/LastChar 196 +/Widths[609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 +761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.9 772.4 811.3 431.9 541.2 833 666.2 +947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 +380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 +334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 +699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 +652.8 598 0 0 757.6 622.8 552.8 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 +589.1 483.8 427.7 555.4 505 556.5 425.2 527.8 579.5 613.4 636.6 272] +>> +endobj +53 0 obj +<< +/Type/Encoding +/Differences[0/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/arrowright/arrowup/arrowdown/arrowboth/arrownortheast/arrowsoutheast/similarequal/arrowdblleft/arrowdblright/arrowdblup/arrowdbldown/arrowdblboth/arrownorthwest/arrowsouthwest/proportional/prime/infinity/element/owner/triangle/triangleinv/negationslash/mapsto/universal/existential/logicalnot/emptyset/Rfractur/Ifractur/latticetop/perpendicular/aleph/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/union/intersection/unionmulti/logicaland/logicalor/turnstileleft/turnstileright/floorleft/floorright/ceilingleft/ceilingright/braceleft/braceright/angbracketleft/angbracketright/bar/bardbl/arrowbothv/arrowdblbothv/backslash/wreathproduct/radical/coproduct/nabla/integral/unionsq/intersectionsq/subsetsqequal/supersetsqequal/section/dagger/daggerdbl/paragraph/club/diamond/heart/spade/arrowleft +161/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus +173/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/spade] +>> +endobj +56 0 obj +<< +/Encoding 53 0 R +/Type/Font +/Subtype/Type1 +/Name/F11 +/FontDescriptor 55 0 R +/BaseFont/FXSWPD+CMSY10 +/FirstChar 33 +/LastChar 196 +/Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 +275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 +611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 +820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 +666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 +500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 +444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 +777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 +777.8 777.8 1000 1000 777.8 777.8 1000 777.8] +>> +endobj +57 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +60 0 obj +<< +/Encoding 57 0 R +/Type/Font +/Subtype/Type1 +/Name/F12 +/FontDescriptor 59 0 R +/BaseFont/KOKODZ+CMTI10 +/FirstChar 33 +/LastChar 196 +/Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 +306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 +306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 +525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 +743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 +460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 +460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 +766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 +511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] +>> +endobj +61 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/dieresis/visiblespace +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/dieresis] +>> +endobj +64 0 obj +<< +/Encoding 61 0 R +/Type/Font +/Subtype/Type1 +/Name/F13 +/FontDescriptor 63 0 R +/BaseFont/RRBBFY+CMTT10 +/FirstChar 33 +/LastChar 196 +/Widths[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 525 525 525 525 525 525 525 525 525 0 0 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525] +>> +endobj +65 0 obj +<< +/Filter[/FlateDecode] +/Length 647 +>> +stream +xڵUM0W,kWb$VK7{H,8Ҷ\{83Ɋi1~P,^hB&Ϗ@h&Z|?b5eTctmV*f乬0d.E D!Ԅ,4dCLcgP(utD[ Bh>@\ +2l3D(aX(s2,gJ#9ּODUA2 SC&f]i, 5uMt)R(:dȻPoL݉6 qIJ 2Oב0 Pvg*<|:,_X~,vǢ> +~N ݤCJݟ"=4|X mf X. q> +endobj +49 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 66 0 R +>> +endobj +69 0 obj +<< +/Filter[/FlateDecode] +/Length 677 +>> +stream +xVMo0 Wh7#a첺KivG[vaH + ۲jޭ׊IbHq4[ 0RnPFOk8SzH 2e=zmTV+pR<*+J(Z~M a 1=[(F@WEK  EeMQ kk6õ'Ȟ DX1r2l )РdCizJH֞1Tˡ>K[5]h!rC%ɾֲ#v-Q [*ـtP̘Kq)C;[&ҀabQ3CbۍW*ےpTA ?p5O abn;-?514!4UK>O!H++oTuNrwxɷ%ObE1˒94S-+">{r/@ 'tl@^4gw9sFEiQ(= OaH{U<gz˲KN1>bl~ _Eߩ!O1QurSuC ݘJ+Zmu5wm{|<l,i)gt*xE}Qu߂#8=zx +endstream +endobj +70 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F7 35 0 R +/F3 16 0 R +/F11 56 0 R +/F8 38 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +68 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 70 0 R +>> +endobj +73 0 obj +<< +/Filter[/FlateDecode] +/Length 821 +>> +stream +xW]o0}Wik_W bC &%IeIϵ6NFL0s8'$.țTTd&*&Y=Ȃ +zr..eDq0?53oBI2#>'۬B3Gb>yl;D+Bw_brB aq[δ$ dvr(NNڨ> +VG@HKc@Phd1=sL值cBjd1vx'#svÀ^,Ciu)˂zg5:MI?2nMĥ1z\"VFb3QsWWe]Ӫz΀'% H-pLQF ǟ:4_I/ +endstream +endobj +74 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +72 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 74 0 R +>> +endobj +77 0 obj +<< +/Filter[/FlateDecode] +/Length 1157 +>> +stream +xWKo6W('+>e c^:v;%[By}Ï2`~c.>*IJsۄ3lhXn'R*f-\T\>NbZr32kI'LԮv$IF!.65ȫ/$*=&QV>*x2\9%O(Oe?$KZ,f)|)<ѵE#VwMzg#]ˍo!.HU#a +V7N9q{x_Ob&eZIkEÖ~d[[nhz+h4hh+kE蒔u"t2]q&J#ZFD6?:<S +j'sߟXALVQX ޤѽD+)@*;"V,J=;3Abuj& I3{.<{`oVv ,eM08 c|O|F,>F:@rB4<2"q2BF( (S?0, ]|ς޳ ·ֆ"KYdl:pX|z&:nWA:A)@'G)JP+G+3:$~[G:r~OydQzZ$z~c4+3v+zӿ- +endstream +endobj +78 0 obj +<< +/F3 16 0 R +/F7 35 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F8 38 0 R +>> +endobj +76 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 78 0 R +>> +endobj +81 0 obj +<< +/Filter[/FlateDecode] +/Length 456 +>> +stream +xT;s0 +8RmɈQ c@Kt!b/ο/(Џvt> Q$iJlͽ"%/ W$7ܔwiݻ)h7423n6F)XM-.8y;&2>D$}|6 uG_Uɏͽм{#G89IgYó"gpjitIg KɌ +ذlZ\C}dlo#R*ĕLdyF cf93 +*BjZn\e z#FYf]a/4ԡ,8ۆHW'mH-C|br~!H$ cZӥGj8H=<Ž:vnX`|<4pke|܁HYDi냴J\* y~ eC +endstream +endobj +82 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +80 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 82 0 R +>> +endobj +85 0 obj +<< +/Filter[/FlateDecode] +/Length 719 +>> +stream +xڵVMo0 W5#[rq.{+EZ`޿e9>*[#IŌ5{v9T HŖߘAVl:ӓQodefqvioi_U`+klŒX(#4ΰL( zfWDso߸c$oNODq9vU{|U]ɱFA5HIM$)18BAP$J7FKCPVz8R+9JHTP:1 N1EԆHV! -@-zĐK4֛6+GB}7$ jچR]ޞ:JNfh&@Pni;S +)A{l~oP{L{ 4:=z@QY1]$tKu99@%*ޝʖyu-WE"EVN볪Rލ矆7s%8opGsr4]VӀb@!`o=C!j|?l~ܮ9n"pӴ.NojY5:(I쭳Z4[}F6,+u$b$#+ɮDX'T#}JzeW(-Puھy_*zO]// џ*yp+|ay=9Y +endstream +endobj +86 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +84 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 86 0 R +>> +endobj +89 0 obj +<< +/Filter[/FlateDecode] +/Length 1143 +>> +stream +xWMo6WRJ"ߤ Т"=&. +z ȶ6[4ChINE/8Cr(=8}'PF2fDg(՜f?}1I%]5 _u~L>~AJJ#=%)x;n41+. +Ey⍌VMhXduK +pmrc56,(GEU e^7HR gqK=Bj'X,(18Ċr +Iko>Y/}q8㺬{ʗ!yް?m}8>dӸw`x5>e/x=h'k"p藦IH7W_;}q>OҺpywSz->nSe2 lM2 +$n*h68#qCѐCtKV)ų/˾<5`cToγma|l̩|\<>a]η{7 +XB[x5ސy[ȝ]GNcu~z>L*wai_ԬVm|1cN N$7vWX7_1J[DY38c@}H1햕@e꼈0 >,㮊(AhBit֬T!32I7so]$\(wqPњ:W,Qh2tgKgWut e\!b,VÜBTPZdHBղH0C:GjCu 865܀j#{AƘ z13&fߖ). ,-`g[l E=Ǭ/ࢨ, Z8~kmx9ɀO4ofgoѩlz?uop!B!b! dӣ8 r2zXKֿ*y>ͦ)<Ry^mHMɴtkA9~W ׮Z3TBHQI%X }* GU=u߫_Rqkg)H$}0n!ߨ6Li½| +endstream +endobj +90 0 obj +<< +/F3 16 0 R +/F7 35 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F8 38 0 R +>> +endobj +88 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 90 0 R +>> +endobj +93 0 obj +<< +/Filter[/FlateDecode] +/Length 665 +>> +stream +xVK0Wp4I yH9jjY=VTlURCl32,KKv} ;yǴ`9`6[ >}*K"nSVfEA=hd48J? +bbO)>*ևβW> lpoC ѬV98)3$*\\*Ch'̰!!B'+mlkFCǑM}Ň:+w,8´4I~w{Yِ͚B2+/`e +endstream +endobj +94 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +92 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 94 0 R +>> +endobj +97 0 obj +<< +/Filter[/FlateDecode] +/Length 970 +>> +stream +xڵVM6WhM Rthsi]NڪCQ2)QZwZǑ ?[IBïDsj) Pw+SZwUVG9*4ֺ_BgdRR">>$n1YR[j5D K ++ӆIyEe08Vy}Dʡ**5ar,U_~ɒu_)2,qEHȀDZ.OhrPG 2ޚݐ<%v#@MIM97ҸL\Pn|n%;Xmn!㤑$Lw0cl +$/**S%@*OTx˞*fRETtuTiFde'*B7 +i:\AcNΕpq)WrˮF\]#sG,NO؍xsY)`h|ɩƆ$rx.ع\1,櫯I<v3]n'hټl)p{~` +Yϊ,pE7T$gP*O\ +Iq҈|VAu?>}9>/jŷժjUMSUIvz]Z0;u G JԲ؆16a@v!<::Rkq~Ke5ghi<tߟSi??0x~E)k;Ժ&;D:OhݾZ=S[u{U`۠Z/Jh?W[c>#>Z03t/5,&Y0Kbr}]9 zpKLp/m"\)`=tf̲1U\|g|xie^S'tYW9kt ngwϣ( +endstream +endobj +98 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +96 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 98 0 R +>> +endobj +101 0 obj +<< +/Filter[/FlateDecode] +/Length 281 +>> +stream +x}RAo WplP@ja-ULZmݺ?*ښLwzރ^ + xRu}K +`Xr7A%λz J?)&K3N..+gEdx?"SCN't۹x&~:\X7QǧNkuԅn·FmYW6秣d.iOA; 3P/r3=[UnsY{hA_k˲?OFq324\p*G\sf^nw2Rw^ +endstream +endobj +102 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +100 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 102 0 R +>> +endobj +105 0 obj +<< +/Filter[/FlateDecode] +/Length 680 +>> +stream +xڽMo1 +7 ύ p[ti#J{7fD  a#=y;;K̾(B Td:#9L\֣KMrȵWpAאYr$*!)!3W$? ޙPmj"(rж$Wm ;E, +& M<@ny W`1 +QCҮaxH* %K&C^C93`=/As[{LZ9@JÓ%# KZmNZē28@̌ (gR$pBz7O av|=BQ;ͺIxN[Z f=jIL9o5͗uQ.rlmW!*XLLn[>Eϋ> +endobj +104 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 106 0 R +>> +endobj +109 0 obj +<< +/Filter[/FlateDecode] +/Length 735 +>> +stream +x͖Ko1| + w@4\hZi4RPZ׻}$"*Ż߿K0F6\ޓə$\dhFj"w#QQ.{i]?N4qt́!_g)+j0P .FJN^$ >&T[wT)o`ЕauRV";9@<+rʸȢU4dʺ><S`x/@69Ӹ+n]^ ̀c`m^Jn+`MV+nRdvH@ h{,с^]kA +Sl X$5#dJPrیSEHW/h+R^i8`?Fgenȋ#p"7NQn*'<ɓA?Hmv+p<4a,+aeeO4zMmv|Qݮ*+;^zPzBiOŨ,FI1^.+|]TԉM*1?yVepw9n)Q)w! +b?A!2Fit|C}Z<׏9npiіlw'M٘ON7n~otXnis*\NwTwɿ>VÛb{[mtt|N_+^ +@C=깪 s6gg +endstream +endobj +110 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +108 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 110 0 R +>> +endobj +113 0 obj +<< +/Filter[/FlateDecode] +/Length 987 +>> +stream +xV]o6}߯ y)y꽬j)cS]DIV <"'!M8ܓv|PL*&*&1Okt3.!+2%} +ېCZP*V)e͠TvГdML30ah8rTamIPiWӲzxf$^Bj~`HB14h< Pd=-ELwbu+ Q^vvۿ# &'@˔Lj +R%G-kْ4ݓe#<{[h2bICt̻ҫYt;^9U86FELobQowMSf۵Gދց(MgvlcSf,juޝ:JHMS92}Y 2(*y*@c]) 1\@l9Ncs6TbLm.ʿż=LQruT*ͷ/:8>֮O_o;cTJZԍs <ʶlv|2I9u5vYHZU^D**P>_~Q]S5>?_[TA{ҨWh/pGDw8^9DjAkcݶmR%A|՟An~.뫪uik_|@(60Roħ[hq癉[AKu@ +endstream +endobj +114 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +112 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 114 0 R +>> +endobj +117 0 obj +<< +/Filter[/FlateDecode] +/Length 334 +>> +stream +xmRr0*$z˦K$ep0F` v&|f-E!jam4l,4WP8=G!U붝;wڄ9ep~s>aԦ +endstream +endobj +118 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +116 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 118 0 R +>> +endobj +121 0 obj +<< +/Filter[/FlateDecode] +/Length 1011 +>> +stream +xXKo7W𨕲4g%thhri6v% ˁʿ!>]oB{旟OwRMR8[0HRfԴM>zV;Õt.tM~ :X Sփ6gG/ck<wTb2 R҂g=P0Íj MJl5J3er#癪ŋ=A\3nM-,!02W^CS—&ܴ:hxFicxδ ch$Ai)M@Jgl4v7H2=}~=?sqis>M qyU\E$r⼼UE39歬HhQߪXd-#A?;v$ӯ692bZ8hY20^Pȸ=gpQԥ(X~oa`3Wkl><<> +endobj +120 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 122 0 R +>> +endobj +125 0 obj +<< +/Filter[/FlateDecode] +/Length 728 +>> +stream +xڽVKo0 Wh'5# KئlY K?ʲ#ǎ CdHf8gY޳5J,EVVջ(nBX'T -t>ؿn7aqV ˰V H|B:0Q EN2sfyĘcX &Zȧب~X&[ԑkNOYr-Qb}6 o=}NSpX&a!Oxy}` +endstream +endobj +126 0 obj +<< +/F13 64 0 R +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +>> +endobj +124 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 126 0 R +>> +endobj +129 0 obj +<< +/Filter[/FlateDecode] +/Length 618 +>> +stream +xV[@~qΝKCMɠTI]5vw;+nۤI˃Ü͇qVN|tǓ^+OVCzt1.fw|t>F6 E׵ kmNɠV}㎣_ Ss2sLY1X2,Lh :IP:J4qw\ү,qG*AR&n7ƷBS"V=i3J*,`bU1<&3P>J?)(} vaJg(> gn OS}ygq/:,TkW'lG8v5a )qPm'4 3 E[0PA}a,ʕ)o?#;ǒ*c O𰩥zŠ~phZ8Q;i!:hh*Px /S{pYEL>}[L +t=Sv[5fl꫐U G' /JwluȲ.is]K>2ق RŒxAe ,~YJ^ +endstream +endobj +130 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +128 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 130 0 R +>> +endobj +133 0 obj +<< +/Filter[/FlateDecode] +/Length 1033 +>> +stream +xVMo6W(C.9^vͥQ H1]*CQdd 3yȄ3iZTd&S S!@g"c{mg!,S20xB!$xSΐ=ȿDx`59C!` Ӯ{?wg߄M2b" Cx?Qd\5S\i՚/ DkfΚy<ͽ7} +rc0@cbA2 q7"k;C 4iO \=χ""o`Sd妾My6˛T[͝mC쬀sOP5#RѽݮZk0pXڳ4H{u.01V+U!!b;_g2{Tx8T{3 +k4]8wa??xxz{ clOWG3p3<}ʩ2{r!;=9njuZXU\ZZ/*ux(6eoY䛆ս69OVbHWzKWVI +~@kQ߯Jx,u*C*W*oooweI꜏H3̝9/0w/N]+9k^Y"K:KSEɿnڄGe"r +endstream +endobj +134 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +132 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 134 0 R +>> +endobj +137 0 obj +<< +/Filter[/FlateDecode] +/Length 429 +>> +stream +xSn0IˀuvtUVG}I_dHN$-:oK:(F2-Q(ʪeDOM7C Ȧ]7[ۡWcv<1M#1 bGEM<ZE  ^&ԅi%VG .~ ;71 c %#Ѕ:,! ђ1IJrep;q q&n2?? ЎM<wbx9ɮ^[uUz5}d'X?}oAC tۗw uUFDhxa8`E~痪lZ{)f<}jVlP:fDs֏7$&pU%v5 +endstream +endobj +138 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +136 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 138 0 R +>> +endobj +141 0 obj +<< +/Filter[/FlateDecode] +/Length 1152 +>> +stream +xXMo6W ۀ/E=6K: U}>(QH\i88Iʒܑ0L~<% I(B 0w. 9;(~_kޅsä!tt#VP\sӐo`dBeVh͔-O0M\I,UD4Ð/}<Ϩ6yIM`>%Zf11*J\乿;4vhO߄绌I#^4W8uH'@$Y)W~DO av]mH.,BŮNUq{>ՏUx\jJ F%;ֱBcTm47b[mm;V Tś=/t]JI2 +5̗ej IGhpts:@c]DZARꇪ8CF/wLS\ewih9D-lXN$P˅ҠLǥĢfSp@)Ejs|~<}_> +endobj +140 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 142 0 R +>> +endobj +145 0 obj +<< +/Filter[/FlateDecode] +/Length 373 +>> +stream +xڥAo0=ֶVH8lQ(Ց(M*EtsNx~('&v@R,)@aɁ?z{o 1 ;6!8G)v̅(X+vk@]0̃yf5IE>嫶M/EQHX\r@D '5i `;.{&*̆SŅpBT?6SyqvoF.Ö\"3٘3Mͷd vZ7"ulOfvfiƺ39Ԕkv03QG+fpCDxƔQ\js4ɋ0)PFwpYԜIG\f4 <11Иn}D +endstream +endobj +146 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +144 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 146 0 R +>> +endobj +149 0 obj +<< +/Filter[/FlateDecode] +/Length 739 +>> +stream +xڽUMo@WawH\&U{ziJ6D*M)=0`ܒL>Ɨp Bo9EA>]'\sT587#қ&dC87 g,$'TB\;C.f I!$T[ܿUU'ƀ{E +' +&2`nǰdm\ +2S4XECkf{\).#X 2e5/=@;$=(Vpe("COJCv,ўy[D$2mjsQGC?l8̶˸%qan7p Qv g`yv¡z4=(Gl)=)GN@|,)UOX+}Lҫ`loLWxZ IqyKw]߇?WU(?w1x)PIcnE* u8,9q,"vuQx粱6bc\rlV<=l9|]n`ЋD}DYNKgQ.> +endobj +148 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 150 0 R +>> +endobj +153 0 obj +<< +/Filter[/FlateDecode] +/Length 870 +>> +stream +xVKo0 W4*Q/;@iX &Ead)b'}`Æ"GR)J-qL Ҍh%^& &E8ɂb%De'L4qr'OgrSj1"c$nh|'qb&LDZfT҄Gc)dP3gú||rSZkNbpx5DygUsɮFvDp"@jAY bk`E2j&6D,cʈH=k`,Exh57L(I߾$BûeSXGJ>N E,Iây֮F.uޥF|De1yѩl@.eR$J$9"l[ZZDƘ*'i!, ӻ|z! +]R[@RsbSd|{G!LI;<`]=lO2=_q_Mdqmi;P7pLߐ<6>(Fc\ᨉe>VG;kx[> +endobj +152 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 154 0 R +>> +endobj +157 0 obj +<< +/Filter[/FlateDecode] +/Length 884 +>> +stream +xWn@LRf:sH]h,iP݆RP +"=wDZS(b8s=I gKo"B131YMULxs2vJ=9s zzxdH +SLI_)FޕEbEo_,+ ق3P.pEQ9Ӓ`3ˬjW8 Yd j ]%y ǴJȁɚ696LW/Bf> lNmczp0980LKy'Άp܋/ZCè$2Ue{v3 }:q%*nnv(hPF+\%JfMF +Fmօu\UcW&mTgz[J PR[oOVK rv]NQяmsl %؟-߳uzm=\Ϻrҥ IφN /nE2+#yMavG] lP0Կ%-:_fWҰVNWj=oj +[{(=NώaUo,/՗e9ٜ~9fɗN?ѴFը V?>Z*T1o\s&d[$'$k9]]">VP5NY)4NPN/ѧ* rcLȆB#qH/: +-/1zr16GX z~RҼUc9>Y{bۢt3¿"]N&}Z-O +5:ڎϯ7"~xIr9lt~>?*ZOhZlwPnXmu98 +endstream +endobj +158 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +156 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 158 0 R +>> +endobj +161 0 obj +<< +/Filter[/FlateDecode] +/Length 958 +>> +stream +xVKo@+'x}:R +# 06 ¿ga=e~|^"nyEN^ +催>Ũ$ׂ2FV/>̘r@>Kt*zsRʆ06.`EL 䂖޾veд4DRpV>f5t +ka%P [5vn{@XĤ9"RA4\Xnz @SCARUXxcTiiO96x*,=E}rɸ{tO1k PT\̖UauY8迕)e`(7u 2in~Y#1ݘ{%?a7^8XخLM|AQ.& `c' {5?n]KX[{K>ϽU7w_6W˦5oA·ӛ9ZX?JEE!>48y)daW P SwʜQϢj6~٣`e02ۥ UBZz>P +"=G ac(dsQ'B/2$5vez +Dynq<<NfR:=g} 2QV,OQ$'WY^YCYɬżN-'$kc?ՙ8^gtmDgjG5_\_o=vw<߆f3>byZysUqtt)GVX>Ww?z _O~K +endstream +endobj +162 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +160 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 162 0 R +>> +endobj +165 0 obj +<< +/Filter[/FlateDecode] +/Length 1029 +>> +stream +xWKo7W𨕲9| ]F4P PwH.Ɔ j9|pEeܓL~RS 0#RmB&oD 7&խ6#4ve2r32Yuc20Z=HKe0&[y(@BxZjjDPHUqR21o5o]$alk1KQḖ~=jnHǘ)YxBI*5){lIwv2&&դgb2Uh49 +*+`i2zT9ͤ!QAr5ZPΏVWj x٥F^,fsy4D.HT`=@ R`"xsE_̍ă#H"ax *Χ(saKa +A,F[Gr6|_m.jSo/*nEUTM>6KVaSp1B::g`[z3.gv ЪݖvKٴUqxtv!?WÓ0IٓFh`4!jy~[}e®ĕZ0 LC +}%j (!j{|Xm/N?' t+2U'BU`Ynw9 w6)?Ly֪+5Z%X& bEi;{ovXA7b,zaz᪮˦yug"v |MťsnH2=!xɖȥy-y p`:t]'w]׾y;M +endstream +endobj +166 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +164 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 166 0 R +>> +endobj +169 0 obj +<< +/Filter[/FlateDecode] +/Length 375 +>> +stream +xڭAo0=b [e;*Ju$ +po'Eٖ^}}{  *zG3f!pH2C2DiH+&d:x_EĴ M1f8@lӍe +0G`OxZ!B)7m 7EQDXa\r`(ڃӺ^ݷP/Mis3gj^yN +Q}> +endobj +168 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 170 0 R +>> +endobj +173 0 obj +<< +/Filter[/FlateDecode] +/Length 1094 +>> +stream +xWKo6W#f^vͥQ H5u'@!)znݢ{.oy +^입{q#H.$;4pXnKŎ߽avÁԌ>hp) M~P$ Y.*4^] d0p \[n5![X肗&$z(;$zcEPHIE"f,W_΍ @+Nwz8G&$`ȍ4'Bq"[ +0ɐ(,ז8)~#1΀.`HeڇPkǐ[;$"}V jTVE1gofΘ4kLθrRL,/r!*>yIPrsϏ r4 +h.5htRp`p]z~{ ^aRbѷj=\5AČ*R\dx*:hm@ .e=ؽk|\ы:u'2((E'1Uuzxr]s宺h.2eYO˛9(hSPPP41B'- s]E +2?zQ'2;X{eNPe|&cg&~\!P{>1ߦ ߤ8ly'uR7L^ cF2wUe^xM)+yGOOCT|]7N?r \o( pWԙxQz,UIFh(%z,^y߬JQa^?O=5 ?wڠ@j^ՆTrj+=yDww%W +MVj{vEk} idl S!`VpkO[54 +f%֯P? ?rt_0 +endstream +endobj +174 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +172 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 174 0 R +>> +endobj +177 0 obj +<< +/Filter[/FlateDecode] +/Length 312 +>> +stream +xڅRMS0+r @`cM> +endobj +176 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 178 0 R +>> +endobj +181 0 obj +<< +/Filter[/FlateDecode] +/Length 1112 +>> +stream +xXKo7W𨕲#rKQhri6VP pܗ6rM %r^ȌF1@*V"(߽^r!P^7;>{q{co <9J*B\"TA]) `#Xdq !}=f'VHvX)щǘР\(VHI0^ĀpUs*!Ìwo"^@΅AVps2!5` bU{X &4}3!:jqD +[ ΎNBCf1)d9 , c:aw}q̽|WJja?03$$у Ӹ0 DH1$&RLJSoG/̀4ggJ)=.8y=Tͽ"Iz7,&%(NPL0|^f }O㱦^i@- FoL` R| & JӧXSzn 6ЅD4f|$e!ĂR0:fhHN,#!{%6DwݝSkөFS@NgADSXĶXUr]u9٭,U,VS7f̅J\Ӣ +A"Ժ ߕeޒ4iMj$d_-5iB!E_jUnI``t/(&~mѳ9W3mI! 8|EWu}?=>R^fp8p}XWXdoìҋx"#TsJ/e8U% +jT%*inNNiw -b.wTҋ<}n՟1ખ*p6B3cC1g~KmN2?LsMrM&e3}Q +endstream +endobj +182 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +180 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 182 0 R +>> +endobj +185 0 obj +<< +/Filter[/FlateDecode] +/Length 383 +>> +stream +xڵTR0Y$Aac貲FdPqc6{r_9TE9t%;@N\@t@FO+ B@_ZZ&+-OOSsm̛%:^gwilOz~/9'Tn÷ŎWv_O,BJٚr"8"|}Wypv[?n*UPJ\&gOMb槵kyaؕAaԡ6G+b/ǹúTmcmK> +endobj +184 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 186 0 R +>> +endobj +189 0 obj +<< +/Filter[/FlateDecode] +/Length 725 +>> +stream +xVKo0+|AJc Zv)iCYiIm˿gl'w[HŎg$(ݢCo'g1ID/H3b o/SW%ZəF8!! +OуQ'.Y}m`(Yc0l31Kj"6#V#|p)41VG :4C砽 aO@ k( Ҟ&eS|9J Fgup{0K]"N0@rbjJi-#^33j|2uӦ~9Oظ)mBCl]M}sS Hڶ~ڬsh$6F( @5w˸dCis B\N_k'>@G0u;]tFa&z[+xm"Z|T.,3hh(su7v><Lۻ[,RvṢ^38 o^Q83Ut0Td\FǏʒ|x}<~-wDŽOC47E\ +eIOjawϑ;]F(_13qH3r=G岫njS<<%绾^;w4x륓ƄQRڿ|O!*~?~i_b +endstream +endobj +190 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F2 13 0 R +/F10 52 0 R +/F7 35 0 R +/F3 16 0 R +/F9 45 0 R +/F8 38 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +188 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 190 0 R +>> +endobj +193 0 obj +<< +/Filter[/FlateDecode] +/Length 516 +>> +stream +xڥTMo0Wpdo>$Cn8,+UI} J6*gϼ10ʬ|>7'r$%EO cTMlOElI\ţ 4yy, +GsW J␙x}.o2 GMW~ ÐX^_$HC07AD\NC*H!!3zAxgCAXYд]R'mdG!C]9 -;;!I8VsM! Wz(ܙWrc>4Q'[RTݶZ_07ێNʐBT~Hx:LE4s(#XTp8խC@< +5)ʈVt7bV7C?}26)Drkj4{V}|.*5m~(_V+)?HQ7XESB.wr[D^%@QLma1 +endstream +endobj +194 0 obj +<< +/F3 16 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +192 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 194 0 R +>> +endobj +197 0 obj +<< +/Filter[/FlateDecode] +/Length 997 +>> +stream +xVn6+ ̈́4yMQht($[u Lecߗ/=)=n S>\J=r; \ïH1%Ja~1b@&٧QX;r+k˜QօzT43DHbel2"Eo XW$"^\\N,f$S*w 4Rr"=(G|`I,S n 3 +s`r,Z>F0mFXp/[R3A:W#;_z 1q}0#_)LuQf6MڒN.cՏX1a(dy5vl7ہl0@T& ˦DQ{3 r´檨c}:=%>w0Gb$WyZ.XFmX/sf-R6Edϟͷ>%,s8c]ъٚ+Hޔ7?.j3c#=]BRʰU&z&=p<g&uBbƻfBFzOţ Yrw |$:3F$]a祼bݾ,qU]'<_mFSx1p+ary}LS>V۳<3*BZ\XWkhT'EIQ/> +endobj +196 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 198 0 R +>> +endobj +201 0 obj +<< +/Filter[/FlateDecode] +/Length 414 +>> +stream +xڭTO0WbReA۱q3z0Yۨ6-P(h<b w&, I\Iԕ> !߀Sᡌ0N +qx.9T+ 6K OFT!&#ճ"уKNzk'uyqXy7m{k2'|㟔(:O*i=:#Z VU oma2Ѓ,Ǟr\nW[ˆbם +^Dr/V$jwD> +endobj +200 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 202 0 R +>> +endobj +205 0 obj +<< +/Filter[/FlateDecode] +/Length 1141 +>> +stream +xWKo6WR@ 9|.|)-c׽tMJ]Diڜ'oH'2<&~>v^&\R!ԨhC%~c +rE8~䟶Ǜ:jg9* B+oK,@:#Z/,QB=(* +y:*:a^\GxFś %ѭ*HMfVM4S`XnTtL5W,.;?GĒJVޔ0F43Fk˳~_{놅al٦T m3m'坓Bsd9"2A_${dL|1-U$cZ +~L>xvۀvhR.is|S1ni$Kְ\'uh\ +ͥ2" `#o-&"ʺ@B)z3SaEȏ܇ +ߖrj~aų-+}G"𰀾 B\>c3*yYaDp/j4@2 B= jnj&ci0p9y^.;D5|[X[Sݰy §afd+-ky4&Cu|5RjiE#u5XZSx*|<-MwC?u7uI2 +笈a}>LѸYXq_:8c>B} ,9*=>? sX6a)gӪn:P;wչ޺)' ќtʎ(P6>,| iPEƸ^ۜO4ta4<=?cR:/&<RL-rjmӺ$Oa]zh5ic&o4k4Nk<` ʹC60ƃͳ94UK;'YP.#ZӽT;mLH\1o뇠s~s^⸟ Ew)n2"p{ +EVq(HY^q?Y `cMO]x?.0䅗[jP+CZ޶0 =;;=HNү5Pr\:;`uxVg}7_ +endstream +endobj +206 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F9 45 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +204 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 206 0 R +>> +endobj +209 0 obj +<< +/Filter[/FlateDecode] +/Length 579 +>> +stream +xVM0WSo'HZܚ])"A@aWMkl Vڪixy80o1Q _@r +}DGC cDE.%D[bՖb,"5x :R}YbC978T84ϲsdx㡌EPh]jJ.Cn-.)cvjl$2$ ?jb=gPz|ΟJ}gHh9ޥyIovɴxިިo5Rsٝө|V"t1]7=ÎLIB m Տb4ٻpڭO\ê8gL-ix kޟKKQ$ISebGU_Ү6EQZ9 z*f@,FYFYV 1q̴TlۣBXܴ 5{d`AGҊ^zu7n.]n?WH_xHk#&S{=˗}m*:?It7t岿CSzu|^a.P?7D$ +endstream +endobj +210 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +208 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 210 0 R +>> +endobj +215 0 obj +<< +/Encoding 53 0 R +/Type/Font +/Subtype/Type1 +/Name/F14 +/FontDescriptor 214 0 R +/BaseFont/ESBUTL+CMSY7 +/FirstChar 33 +/LastChar 196 +/Widths[1138.9 585.3 585.3 1138.9 1138.9 1138.9 892.9 1138.9 1138.9 708.3 708.3 1138.9 +1138.9 1138.9 892.9 329.4 1138.9 769.8 769.8 1015.9 1015.9 0 0 646.8 646.8 769.8 +585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.6 +646.5 782.1 871.7 791.7 1342.7 935.6 905.8 809.2 935.9 981 702.2 647.8 717.8 719.9 +1135.1 818.9 764.4 823.1 769.8 769.8 769.8 769.8 769.8 708.3 708.3 523.8 523.8 523.8 +523.8 585.3 585.3 462.3 462.3 339.3 585.3 585.3 708.3 585.3 339.3 938.5 859.1 954.4 +493.6 769.8 769.8 892.9 892.9 523.8 523.8 523.8 708.3 892.9 892.9 892.9 892.9 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 892.9 339.3 892.9 585.3 +892.9 585.3 892.9 892.9 892.9 892.9 0 0 892.9 892.9 892.9 1138.9 585.3 585.3 892.9 +892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 1138.9 892.9 +892.9 1138.9 892.9] +>> +endobj +216 0 obj +<< +/Filter[/FlateDecode] +/Length 1024 +>> +stream +xWKGW%x4]oDJ%#Kx^)Fʏ7hYUT}]}`'}bTlVXY:{ o㧆yM0 e\M4@tn$Ρұ˽c{m%΃X*͕a"Wp\ZK41W;4IfTZՅi"ŕJ:!(b&E܂;WI=$/NOzHcӎP u#MQ&GKs*8]4x+lLp6X ܝFXHfԖ-&{dO0,}p24"~s ӟPw%{zf2n)hFL@nF%G hT-ɼ!>Y]MyrkGBdNV6m{UjnW=o>njSެ?\n6xhh/ºogE:;/ѡiz1kkuUbBe)Τ +]dY\#WUZM\̫G + 9 R(EgOWEUIz|o\v˱r1>OIP^9HJ5O +endstream +endobj +217 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F10 52 0 R +/F7 35 0 R +/F2 13 0 R +/F9 45 0 R +/F3 16 0 R +/F8 38 0 R +/F14 215 0 R +/F11 56 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +212 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 217 0 R +>> +endobj +222 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F15 +/FontDescriptor 221 0 R +/BaseFont/YBJVEW+CMSL10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 808.6 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +223 0 obj +<< +/Filter[/FlateDecode] +/Length 266 +>> +stream +xePn +V +aMZNT)@\XK~^fٝnM\Ɛo`*򐽜wMz6Í17X\y eԕ'ʤ0і|~A?%QXdvڎen0ǕYOMPo 1II_{Fd +m3V0pe!rҞr/rSʼOcU6.8\_a͕B//uU4J[)zw +X"Q-/Ed +endstream +endobj +224 0 obj +<< +/F4 25 0 R +/F3 16 0 R +/F15 222 0 R +>> +endobj +219 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 224 0 R +>> +endobj +9 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-33 -250 945 749] +/FontName/FPGSSG+CMR17 +/ItalicAngle 0 +/StemV 53 +/FontFile 8 0 R +/Flags 4 +>> +endobj +8 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 3815 +/Length3 533 +/Length 4366 +>> +stream +xgXۚ (0 tHPJ^EB tMD^Az"E# ]"ҋ{9s>g7|ߟ}{ֽ޵RjJARAA GbКP0&0aYۧ>>AdhaneYw6H'AP$(VJU51A1TiTDY_R`WWmH/;\tυ "_9'ԩ?WځYmw  +xy1ھȡNz47ZdO|ĭ$^c[X .?r.ђt^1ξux˹lwuW0T厗Bk,LS*dkj!%[&Y {1ֶ] +;C@J]24'}5[BD>F,; G^ɇc jnl~Q[FO~Ia6+%VO''-1 Hs'-p| oŵDL^D&%x(6tp"9eS- J&X Yx;Z{ +vb#Δvg>[Qv /N}&e|rһvx8^)VTƖp(!gJ"nYqE}Pp)VRwMsT!IkQa1ye9-T¿Ӳ84Uv+cݏ㳉TkI2Wpjdr*t~&fyPZ&});]=cG:!u?~+oI 0:x917WL\s dt0CD`H~88ܻxG0z:$!0@Jһn;#ɱ~lwl9)ۼyJnA +1yx;uavxNMQ=ʻC>v{ _$ZW9ڍHuY/}!U",̟3l~qWЛkw5vH֦[E{YKM@X[!Kw*3.(=`k >gϖ7fzW&}}Y$U!Z=eBYuigv2{g ئJ:Ki/YY{l7{Sz[m" iL>Ee +-a 4FXNa!~ wkHY!!d~vCwcDxO.ԨmHrt .CnF/ɤ!|Uɜp lJ/#Pahذ)(60cڱC1`} i.Ŭ }~=A%ҍ Uْ7X ㆻo \*Uӯf 0 @aFA/4VzɌ;tڻes Dx ssx|׼cMDyO/$?Czt&7BR)cҜ *,WDx1IS{ qbOee@@ XȑV57mm`JE^~kG K?Y"J cWaϔ͞ tX=qcD;=q_ 7T% dqܟB,E/ <_}Й_QJ8&('w/S qID=,y_x=Yg +I<.|/7l]·TIܢzwN9٪) +X-=o an4JCL ݅qbza@YϋP>A`שׂՏ'eQο5t]h"in~0( Ycmk0M*oxzm:aPIm} AKKh6 |PP5sjӯv'44:SZ9pr%/Li|&7-<)5m%}N=cq9v/p㥽N\=ޚrÏwh~['w3wL]~s'eV`*"tMԚ$^n-bC466,!K5 +Sݮm{3˚iC%uNT{ +M| b%z8So5 (Zlx_$~˥uN+DgH6R+bZ?2-\v&MM~]決E/]Y V/ MWD)nDk*rwU?v'AUBV/vd)7;#!jR2xXzv⛅3UJ}חf{$ tM@ ޏUs{oNTi|baw7aiJЋCjRpwB=inKcc7eDKK(]t<GםJ㤼\y'Uz}x途ļ'(sؿqj\A^ULb9 +=T"ݵ/rHᙑ.oH\Lba¦Aѩ/(?Ҩh-γԭ{.PjgfTx,"e}vIYη0~r0S?ԏ H8HҟUG(gZldPUhBt[i没k8>ab[ɴA^ߴg[0\PjDS#5^:l_Ɉ$/.34[$?~;ZJ> +endobj +11 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 4386 +/Length3 533 +/Length 4937 +>> +stream +xgXS뚆%(HhIG{@DJ +DЋ H&" + Khǽ33sy]K\LvAhbRR@LJ c0," HKR7!2r aX@H]-@ A¼C;ѮH'(`?  Gb;$ g+~S(G$пOCfc7TG`^1kü(^>X0D["Hwu0U$~Z u`(?ğ:wsAHVOWZ|Z? {IqIIo;L GzX7Kw(55tP, &}C +nݐ >Ko?BW!))yK^OAxc ~t +(; y:1^릏&ⵌ{̃7hPwbyLҒ~$q+UBSp8v4[_."(6XgG.ѶHlt-DI?/a? 3'؉靬Y_l&i꧊:UQyYqUҌa^2N-U,#Fju+(Eþr_'_YM|v269~i2ؒ+"wHI#oIYXf!z˘6k$gM){!qW8}^}ή9/k#jImJE3$",:ۀqd,AImt>14F|S'1'ԛD3&ݪO`A-_c|T;wԒ1WY.]S9o/rjvQ}9ơ7<,cƽO$̪*0C {d#KDbTv9e}t0Z6ۺ@ڵNqH7g +^Sp$)QRp+/3(雵0Om7^{4&.U'T"/rsZK8njo>UBi}/,Ut]SV;2p& ]ا8n~ǝגZEo\ғfϞk*)LZEDX?Jb&b8cPnL>cn!]l(~R`fms:Py.9=ҧwWD?.-[zyj*r2d$BjI/~o2u64ZU]ד6Dmr + ^r{$nFIjRJF +Dr 2%EG- 2aAXp#'\{ED;AWz+cofŷ>67x؛{cJ +;42Iݚ&XtՕ]@(YPq{`넛G.5lMÏ0m]#! ڋ~l6(jW*ڒXZ8ATy/%:ak6N~ ?:;ƾIZ:::n,>2Z?)@Hɉ㍼ֽ/A}[˖{:($!˲Pg璟#Je9 utDe:a%/Mr=dxa%Y٤ѻԑ>L58N?r].h|R$aG:<4_ŏ\MuM+Ub5N3ljTk or[Fg-I^4ߠ@G!ݕtiS7VC+7唃q -yܤݶ{7_d=a U./0uEmCϨtu<-Gǐg*!3OlvU|W&A[gpП8~9Sxd`lq|'8fxހ$x6hxj+UxÞ!n2<{sCz*r[T +@Ty~-Mbz_? W_)(9hUh/'y^DEc0I3# |-uODi+ +嬢;᳞>^\J(cJCSgD[k̹T{O]M`s*1aC8,"ju]erU{;`diL_y)յÓXG4mh^ +@N8RDa`|*,~d9ј(o$"u5LD2c 8Ea^?+ARC0tg=}¢t}!ڨOaG r_SWs^qN] +S43ukY>: jI;EֺJZ 9QF}T5/~u)[0 *<]3xHH]Ai)#_G O +3 :=+eΘ-_F?\F{A^UAYbZ 6 " Rw%Orݒo-÷!65-Thy$[S .'؟#y!Q"}ۢZd-*uf. !ZU0ux)콱 \澐#:.mRzN eRׂJ ΂Sʬ=6ngk2P/K{W!)WLk l S < |ʆ 2x!<^GAnLD3E-;}7>sšq!Q S$^ZD\(ֶ([|Ye+kp[+âd-2BKʁg|)xkY ~ԎW}7VsUJjeM\9@>YN~_F|#v 8ҥ!,~%|?*/?I2!B\ <`dyźc:~0p?GZae+Dp~]kǁLeu_p1s1u5!2NTOnA˩pPnXG}U,Yg/ M(]}mwU.SYtمz_zDKnW8: /#|@t菮ɼ%PKWs^A W^Lg1 +(13.+@]0,fRG@vHLʮʊbm-%U`+DҌVI: vmx\VFl9-@-o8AYá ]ؕ~U<`SZ}вLp/{Y7;1K;?6%RW:햪VI~,Y]ET}x2:%w9¼aP#~ 3sgT4+hab@%DfԬUzƟV:9(m-7G&ƅuAz.=rؖ;9Y 6oI/pE!`, ݼ +endstream +endobj +15 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-251 -250 1009 969] +/FontName/KHZWRY+CMR10 +/ItalicAngle 0 +/StemV 69 +/FontFile 14 0 R +/Flags 4 +>> +endobj +14 0 obj +<< +/Filter[/FlateDecode] +/Length1 720 +/Length2 11374 +/Length3 533 +/Length 11928 +>> +stream +xUpAŒ%[̲,fX33Ibfffffffff&zfލ/UuV>9"PҞHHZA@N.d ԷYY +99D.V.V&HdbjOD%D;doI$oo +kboNheڻ );"hD02 & K?-6rϔ#/?IrYY2V?p?Qַ=ЖHhkRUؤF ϊ뛃 ,ḾD +DA@#9)qѿC?%4TiJ,\oylAD Wϑ-&bihe4!R׷4ҷ5rvebe$g DlRd&be```dghiN97 4x+KSQb1`QPν(F4'WS5Xtܖ~{IpGy𜈯v^9-_i=&".j; _\‚ n5Y2V:E$ 7lr1"paWAE&Jtof0o~ɕM $دAϰ4~J}X:'a4{Lz_@uva'*0ʡEM6o ͜IT!x%D" 0+KRpbL\LPO601\ǵԓMcng4 g=y$n9:X\u;3BcPS6ug.v3e8GOe* ]bccBEqR C+Eifa #R,7+Vϲj?ƈ[L{]])ɞ-JN-sgZl޾T;w&a@X+Nܵ}U WDVvпkĬ/; *`Μ1ljD0L,I|-{ GiP1o?ԣ:X5X~'v9,b/Ǝ@vhypA~\#;UElENE&`Y+olL6n)%įGWONHx$=ps"ni-&Q~f+_uI^wBطw zOw%#yzz(h5mA~jǧ FRNy4۷ڳ/aB@~٨4ˊ/a04Ze_9S$؉sGN-nRBw R^[n*rSѻi1lGgd2r8KV2p!+rc_xczd?FZ>j3&ꃑaa`Im bM'+2i3|\AqMYx /z1fHM +NJ+%`hs<7%# A3AE%O󘲔!u%ͼ(;z&-^_k9ZAva:YxccLTR;aww(v>Ř%la;.7=)ʘ l{Nكxq wڬ8څjB*%-v 1t@K fWJfAT}IN>deupȔ*QbSCVL`SOQJ7bqyqeXG.7mc8uJ_* 9\Z s!Ʀ\*NpɕEWRY^bo E8%^dbzJNHRBuYw8,UsE4hM'S͍ȁ5ot`b>ظ\#mGV¡D$k̹ښ.Y(4, 9Y֍N9FE~u.v 0D7UkJpF=דKAId]AD9{򨊽a[5R#iJM8ֆl;00/SZV3Dڛ_%q*;KO~XA[j8$l̃΁!wյйE|ϸ(@,bH.{sF_fJEJ :wW_";"iE>맜% t&:,.rAdLk86]qj\>-<*`)mNk-x! +~02/: +Z8x>̚A2͌o K)2ehqOm! &v>WY=;_]_x+ldHyyU5-R!,}]Y&}eiVSdLD

Pb0@&lYy $ ΌS[;r212M߀ϳrKӸ垯c`4Ifo5&8-`j[q"sVAT߯}$E?2Zh"fB|6$dqF~;Q(f3Ҽ?tQd@z<)swlUeY40e@껁SV, KK~uB lp]{Iw".c57{N!BsQaJ?8$wwqKzRFn=PXfu(;? l,?j&PիV8fH Ue- :`1R)V6J ͒Aaa3h1tn -Qr{Hҗ}y +ߡ"6mZuu#QvL)m[XԨom}.{|p87A>:8P\0fl O۽#;6!k%ѲE >f`t6ƷnD9#Oz56uےJg +d@JK=i|~M'$]_/(>x8C66+2=)=0hGk# +Nlj4lp +eh4T#1i2#~O,W@{&~l˛\6ڞtoŪ@.댖jFO*º?-5牖^~o\Д:W4 gl79qzTKY<{Ė }v~29^-c-k@?ՎkGײw7.I5!r?攲yE${cl/bsIS;EM.0V X$|s4+2=ƫ̕ʙv2ʃaDԩL _H$Iڈ)2Ƨl̼i F[}M<^dO`!tlz>VoucG^Trt$~ 2  [fqr4˻\.QG|O m}] "ĊbeFDeءq5]J~&h/=EHp5ۉd×vPp)8g"hqV`ܚ~[̨ +p ʵc V? k4_ё/h)UW:8"M+T`KÅdc+%j#~!EvC~żd3d:A72D?~i(9h>*\21.ZS+`TcGeI1fL6ɧPϒ2U2@CsuS˓!:ylRmvNQv +(j"=W*g&b m4Ș5 9HiF8ӗw!r F@wp,Y*%xO}'Fe2 +a㲉VZ3Hk$)EXyƹJ3x +L면 mDo4.uwjw};><CקIz1HǜXEb5|ҲQڲ]D_¢@f#3`N B.`w|`h%Mtd?^rťw@3!^x an^B2"Ėxx|G mj&_!ܛc-4R:VM5j'LjANEjf!dn=f`)WYzބNʵzy]6gxU!fPCsJ44҄1V$i]<~uĀ>S9bP(:Uw%dz0 bFd^ +v-5JfJLj. ƛ7 !/"ݮol}J.LfWyU֠L矫<6}$ 8 6=rJ64WЃ͌4GD/ow=/v)p3%ݧeo.Cd'w)!ud]%nf2@=v i +%MՍz/lϿ6DwP(:`T0lG[L`剁abK3,".UQq@!O {p+dʨs YQ:۩Rfܹ?|A1`8Rޫfhą/ .+!8Lf ʬU -m&=ZN/~ mNx vbU̫P _B˭)֚x_GZ^Rԯ- +eI^ ff}@RV7=ሰQ lYln/\Ax+ϸ"5=RD =YePd ኖf0?nQ{';R+pq')7o陣cf P0ۓv;ъuTv:;w]oRv j(6bkY \^x8ɆIcz Vc~X,8њ RfĆz2/|'vUwR9iJJ?nCC3; + خ o.oKMt`IS Hv, z)VjO7xFB԰O)E;mblk*z=S {#4aȹ3[TKZ l%hAlvdML +rty$cփD֣hUT؃|uQ"T6Iw@ ۱QݞX9_^+#2It>vp-wG>LA.%pRg3>p[7$yM!/q+wݚ +8 ;V,m'Y& +aGNVc2!`HTFʢ$E=,Q +QljY\%]͐ۑ):8_ &pWgd40˸yif*j$T9)r3nQt)6ͅy B +ѭ6? 8Ir`]\^%/Zn>\z̘M·%tRq6|ȣXL28l'z,)Ljq7Xt +n6?}fet Uל+!4AE1ua]<|y}YHKƠRǟ&\,ٜ\He&z{8$GJf%^誩D_mP/ScdM3.%^~K;և!B{+]Tq?ZCa*6M7aW^T[~]ga>7y )!|\0 * +#ѵ7ފ|]Ec[Q;y(%K%D&$nK9Gw-O<)Z4wm`j}R򧻽V^ +o]YFq7&nie1n(~~u7UjJ,Wepe$Eh)u)"|K03!EouNf =&*|NЭC]I~m.y0qq یi0EE)z }A9( dEn6'3u3o*.|+?Lgqqw4{`)jkg;vB(46*T 3,=o1vN,5`6>zA<7;\j_P)|sqCY1 α?StNIo^TN_OyX+}t'"DXf&jE!*tթL:1E ¯lg + ʧT9K'JJ3*@\a 8~6Uۂa/3 ؏f,sY[)hlaQ=fT@O6F쳯S}_BaDw.6D=!x!L @ =ZB ]`9"Ч-1cnk o[8b:Co,m'PZd٧Yn&]$' EKz,|Qw A +ٖC +<(>rG%N1nؚlz"8*5ڽ A-vu':"aH5Z4t@?)-ΟobhYble"9G9q蚢'@eg7+ p9FH#/UJxԝ䒬!{x  ʘnj;8;)Z|[[P[pi|oVÐ+7-|+L>*B5}!"-ayO= +wM +[W/|f@UB}xB> +endobj +23 0 obj +<< +/Filter[/FlateDecode] +/Length1 716 +/Length2 4421 +/Length3 533 +/Length 4968 +>> +stream +xgXSA$ Rz %"THhB4AzJEH"MJAxι3ΗyCbAn$w]_pn(G 3 %_]c8 +3ǻ+5?|A6qߦ`(3  XĿtI@APHN_ @ r +^X,7PD"Y(co]"JMoN/'~sde@j?8O_Pk,QΞQOQpK5 yIb BCp; +smؒuGۢ6-kT~S|AT2i_T <ǛCCf[eFt^ӴM(rqJ;_OGz-ӳb +](;k43l]Ppk}6oC*%LPJz-NpdM2³^_7Bt/ָ"xA6ߧ!|~![jۖ~S~oӑE݅)!%l1 WT͕WWzsֹ{GT lWEۻLo͂t~PN&^ +h˞Jm]~Ž Rzs,J#euZdpLwCYU9=E`vle;A|;L3w07ym|fN<Xȩ?[+M[??\-pV6Z$ȍ z9Q D8Z(J5Ɇ^81eF'3}k՞lK}]@%3Eˮ{3( b=k.e +S0QDօH> BŜ(D@gt,3,V|_ȸK TDVP Ǟh$ns2KI2u߷!::W<idi '>Gt08l{߻VK'5CÁ> +uM[`*̑G&qG?JcoM6k=V_T޶J@BˤpA}pčTsm^'tEdUZ.9[G(=e&@ aT{YI: AO~ +i^uY*.A4i(e<MZ-y&6<=zQ"嶌 _zrhZ׶f%CW6vEc4͘$($VG䫨#>B/ t ?TaKUԶ,$\`c-kW rhvykرR_vvl^QCF) E"*m)sr{[zSZ֮tIK1\2|g~SuL2kc>u<"5hO?YU[s#5zP%p@`;AeJxzv r@2Mwq9|GPʖk~ʭ}9$'.u +Z*%s=rK+یn,\o{q74йZbm*$"9A/Mo@Z򓋅͠ZFm|T>b,bm#ZGB+:zyO:1(Q>:#Z$ v{R4"—"ъ᣹ԓBAp$A6HӇ:E: \!eÊVyDŽ.t7AxbCB p=9=ګ#m|Ue:91}3"A*pr]&-w +T̢?%iycLR!Xe<9W3CLnV$ɲᏬAV5-J|ۜ04|97l5ЕYBYntra1' Bhm锭pf5;G_c^!xtQu1ТJ1`Q\z묜:͍U!* /2 7ypm] 4|Y6[%t˽g ]$#'1,ˆz\PUy!v۹&z>^촫<[Xa_J5|;̑"'xr;Յ;B)uM&?/)l @w lJV]ٳA9c;4z!vmQ'4&* +UXSs;zz,w̍Vgr3c +I+emwfpSh25ґHh#HKzL)]ځMˋT //vZ7kygFv}78ck8Yi6eVQ=0,",8NMZpoEMfgUW<w6jZ;]\#ZȒ*W i>1kLiHMܬy_X5?їួqH(rvdl[$km܈8z.^)K b8J(GctPTcToq7&qynʄ{lӄ;ru }!'gh$ӮKR)G[ Ie*`aw8SFc6-j +qԲk}̲_Ysu [˿JWOZV3u '3 < b- Lw3U$tNveZBUE.U)?F|(3x$Hէuryz{B ^\Y.+tB| @\tgƙ9Hnl٭axTԥ^Sd:8.Mx+Ms5_1}r;ONu dܦ*gbu.}Cb8`{].L .`QNL|YsjHD}6D91%lVo_,`o@[R}[?UܳEzA(M-pFDun6TeT]ٖ* +{ ;gZ,gWZ7''>NӒKNDn}/:]q +7A%WgQAؼpmp^Q sulSԡC٩wovXʦ.;0[k?ٕL<'6#7X&bcyl0uDiBwGM0} 度<t"l@Au¶̻]j`~%}Hn2t+;n9|Iy {k ^66KNLC}>:Z> =.#yO@pԙbBl1c p+h&uLC)S9<E~K EĦ-`*3˻'sYߌy7L4&^ +eMxVwяeIL;R%ǔÉ G?1GԳwR=\K;?\%hFFY28rO_f>)'ޯ>Ҳ?c4VY{~V: _,)rhFAq +͖뇨^&xi'M>Fv 'b) wn@vJi6빒> +endobj +26 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 4447 +/Length3 533 +/Length 5001 +>> +stream +xg8\mEFmh0%:Qcme!j!E-JH-"DH Z"Ǔ}s=_u?k^[RBuAb18 iIi%4(- i}0 ! Prxd@PtEET)5+ 4< W +huE"p@& +_㏀K@8tA#1? 0nX_i?K .oRQ'A7-E? +u C#QP`^~8 G`."¢BjbQ W!q@7;p1RfU`H *__ot0X80p_I/$d.,"+*oc~@9 ;~Og솼pYf:U^?- P@DN'/\>Ui 16:U*JDd ?PY7~=5ƭ#ڽYyԷ -)*vR?mBq12OEbMY>i~+q594|=3e&<c#ŧ?P_{ kU߱C?y;dU/T_c&벥Nc?`0& +h^5_;TcB#m>(#Qfɸ^w2kjP׷LܽbUf氃F}AJB -cM0~Q^EEfU2ǤN!u=KkXDk  U s"VXIas>dukʅ=d=#H7I=K;أDk6=(챘kN? @yTի>_u_4|TȢ킵dyY+Unh3-z1f0L5%r~=tM8}od.1]|dЎCaQO{ZfmKϾP8i»x-p8+iVz2nN1n +3;tGHm]奄ڠ|0=+|#8D>1eQ\QxA`BpAሰ={W:cS4h+.eR$bAbU]#OJS/H~?6]'Bo='FT2'Raa˱TD; +F7x5ޔ!t?VC.Oۮ`{}]G3v6#;krAM3< +txs_כq*mWh>Z|^ϕ##RT;\ԷZfq,8PuA;kI0[oQOxw\eصn3T5S@T:|6n8q%3IÜGH +8(Zc'#d&wTXdkGKh8cc=d"vz F(Fr̩`A!XJliI@U.nUR8|Sh}`i7LU 80W%y.Қƥm3o16S4J=EB sϹXQdlՐ)sw%dSdm\<1P$h+%X^jPed-O~ǟ^M-@`x| 3ьNQ8[3q&_JeS*yL!rP_ɄZdM4]EqNo^y+VY4ܢ~f}"$Nz꒵-ѬR; ۿtT*.1xT(~'bh0BH2q\&R'jxc#J@V U2\xgb2GGC}(WN +z|ċUԖW\8||B䖽۳Žq~]=*Ǟ5v)~zVm?EWrN>(nGz$촞ςrʺyũѥ|KB"3?w03{A7vw<: ^R*\9gH׺0.^Uڕ<)5 [P,;Yt!Ų];5y&5B{Umy&!};lܵԿfGOr勢PJ U=dJ*Ifa/ab;@pKzEhHNWt ƤTT6[{L1Ab4yA'S#LŇlsi^zyMPzAyLs>Q3vA}VGq;7neU$ nP$ܳ67"Z"˝QӶȗ YDž$%MW3/ }mCZm{Ldn9ZSQ>2X !F1rL>Nt[z9 j+9vnLKcT8Ehf )/NAȾ蝽cb]k rF#$8X;s!SRs4kojF$V"Eyyoy&0"dM$9vE776$9 Z5%ƒr֣Gz䅝S0h|e}ncr۝}g2ӣ+N$|ڍjo൙|t'd͕:G20BkX[U'N +?U2Ħ&fxd ϶@q1ڱeP&u1 8-]F2>6-u~iu7 ;b ~DaS8 +npqh&DP8%mY%{Fp%>;Te/PlTQmهi fPDvAɬynUyWj~GxE&U w,¥V71GȧK g f_O((-SY80Z(_fw~mö7._(DBL̃mg/ף+p2;jO VidᰆPkARL[D"ofb2 h!+#8uLrd6\$ 5z;۫%dO)J3%e@ ' \QxQ +endstream +endobj +30 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-24 -2960 1454 772] +/FontName/IORQIL+CMEX10 +/ItalicAngle 0 +/StemV 47 +/FontFile 29 0 R +/Flags 4 +>> +endobj +29 0 obj +<< +/Filter[/FlateDecode] +/Length1 930 +/Length2 1975 +/Length3 534 +/Length 2622 +>> +stream +xRi<{ *PxeA!kFjRgxY0KXB$"Il'T$:)$;Ts:~{|y}=WunJ{Vt F涖($F"a** 4  4PhM{46чTsyy5sU0 H7H5!(,6R(~La0 + AD zA4bF0 +L/@mը:I(a7}S(8uZT TS,I l$Al,E@DS!i# &4&xɭY@`bi~Yg9~]ըo5/ CFY҈tDкz p`ītH`,#itK% ՕQi򄼼V/ ǿqYOb}{Bl~ xb^H@!AL? +3f33zP(]A]@ E"Jd3xZۼ~o<3 É,50@BEbb(9p Cg<9!)LG(-閍n&PshIq~`TkOfvESH̏UHi[Bw}9ieC)nU0.Is oix2yW!beA-M Gm#F$^;*d7q(&ޝOTG,ٌT~e/W-7DwMVoz =hgz +)Pۗ7)#HNJ_/@3P?Ce9?|!x_"v>z(a]Co?JRu[`øhw>O#*R>6L]cB?|Lfo$jŦ5OZi 9uNEvM$Yj?6K{bb{.δDPf ؖ3a۝f_0R7rVN*P9.|el-)7%2UR=5Vu1#Wul{L^_N3?6^\ZMR~0{a)_{w'ZM<h;TX4C_. K*jĪJVʗW'VT9ej =%kM8!m+a>KFI@ NΗQjԡ9-3ZoGF,UAR+{%3Z)t'+-1i-qR7E~-w{$/JB6=FRR3Rtw,>)G*Ek0oUǎy]NxQsObss2>"-[G:ctfn/R%+-Ne\X^S#-(Q=OJk\fkUD(*'O%lz~@Y9S% 6rNvYܖe@j}@ 1.>\!ֳI2+T2${*}͘sN]v\-i|vz|'JDk MUorД4tyw!Ub6? /:nfW>5/D֩}Ij`ep3zƓAt~Tq.5-< +޸eHZM^c"Xlszn׿8TaFu7  S+~PYԌ|o~J]H1#e.Y%=ĻY:YJԓ5)>%S.;cGy);I; <{W*WnݖE/%-G+_º.0IqZV5ؼI6LؘnI z.j;>}^p`w:%OP1VtJ] WYPfMt=s768~#ږhWs{.>N /ߍz4'#-l;y}w"iƄgŢe3qr!~R<&Lpo_NdۚTR}Us' +5k{śFT0.X!4d&˨?:sT,DVコMCuPjծB+ɶCݣq]%jgG'(}u[n!sx~ +% Q0!%Pǖ| +0~=Y:{Nbׁ"UCb9v>/A|Q:<PzF}ϼj6{(UEUO^/m^ŝc3 1mvHQNWn^J#S-GaD +H`T] +endstream +endobj +34 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-32 -250 1048 750] +/FontName/ZHEONB+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/FontFile 33 0 R +/Flags 68 +>> +endobj +33 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 2496 +/Length3 533 +/Length 3041 +>> +stream +xy<a4G[=m3Mʘy0ƌ,IdY%$({ KɒP$GsK[)T'ЀJ+ (@vp8DRR$*EOQBSS2Ȁ +GTPjHDХzH.tమw@{4OLtWc''VT )L,o,Ao! t t!Q J߱(TS&2|3igH  UB511Rjv&*ⳙgHIH?/o#)&%gʦ +7lZYØڑw=,? U j\{O]xZYG=,CP"\te%!x{Pwgϕrfs&%:Tfb *o9*[{UM7gN'MJecԌZwXà[32IZ]w!->#.A6ZqzgNtXʹ6U(JᅈOOƙUw2]~ sr#GGݲ=OOS5_fY6o3~!cC.zذpBAڃJfVWQ<`?pW坈Owh{연g;Iɥ!}_H~`[:nil܃0&3@e +WjFG V6$**krCUS^ܡ.UI%tI[a\k! u֊j>kl ;iT˧caLjBRPv~R5 <RmpUz IP'caсwK*w{b ӏ +0vBƯvϿB̑4yb[ܣXg}jMKzjf=ڪ>oêǧ]IY0߈lTmV^ &`M}M{^X(7WIc ky:]ZKۍH"'D`M1d2Z+ۂhQ-bBjו]̊É+KvskbxMp2vgk m[AUɆ&ۓ\`9#UPk c)(JՊidhr=TD4,^ވ8}^ko*<1`0rkUސk垍ʗ~a3Ms⑿IG' DX)@DT¼8gj +7 +Z>j\{&5+)ꈎcaR9oPܭGV,G}v{'(Qw?kLxhN۟gigc-1T poqu7 V'J*~9{>}OC1o[I=*O.8E*L-++,"y k-2.ɴȆqg6g\ES_e2\`Aw GNvs2{ДO'wPB %Oh4Mrw7Xt<%0 sj˅" gK#m}G瘷M,OBa標,϶&AO108ݏe5c鄛nTa6_ kWu9ǚNt6U!3c;{?FӈyxrDjT‚ݶ-u +g/뻕?tVd @S);3 +=L)ȩAĽ(b j<-|0?'?/+!+!W]Ŀv61\\euVMGsetЩشb|ODBq}8y ʕ=_1Q&Qm9#iX6ƹv\?(.g?b]7='0̞şwX6R^\|Gܕv)mу0ܮuv6fs qQ"}w9骰VWB +S'F^~ɫkſ}L(j9B+ՔY.~SZ>ޙI}^ 'CN\W?Vǜ6εjZ5ڧuߔ^yy!F!Sp3xOc[)ϼd񺨞Y Vq Q" +1%O> {[[tT&l7%NVf\)K꿋QIM@7ʇ300=j_o̊:l޲^ӖMW *? vtEF}Xz[}-i|huNsH2\kn4~8oóUxrUgq%4g3'\  g-/UZ=8vw<sCIܮ\Jd~kNg}CWiɌ5Rn=6~rqy&cswֹ yrֳǾ]-%:eKΞEH'$7|yqMP tcuDK8|G|8>^6'@ݘ\3ŋhwSH`%ghj'y՞vDjIBTq zxYgPͳxx_A^pic6)SDˣPAn@?@ xꁧC  N +endstream +endobj +37 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-27 -250 1122 750] +/FontName/OZINXB+CMR7 +/ItalicAngle 0 +/StemV 79 +/FontFile 36 0 R +/Flags 4 +>> +endobj +36 0 obj +<< +/Filter[/FlateDecode] +/Length1 712 +/Length2 1964 +/Length3 533 +/Length 2497 +>> +stream +xy<%Ȗ= 3fNGa,1fґ[Ttd_Ѣ9H-h c'3=ns_~>}?83l! + 8(C$L[ۆnKdX +`P +lL c:6]& dA$"p"4AH 9`E \`u$`(@Hl@t3=|mCJ'@V pJ2Nd0pfV,1ֿ6>Ju&> 7H 3 'dѿz_ќ@2BVu`ɊNk +@2bDj0BqZˁ~pDv0JlRY Âo!_߬eG'1D:";5#줁 ``\ `FF0 + +l44|$X g a v1_ K]~ǝ~brw۴UE`lq;\b6QN 9-ezGI|^[^ˆ ~޵Qٗ6qv֨!r~c`x]!,.1]bg*H!;fS}u;bɺL7H|K2O'{Aö{ģc("#7ONn֨qR:Mrb3&648X:_?r;0t'6;'mWE)Tٍ9:.HȥBr-A{xeἋK5̅S7}|>]OѿIzd=GyiY5jGcGb?JI#p] HZ¸9cǘsE4զp[i +Fc'2i+G/h5lS]bStkYX&Js=1- ˜g3Ӕ_M]c2.23}*uDe3}2I 6,,Z>d6s ݅OrbzŨ)ĔX$ XO$%.lsG:ˇBr ߾^,2״7Wk.Pzf=f S;Ğ0 +-Z4OxpdH4G> >|V3_)倍lg\ն聫gw>]zb63nkOݯKDxG˩#o'ol]E؋{]Nn>ѤyˏCj{e,N1W6y +>c2ף3=ώlU; JSryW3%dg>_/d9?+\ɦW +ء5Ʃ{nN]ʢ 1/eos}ez-D]z^,Yl!-njaOiSn*KJ8y#߃.%'EQ+IVw|ΨE #d_͡ MMGDtn{$Z;PbWb0|b~p?(nQ{PfsntcX!Zr9U#ɚUFXwq!]_0G%xuśX`:g/])1<|dV#jX¹1)=;|eg7 ]C/[.MO,Xc_)O'V)FeN^3>ē %挱 +5E{*Mڊl| &J1LΜW7J{i2Z=c*4+qwrMS2=BhʥW=\qu^* z=YE.^/c.;Qu񮧔rJ-QҘ',M/I\fkE/\b0U޺gP ;E,vmݣ%?7- +o[4*Q{[|=gX'jjm5Rq(x-Nm Y-2_>O fЈ0EB +endstream +endobj +44 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[0 -250 1171 750] +/FontName/NBNZIE+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/FontFile 43 0 R +/Flags 68 +>> +endobj +43 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 1588 +/Length3 533 +/Length 2125 +>> +stream +xgXSii*x( 14%rGR0$H`Cb0t(HDaQ`(B1"D\쟽^{{>~/1,.@`H Y0 + YY 09L]L>l'ĄA: B!8$^`bqD>" f$DF#X,@Y@D`Y&ÿ"!f 0^#5ĜdPb!`p76Ji?/mS900hl<dI}f0upBnpDC5x|k;Dnss?Yޜp^1(Ac0XQ|Y|nz0 ) A&_Q1enX,`cW>ʆ|M f3vğ((oIa6nW_? N+6e{Ehy;1qjz`ehC~w+]pW.5ąs #.ӊoKyV(tYP8'#*^QeQR)I4 dHO'yN=\Nlӓ3oZҊWyO.ZP]fq)ovV)ݫɁc++m GeÞ$鬄 T;܉* 9{V* /.O>:?aà[Lܣn# )&m+Yp6IiY6zT}=1!z>ډb9in afdR/x+Ou\CLu9e^pkڣ^ ~FOQH ftwꓔdKם9ONvӀS+BG^6W&~>@\,VN8|t]}Đ~U\esntKB;6zqanmѾSj*a)ĆڎVG<զ&iƧoj +{<̌i j90ڃS[՜"gIa{KAf3x.C=Wt1 'RE^[#(/'YoJ2׺)yY~"j̳ +SuM6ܒ'}*^%o}Cbc?Md(4>!4y''#Oy3e^75&Vґs5qb6 +sT^Ե@7(5n{Lno;|I|߳K[Z]s?%Vե.c~d(Ps3DnQ Q;*K̸wK1vMI* iQ*Rr&^j^9/,c `*2Y  C H^lN +endstream +endobj +51 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-30 -250 1026 750] +/FontName/FYUDNE+CMMI12 +/ItalicAngle -14.04 +/StemV 65 +/FontFile 50 0 R +/Flags 68 +>> +endobj +50 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 2893 +/Length3 533 +/Length 3448 +>> +stream +xyƾe-˘L d !d(d,elB2Q -򺻟}>Oy{?uswyבCvxM!ա`( +06€5:rĘF҉ N@P$`6 +B @#1F#ec?]Z!@#dK'Bp@#a`0 $p h!<B<G|~D2HO,s/KSnhA{\OR`O!x/HÆa ~ G`Iֿ$b`?5N]r9̠*PՐӳHGKF+NVՄE -mLȬ[F%m׳Ny!~BIx-Pʝ~Tz}Ec .,aڡHSsb$@缈:M}]v\|p4XȩTW/^:29V05ȓtjX񜘨^FBˇ/f޼̻rE*g/c[e-AddF]ϏvX) d&x(2CMfMT7Ȭ1$hפ`~5WNA{p@Ւ/ym7TU_(XVlJvjn/-.釒$4g/h-Og^TD n8r=#Ӳ5  +wn y!n8RZ^O ]1n !Q:*2F-3ɴo TyFy|ӏGy!n➟{iXk=7\M +j*Vn )EmȹA'tS;*ClIޱ/SUI\Ës %:@Iv5:_GD+wMMtmFV0j2hl6m]4}j?&h3CBxnNSPK+,]'OLE8T_ok/h݈CyJj8#Sj!f Wp/^,VF#^HhvV-`A>fӃ5)QuܿhLH ~{T||cq ks֐a(Ygd 3o>$YcE.!gе" legI}V ꖍq1͢,{X 6M{,s~2Zm/glvA;6߀kfQ@Թ7-n(sȕkw߰h+{2ͭB/U+n(j4[h𚹏oF4ˌͼps4yi}l@$WL_Nġ-ֲkzfl$"aU}=g":JC#wn>䘚@KVU>-i jH}|!ul8i;O+z6E:zeagBo{`|}fcŲ]<_L~ׯ =]rNvEg}`gnF`yV+j|X|ug2zMw!r)'iIɫR(.k{]s7j>~7KWa36ݭث Ojv}Fju?C~S7=t8*Uni7w{_S5=),TNJ_;[A)>^zeX(>1Kt3^usUޒ7]b~ueć}tׇ÷P~ G7CDLR_rRb"Tӆ] +7#<;_>={89*TrNuDhϘ 1k|}jj1}bԲUL4H?oLG33:5AÙjJ\~Cَj)3Q%[|tGE`g9 G\=-"WOk=4rZGߦpזGxO -Yۦ(ݗ̶vTӹT}lkYH > +endobj +54 0 obj +<< +/Filter[/FlateDecode] +/Length1 724 +/Length2 1294 +/Length3 533 +/Length 1830 +>> +stream +x{8T)vDɣNdQn3KqiqK,3XEk0doޒlivRmvdp*SHTml"r&vg?>w?~pi0ȑB p8 La!m@ +Y +Y8ss@,x رv> !0dd*(l* q@d0ϏpO!1LE00FaMFb #t% %b4(cʖIXcC9ܑ`̏2aFܯ63B@f m!enV YtL & 8< dp>ĢmFoяnn B!}VKƄ< k$F+xj,*Y4{*;e`lIg/͂Or1ޠrbAOu8, *HW{6;RN@nk_Jl +5?SO,gL}_ld5vbgzAUc}[.[f.t*Yq¥,o;WD'OJVSC8@Si0b]ўy&;Օ, MɲL|WmKw*>T9]|ߊ1-Ya&#wĊ=Q5wduQ*VSrD + 3 +8R>\Y&K20ֈOwvk)m6Y򻝭5܃I>ˮs9K!_dw@ԉ'qm߅總qN (l&mߜyxa&u;M'YɋdP/yu +n*j.22*; ~ "jѨ]W$2z^6yg/1P:iu!rK2{_.-l~Fz0Mn6A|^ +L!*W^QT+YR]Σ~}{Hmfy:~yѲe%>鑩g%#GK_nYzcȶ7vL]}}9 jotMLc0yNjC/LK*/vfj`leZn+ExnK|FLgX +mo(b!uҟU}Q81.z=~,Dޡ?FvpY;zh!롛JK aGP䍵t]VY22%.w `J%#:eL6p֟4<.e7O+g{71OOӚ?_>v/M7? ~\ua,JN@> +endobj +58 0 obj +<< +/Filter[/FlateDecode] +/Length1 728 +/Length2 1814 +/Length3 533 +/Length 2358 +>> +stream +x{8T%aO ːDDH;RƬ5c1fD3B&r'Q)Юv))&JI{<~hz@FĠ(%`1#ttpLȆt"ƀ$^KS3KaQLqȯm b$"M;.%a#}N:yŽ}-r5Rn@V.t0Y3^6~tv"_mx-{v,>PYZSpjTl&I?#č__ Q}=z%x/+!ܳ5{C|hDe'2Wavy"dz#x(~S)|@LAN ,F1QH>򅞛XsIM)#b TX4ŹW?:qGFUip97jiǻ6_I>GL{9vS9~6fKyb-"CJE*[4$C(}ﷱRf*H^s i![]Nmgjz%qi-?[%jdkxYi%n nA\g +.uIP'|o;ojPrOQmӯoǦ@Wl +k^E9"E3OP!C{x) ~N\ZAwZ= -iTI 42nG 9yrav1ۅbt=̶~bBҼu lz.-Ő@O ?D4︥z(>1Djl;%1FXhl\IsC"wg%ϙF RUl$gUosvU->>+I}=J ]DS=Nռ\ fo )2C.ǿ)Y H5|07jkѐaMrtLK7q  )]5ksڴP&$,dpbz'/[D~do@}tOnԬjM'GUז=7- +v!/},TKRlTa"'Hk="Ż1v;ԥT/ڕPf7ZZp/`sEƎovsHƕ#){ +\7߲JoyV~KR;Zm̚C?l?4iX:8.ɻYSz[WD229m$x<ifl1޵™I0=%_qt~%qrD|Bv#*909&JYL[ڕ5"O+TF$zW8(`lefxr6`Z|9]q3.3jU3`ܳVzrdR兆ضvBU/[Q[662 t^AtBЈωb'=IY o}h0;[h_Y.ahsX7LLx>V{LM[wLRn5Э#YO+;ߕҚ7#W? ܼ~Py!?b +l E a\ +endstream +endobj +63 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-4 -235 731 800] +/FontName/RRBBFY+CMTT10 +/ItalicAngle 0 +/StemV 69 +/FontFile 62 0 R +/Flags 4 +>> +endobj +62 0 obj +<< +/Filter[/FlateDecode] +/Length1 719 +/Length2 10049 +/Length3 533 +/Length 10607 +>> +stream +xUT\Ѷ;+\.U@!Ip<w @sK~{==ZZC +" x% pq992nK3L" J\¼o(20C%rA-a@鯉#P +eZxqyA ZAl0?`6@.Y򂸹2 s!65Ao\Ql[:A}Cq7ؿK!APO*yX:B` RPwyzyBs$Ғ7d%_3A}ƜWw&vCa@mK _N%-( _e0'DI)Ϭu{3mkkN8̿00>E +8-~Px3$k2?zz{,.4s,a6PHiG =tI;\ګL\t5 nw^Q#N{@*}n5zot?%)[j53i~4:.dF~PQu@\CǠw#Ϧ'yr^973J:m'3E\xf:ldQgW@op9f\ +LЧAfƩj;j=c~_O?S˩| 0`rsEyAL}l8!^2ɚ +S襕"QȢlC,[Z?옇>VO~CE춝7MuT`K1{Tj֯AAW76S?f>Z3"q-A)@Aj"* 53DEmr`h0_F.%H$kz"X2$)q6s6 #ɕ!NaߌŝT^LW4#.Wb~(/QXY筛'ա})#ѬJ +\d:%P˃j}åO{}ڒ%~g ky"r^gM/`QC;𷛮/_8V F.GbƋZ\uД['r XZUrv2&1uy6lDpJL*Ag#ȭaX+Kl Uol^"K-O Mf{/o}SeK@E*~I h/ڏcHv29F$kF>s[6<(}ƕv90,cH]|۸|!=գ`9SsR}qV-Jz5'oQʔj^S\ǧqùOqI^U^{g; :R.2.V@>aJ‹g]4Fu$Wg88,n?}i:0#/)/O^t~pA`>KLGʇ0˗wH O?ZPc"TOR}ɀPw|-cN,.nߍ*5/yTe769M jqN3z zbħ1j>(n^EǶaD+9S`'“|L*U1>$O ƾSJ-l||$Yϐ P&BtؐeCaEIUxv[ڜp~=Gn(^+łJ 6hͽ{\iᱯO"γ/BC zkKSͯ>e0#o4@9?"p +6K9*ZB-/lBq!jv(wVOLa^!O>~ L5lP?L0Ml/D-|D[}3,g}q5 QLj ^b)&)&5"I8"O:h- \uz'&N#Wܭ'+ %]ﬦׯyGnc1?{i3z{:bH@"a@5w(Sٰ~kF߃vS0 ֽHy.gIȶp>ݣ9hP}s*HeLb#% =Ewy!佽C+:W'_^{O)8Apa"tT@5|U^+݈rGw +O;qX^TlhRBL>h%%I%}0+G}GjtwX_?F!XqߍIx-a|ɏ+g^DKxnbD3?Wp+r_7~0;Ǘ4,J@AC~i33D*8*#,VԊU(2fMYҞÖ2Y'sB/SmD=U#ݢ/IiCM;IiD.omKt'OWzjk՘krI&.1Om +oXK&r*BbJL;5LHWi詄A 5Vm7R&aѧ0SC׳A2OYyU w€m0vFSI؂~^73tf#Y423CEh]JWu7QhJ4jKV%1ٙ^C.[xB.\~ fo19ŭUtWb'f[WƔzH6Tm3̬02+ NƓx$Y0@v]SF[,=14sJp| 9!vLcʗf!3.D`)rDZ!Jk׊8Ciʜ&C VG +MZV)dOaASXab pz CHˏ.wi9҅t<橰wc)v7x摘ZUz%o"Qng)BZά‡nY-؜xX%s=O-U`ufMB_~کm58ӵگʬE'Cmß\&?55313h5 +Sȷf4G3*bW"u_ts' +wDsx8zUF3d-ĮiPxeVݮY/gͰ"36LD^껵3iU-ᵳ@^qs$#џ`{=zӚ|ާ bq&3=$Gb<+R?0& i!7~).cKN3u:{$"c {߰ * +;NO8 m}<;Lo^Sn= s'a!l(wXU3gI3G*V9P:H{/(zs%or5F eɜ<ej$Av];\QEBZA2<&mU}TIDĐ 4  w1)WJ: C?6%MC@ Řs̮W.?ƒ1 >?rW#Clc(fJV;V;8:)bi}|YyM:kz.n#fT|";5:DQ?P$ v %:,g!x7eC+.ĽOٽ\u~N7ҋ9^ז.a(6l/%銗Q.zY|竅>%*sYZj5XҐK{$X[ oeme$&Kڋo*%K]ek@C3fs0$^B,cZ`iٴÚzh>9. wYWW֖.Ɂ@DH7S>H$}s?ܥfHM.2"ɚZX{di N/0Qa?G桹#FPk |t/JB+d}UueM)Dw ]F%#u!%KS=(J%Cph㫈폺f:82JG !wё[l4 ;m`'st6PE(u7wRl^ }7o4>WCl')7 FePHbu>q@`w'Uxl=6By*x\suEIcp[@Bh_~ Ƅ; ك/?P?u _񗇬]N.It;U'喟%5lɢ -p`U4B<<y,|>'A}&G"CtP dh ZG{JvrnE8M. w, uokf !OisVC!%Ih~@Zt6t&_i|*.=u]&S4Tܦt˜tx^ܨ0ۃ Φ`B|BVGB:1`W.v9.yOWjf4uwg7Ca:^᭡j2lw3,eLjԎj5hM6GN)ߎu6SQ"<I~OqG⋇th[s6* F'l5`R."|,Dy9fD! +=&吪M:UۭՌ*\#P 2{yhr ?ǑqF2L`=4B$M뻐?܇B4Id;1 GRl_,T2QЩgF7^B4> 92Qm' ݏpـ5[J#v-.}lBbx]w$F5}޴/=Kp-b?g퀜~Õt}Ꮷe*cS”XK`̦: A6sR;xgA~!P҄F8v +,A8 z-Mo*nj\d۴eV M!\xg_Z]9;Ozi_^|O_!)ØTDxj0s-GB|/.os>tW`iFtd^W Z&"?흓άvfs]Z)Ƙ3]" ,JmRpDD;I֏wKj @] NtR$X/g@+Kep7Z1z!nzZ(Q8 $yl&dga$/<- _)D-Z{кm%97e+@"xت&0\[RAY19J^4B&n"Qm>=b6؝oX&@ B5WnI5d [[i;|8On*|;YM|SdUOj zsǮrjʌ]5!!/L` +~[bPPܡ*OϓU,M@w;[lzQK6Oq ?ieinOY2iz-׈qpSQ7gP*(4?ʑJ/D._?QZiCbnTmrZa5ah0M4@hM]JL7&ȠizfU P.pG,x4FJzU 4}`vfaq1 $(B{Hh9.yO&|cF)]'8&Wֽs;Y=\C7=I4&\ls'?ge{9u )@u,uV'@oHI nj1:QqEX.1~D+dKW*T'&A[19K5ulYuwyX'TDCn\ ŽPǸ ՜oܠuڧQLbF5b{Ã9wUB">{SÍGUmmlT.>2~mX* R f4-eF4{3':Xm͒KVν"w` /[կpc7ɻU䎇%񖥨Dʠٴ2hBOʢچd)J3 nM_ן|}X!~6@;J? ZɅVX]}.a#U/  +kU`G G57^XXS (}*9ֽ[h^ 7d'?E>u~u2@DTCu6ӵ!xf#~LO'dRD_2[\Z* +U\7LA qpI5*Zpu84=[-\S&FUKW2^ڜI6ɉ9/}lyU 7EѶX-+Pr>&d<@/OnaW$!WHl-A3wtq=WXyN=Hg~a󅷳Z^0o#kB3mqL;{n ?E< #JHIJe7~}_7=p˶v {I.صcNPjF>clӱt oP{S \I x[yYGqni'1J:NU>~5;\|ee<\StORM4=}"޷>בVtHݹn]g~32᜝߁I)5 0o$Y+ +ӧc<(|l)GQY_ݬro?˕yd2WMjanD_MზǟT>frHF[>a`hv;] 6X#@tr$eR >nְ4S* QDa蟜& +͇g.̰) 1( s5H \d5m#ECu>fQuAAc0z<7Qz=ջ(lw2Rb: +q^:Nx5;~-[;]:IP+X}o)칦=y po<@8I j~kU0A'X/YUzqԠ5ň(B&OrגqAO?[i2Jjf>c>%s-BݘM3J4'^BajrVFw? Ĩ+k40'e?4<" F#b僁nGBFwŲM:t]? ک2~Dxo}i>C6[S.S kG?έ +endstream +endobj +214 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-15 -951 1252 782] +/FontName/ESBUTL+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/FontFile 213 0 R +/Flags 68 +>> +endobj +213 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 599 +/Length3 533 +/Length 1109 +>> +stream +xSU uLOJu+53Rp 4W03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ A!S U[PZZZ4<6Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D5)4Gɀ̼ʂTj0RQfB!P!Xh%d+$$0_Q LC +FF +F +C2 KS=]L , ɥEEy%0 ԊdsD3ud&|9pU)|׉s77Rd(wirkSsk|^1=6Zsas_y2-3%^ Jړ}9_+l5_ ?ܛ%a{TĆ6ႮԦ,؉v3k02<[RZlez_ 6n? qܸs)_Ǵ3٩F&dL淖g2)D^c]Q,'$'Z㛾 l>uy;Mwָhl49"K]9h\8?Lj#oY~8qo{ jVf4HOc_s&z򏲫۽;|]}xNezesC&Ꝧ[֭fS!ES:ZK8sJhOOʝv2+ìRZޖ(ynY҇3 +=m^un)[TZbeQ9E%E\\n w +endstream +endobj +221 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-62 -250 1123 750] +/FontName/YBJVEW+CMSL10 +/ItalicAngle -9.46 +/StemV 79 +/FontFile 220 0 R +/Flags 68 +>> +endobj +220 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 5038 +/Length3 533 +/Length 5591 +>> +stream +xUT\ۖq SV.K &x`݃{p 8soK~{sEG&v89@@ @RYS 90$]!09 " > 7 '@jm0J2;@\es 9d =@W7 `% `:b%hK;qu{0>s2)N0 +]y53뿡{P{8aWw./8e<j)hm yn2P/X +XۻA!࿃<O v} i]ؿjPG3/5_\^C |oI;Z:M#¿SIH8yr8y7 _ڎPwOOs3<?k+ /%Ƨ "()+%˅yk江 X3S\[J8tNl$ɾA'4C %g)"(WZhzF6XLq>:M{!1 ΒxӋص(^n"xX-TD΋Nl 4cFe3ZkdʚF9x}N\+/\Aih *ي2F46)e?Rsd$kߘ#-qײxTw'g#v}Lஃz4| ՜\ )G3v^vO HcQI*=dX|xݍ1(C"n![޹$P8w#'J>r&8'KGsVC :^AfL1;s.H׌V%ښ_}M3G`MD'+-w~\r tpJDu z#gWdB{CچuL!a! ikk +2_ aL%@In^RC >51y9fuX)f gHn\X QN.[KX2``gU \1Bzdu&c.np;ﮭI%.iu塬mAa# #2iQі<4,fVtY" _Ѱ^FzeeLZg<22M#Gz ü ޚZP.NWºI|S@OlڈJ(Kz\hpj,o%йHHG ynf-5^uUt{W}2+8N޸_;a.Bc,㸄7YNd#~S$Z 6˴!O> +d& +׷wPNFzpentiP"+[M!x$~8UӂaF}-~<ًf)ѳ_,p!s͹"ޣfȀ%POOgꃥd| R%6ڿP}7Z$ 7k 20}X/XQTg) H=P-q%BYkW |7d:: S–y?V*FU/Y'#<.w.~ʴܝ${42K<4ϧMƛ@MVnjYT{!FRHs}JzrqMhchlc16d6ʺwt;("_qlSh '#g5iNK[rz^CϱQ4">bX#zάtf4E) !:Uڑ: |iˇM1*vH?\#p k[bD+* KhJwf^lńV9*gvv*9n@URؐJϦo3e}KZetgW<=Ά9f^а4'& +/7s,%-y?"s +WRx.[4RK.b@MMÈ6P:t^{ӗ|_~" GѺDQE'.O0*{F6雘/UstCA쨔.V%SX)=Y_b^ j7|Fύ0rb5p UZk!_<8+RsX #zu7iu# {(6KFUPťtǭ6NX˂Ҽv +*iezeVQj& f_?i`h~!g<-@a$®Ckm +_e+CCTFTzQ(¡.K/Q٫X,|o3SQ~adWo>>gºkI谱> Yr7B2O4y/}xX0 ޓл &)x,ʐx@rBcoAT'nY䕄 IJIG$dIyVH{yE*2Z>9# ֪ߝ!Uh&4G\=> +Oo'` 9.zvE/gmE +"b Wi3]Z߈PRp&n|@xsGm+ݠ1wy؇Xo{Bb2glY+䱹?r1H:`~/Q1f:ouV)YӰkY"fmŢW#ORM-3R-Z.ltֈb#J+݃G97sWxbتw|T5EsJһ}m(ƕ2&˒Aq:ycMdAآVjX~hYv'^x,?od qFEao̡c^R ]bLtT>#&kbM@4 +:\!#^t?[NJH)mfk@>6=ly0/oW@7m*l8!w0YUկT'^ڶ ~4U*)5Sy01WVLWԣK%b?1-rO'ۗ^5 =6ϯSKk)cgG|cS?\&n`4\5ugJusѼ0OJ.1 8o9 +-E 4iৈZIE_.&C`3cKnMðDr%5o/݃a)2񎡆bliT֙z_[#X<`>W4=h3gڏ㍄ᓋ7PvKz8.V}%.˩XvnpE5{DղduQ=JĹl`\!Wegnbs]*Q,m6/|Kc2-xițfKJ&b aUcd<%?ZbDq5[=(FO R_g]?4(NLZdC +yxj6w}DHMLx"fBk+x~:e3f}MbIH3 u%Y1z+7L`#Ebp++}hfw#l 7$lK4[;'^`fM03!8m*3)CYu@GOlh[T ўq3 !&"׭4I=4k"79ȯ :2G]j[_| eO?Ogj jiIu<Wm\rGWEH6ƈkڹjˎl䓈".RoH'eHgtC/ZBTaA1HjީOir< ä[~[+'ZY6nkFg=F\Du&!wբPj[)lm֏@[lURoOW^{`6k_ 1ˡ`Q}ҿN"Lɵ[hNu1nUśk,q]yK\o/Ak2ݼT$?k~ҭ7/OGA' )XeWhckw@107vw{㑅qy\/ ^_lhݑ#쬒v3}n%7%{_oiKnmgWA ٥ZGCiXGX3 'ih5a.i*T&rL,c~oe"jef} S#e@osWu[SQ`ϽSLS4HҠ/EB)׫^}Mu],\Glv EVkspKzCS~)Anlzo8]yz0={ܶacP +Â]liH69' +:̃-&_ʄNZk{Pk*>Nxb~6J6LjR4ZK'ʩy#PZj//UʥMsJ4; kZ8cy:8͚Ugsd@Ƈh4[*+xl8RZ،Pq +'9f${9 }N }d_(O@> +endobj +5 0 obj +<< +/Type/Page +/Resources 6 0 R +/Contents[17 0 R 4 0 R 18 0 R 19 0 R] +/Parent 226 0 R +>> +endobj +21 0 obj +<< +/Type/Page +/Resources 22 0 R +/Contents[17 0 R 4 0 R 39 0 R 19 0 R] +/Parent 226 0 R +>> +endobj +226 0 obj +<< +/Type/Pages +/Count 2 +/Kids[5 0 R 21 0 R] +/Parent 225 0 R +>> +endobj +41 0 obj +<< +/Type/Page +/Resources 42 0 R +/Contents[17 0 R 4 0 R 46 0 R 19 0 R] +/Parent 227 0 R +>> +endobj +48 0 obj +<< +/Type/Page +/Resources 49 0 R +/Contents[17 0 R 4 0 R 65 0 R 19 0 R] +/Parent 227 0 R +>> +endobj +67 0 obj +<< +/Type/Page +/Resources 68 0 R +/Contents[17 0 R 4 0 R 69 0 R 19 0 R] +/Parent 227 0 R +>> +endobj +227 0 obj +<< +/Type/Pages +/Count 3 +/Kids[41 0 R 48 0 R 67 0 R] +/Parent 225 0 R +>> +endobj +71 0 obj +<< +/Type/Page +/Resources 72 0 R +/Contents[17 0 R 4 0 R 73 0 R 19 0 R] +/Parent 228 0 R +>> +endobj +75 0 obj +<< +/Type/Page +/Resources 76 0 R +/Contents[17 0 R 4 0 R 77 0 R 19 0 R] +/Parent 228 0 R +>> +endobj +228 0 obj +<< +/Type/Pages +/Count 2 +/Kids[71 0 R 75 0 R] +/Parent 225 0 R +>> +endobj +79 0 obj +<< +/Type/Page +/Resources 80 0 R +/Contents[17 0 R 4 0 R 81 0 R 19 0 R] +/Parent 229 0 R +>> +endobj +83 0 obj +<< +/Type/Page +/Resources 84 0 R +/Contents[17 0 R 4 0 R 85 0 R 19 0 R] +/Parent 229 0 R +>> +endobj +87 0 obj +<< +/Type/Page +/Resources 88 0 R +/Contents[17 0 R 4 0 R 89 0 R 19 0 R] +/Parent 229 0 R +>> +endobj +229 0 obj +<< +/Type/Pages +/Count 3 +/Kids[79 0 R 83 0 R 87 0 R] +/Parent 225 0 R +>> +endobj +225 0 obj +<< +/Type/Pages +/Count 10 +/Kids[226 0 R 227 0 R 228 0 R 229 0 R] +/Parent 3 0 R +>> +endobj +91 0 obj +<< +/Type/Page +/Resources 92 0 R +/Contents[17 0 R 4 0 R 93 0 R 19 0 R] +/Parent 231 0 R +>> +endobj +95 0 obj +<< +/Type/Page +/Resources 96 0 R +/Contents[17 0 R 4 0 R 97 0 R 19 0 R] +/Parent 231 0 R +>> +endobj +231 0 obj +<< +/Type/Pages +/Count 2 +/Kids[91 0 R 95 0 R] +/Parent 230 0 R +>> +endobj +99 0 obj +<< +/Type/Page +/Resources 100 0 R +/Contents[17 0 R 4 0 R 101 0 R 19 0 R] +/Parent 232 0 R +>> +endobj +103 0 obj +<< +/Type/Page +/Resources 104 0 R +/Contents[17 0 R 4 0 R 105 0 R 19 0 R] +/Parent 232 0 R +>> +endobj +107 0 obj +<< +/Type/Page +/Resources 108 0 R +/Contents[17 0 R 4 0 R 109 0 R 19 0 R] +/Parent 232 0 R +>> +endobj +232 0 obj +<< +/Type/Pages +/Count 3 +/Kids[99 0 R 103 0 R 107 0 R] +/Parent 230 0 R +>> +endobj +111 0 obj +<< +/Type/Page +/Resources 112 0 R +/Contents[17 0 R 4 0 R 113 0 R 19 0 R] +/Parent 233 0 R +>> +endobj +115 0 obj +<< +/Type/Page +/Resources 116 0 R +/Contents[17 0 R 4 0 R 117 0 R 19 0 R] +/Parent 233 0 R +>> +endobj +119 0 obj +<< +/Type/Page +/Resources 120 0 R +/Contents[17 0 R 4 0 R 121 0 R 19 0 R] +/Parent 233 0 R +>> +endobj +233 0 obj +<< +/Type/Pages +/Count 3 +/Kids[111 0 R 115 0 R 119 0 R] +/Parent 230 0 R +>> +endobj +123 0 obj +<< +/Type/Page +/Resources 124 0 R +/Contents[17 0 R 4 0 R 125 0 R 19 0 R] +/Parent 234 0 R +>> +endobj +127 0 obj +<< +/Type/Page +/Resources 128 0 R +/Contents[17 0 R 4 0 R 129 0 R 19 0 R] +/Parent 234 0 R +>> +endobj +131 0 obj +<< +/Type/Page +/Resources 132 0 R +/Contents[17 0 R 4 0 R 133 0 R 19 0 R] +/Parent 234 0 R +>> +endobj +234 0 obj +<< +/Type/Pages +/Count 3 +/Kids[123 0 R 127 0 R 131 0 R] +/Parent 230 0 R +>> +endobj +230 0 obj +<< +/Type/Pages +/Count 11 +/Kids[231 0 R 232 0 R 233 0 R 234 0 R] +/Parent 3 0 R +>> +endobj +135 0 obj +<< +/Type/Page +/Resources 136 0 R +/Contents[17 0 R 4 0 R 137 0 R 19 0 R] +/Parent 236 0 R +>> +endobj +139 0 obj +<< +/Type/Page +/Resources 140 0 R +/Contents[17 0 R 4 0 R 141 0 R 19 0 R] +/Parent 236 0 R +>> +endobj +236 0 obj +<< +/Type/Pages +/Count 2 +/Kids[135 0 R 139 0 R] +/Parent 235 0 R +>> +endobj +143 0 obj +<< +/Type/Page +/Resources 144 0 R +/Contents[17 0 R 4 0 R 145 0 R 19 0 R] +/Parent 237 0 R +>> +endobj +147 0 obj +<< +/Type/Page +/Resources 148 0 R +/Contents[17 0 R 4 0 R 149 0 R 19 0 R] +/Parent 237 0 R +>> +endobj +151 0 obj +<< +/Type/Page +/Resources 152 0 R +/Contents[17 0 R 4 0 R 153 0 R 19 0 R] +/Parent 237 0 R +>> +endobj +237 0 obj +<< +/Type/Pages +/Count 3 +/Kids[143 0 R 147 0 R 151 0 R] +/Parent 235 0 R +>> +endobj +155 0 obj +<< +/Type/Page +/Resources 156 0 R +/Contents[17 0 R 4 0 R 157 0 R 19 0 R] +/Parent 238 0 R +>> +endobj +159 0 obj +<< +/Type/Page +/Resources 160 0 R +/Contents[17 0 R 4 0 R 161 0 R 19 0 R] +/Parent 238 0 R +>> +endobj +238 0 obj +<< +/Type/Pages +/Count 2 +/Kids[155 0 R 159 0 R] +/Parent 235 0 R +>> +endobj +163 0 obj +<< +/Type/Page +/Resources 164 0 R +/Contents[17 0 R 4 0 R 165 0 R 19 0 R] +/Parent 239 0 R +>> +endobj +167 0 obj +<< +/Type/Page +/Resources 168 0 R +/Contents[17 0 R 4 0 R 169 0 R 19 0 R] +/Parent 239 0 R +>> +endobj +171 0 obj +<< +/Type/Page +/Resources 172 0 R +/Contents[17 0 R 4 0 R 173 0 R 19 0 R] +/Parent 239 0 R +>> +endobj +239 0 obj +<< +/Type/Pages +/Count 3 +/Kids[163 0 R 167 0 R 171 0 R] +/Parent 235 0 R +>> +endobj +235 0 obj +<< +/Type/Pages +/Count 10 +/Kids[236 0 R 237 0 R 238 0 R 239 0 R] +/Parent 3 0 R +>> +endobj +175 0 obj +<< +/Type/Page +/Resources 176 0 R +/Contents[17 0 R 4 0 R 177 0 R 19 0 R] +/Parent 241 0 R +>> +endobj +179 0 obj +<< +/Type/Page +/Resources 180 0 R +/Contents[17 0 R 4 0 R 181 0 R 19 0 R] +/Parent 241 0 R +>> +endobj +241 0 obj +<< +/Type/Pages +/Count 2 +/Kids[175 0 R 179 0 R] +/Parent 240 0 R +>> +endobj +183 0 obj +<< +/Type/Page +/Resources 184 0 R +/Contents[17 0 R 4 0 R 185 0 R 19 0 R] +/Parent 242 0 R +>> +endobj +187 0 obj +<< +/Type/Page +/Resources 188 0 R +/Contents[17 0 R 4 0 R 189 0 R 19 0 R] +/Parent 242 0 R +>> +endobj +191 0 obj +<< +/Type/Page +/Resources 192 0 R +/Contents[17 0 R 4 0 R 193 0 R 19 0 R] +/Parent 242 0 R +>> +endobj +242 0 obj +<< +/Type/Pages +/Count 3 +/Kids[183 0 R 187 0 R 191 0 R] +/Parent 240 0 R +>> +endobj +195 0 obj +<< +/Type/Page +/Resources 196 0 R +/Contents[17 0 R 4 0 R 197 0 R 19 0 R] +/Parent 243 0 R +>> +endobj +199 0 obj +<< +/Type/Page +/Resources 200 0 R +/Contents[17 0 R 4 0 R 201 0 R 19 0 R] +/Parent 243 0 R +>> +endobj +203 0 obj +<< +/Type/Page +/Resources 204 0 R +/Contents[17 0 R 4 0 R 205 0 R 19 0 R] +/Parent 243 0 R +>> +endobj +243 0 obj +<< +/Type/Pages +/Count 3 +/Kids[195 0 R 199 0 R 203 0 R] +/Parent 240 0 R +>> +endobj +207 0 obj +<< +/Type/Page +/Resources 208 0 R +/Contents[17 0 R 4 0 R 209 0 R 19 0 R] +/Parent 244 0 R +>> +endobj +211 0 obj +<< +/Type/Page +/Resources 212 0 R +/Contents[17 0 R 4 0 R 216 0 R 19 0 R] +/Parent 244 0 R +>> +endobj +218 0 obj +<< +/Type/Page +/Resources 219 0 R +/Contents[17 0 R 4 0 R 223 0 R 19 0 R] +/Parent 244 0 R +>> +endobj +244 0 obj +<< +/Type/Pages +/Count 3 +/Kids[207 0 R 211 0 R 218 0 R] +/Parent 240 0 R +>> +endobj +240 0 obj +<< +/Type/Pages +/Count 11 +/Kids[241 0 R 242 0 R 243 0 R 244 0 R] +/Parent 3 0 R +>> +endobj +3 0 obj +<< +/Type/Pages +/Count 42 +/Kids[225 0 R 230 0 R 235 0 R 240 0 R] +/MediaBox[0 0 595 842] +>> +endobj +17 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +19 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +4 0 obj +<< +/Length 33 +>> +stream +1.00028 0 0 1.00028 72 769.82 cm +endstream +endobj +245 0 obj +<< +>> +endobj +246 0 obj +null +endobj +247 0 obj +<< +>> +endobj +2 0 obj +<< +/Type/Catalog +/Pages 3 0 R +/Outlines 245 0 R +/Threads 246 0 R +/Names 247 0 R +>> +endobj +xref +0 248 +0000000000 65535 f +0000131472 00000 n +0000138274 00000 n +0000137919 00000 n +0000138124 00000 n +0000131636 00000 n +0000004047 00000 n +0000000009 00000 n +0000060656 00000 n +0000060472 00000 n +0000000913 00000 n +0000065321 00000 n +0000065135 00000 n +0000001906 00000 n +0000070560 00000 n +0000070372 00000 n +0000002823 00000 n +0000138024 00000 n +0000003740 00000 n +0000138074 00000 n +0000003992 00000 n +0000131739 00000 n +0000010815 00000 n +0000082793 00000 n +0000082604 00000 n +0000004108 00000 n +0000088065 00000 n +0000087875 00000 n +0000005054 00000 n +0000093369 00000 n +0000093180 00000 n +0000005990 00000 n +0000006966 00000 n +0000096299 00000 n +0000096105 00000 n +0000007920 00000 n +0000099640 00000 n +0000099454 00000 n +0000008866 00000 n +0000009830 00000 n +0000010727 00000 n +0000131924 00000 n +0000012675 00000 n +0000102442 00000 n +0000102251 00000 n +0000010877 00000 n +0000011871 00000 n +0000012587 00000 n +0000132029 00000 n +0000020732 00000 n +0000104875 00000 n +0000104681 00000 n +0000012737 00000 n +0000013708 00000 n +0000108632 00000 n +0000108437 00000 n +0000015324 00000 n +0000016276 00000 n +0000110771 00000 n +0000110576 00000 n +0000017183 00000 n +0000018165 00000 n +0000113429 00000 n +0000113243 00000 n +0000019142 00000 n +0000019887 00000 n +0000020607 00000 n +0000132134 00000 n +0000021680 00000 n +0000020794 00000 n +0000021544 00000 n +0000132327 00000 n +0000022772 00000 n +0000021742 00000 n +0000022636 00000 n +0000132432 00000 n +0000024201 00000 n +0000022834 00000 n +0000024065 00000 n +0000132618 00000 n +0000024861 00000 n +0000024263 00000 n +0000024792 00000 n +0000132723 00000 n +0000025840 00000 n +0000024923 00000 n +0000025715 00000 n +0000132828 00000 n +0000027255 00000 n +0000025902 00000 n +0000027119 00000 n +0000133119 00000 n +0000028124 00000 n +0000027317 00000 n +0000028055 00000 n +0000133224 00000 n +0000029365 00000 n +0000028186 00000 n +0000029229 00000 n +0000133410 00000 n +0000029828 00000 n +0000029427 00000 n +0000029782 00000 n +0000133517 00000 n +0000030783 00000 n +0000029892 00000 n +0000030646 00000 n +0000133625 00000 n +0000031793 00000 n +0000030847 00000 n +0000031656 00000 n +0000133823 00000 n +0000033055 00000 n +0000031857 00000 n +0000032918 00000 n +0000133931 00000 n +0000033597 00000 n +0000033119 00000 n +0000033527 00000 n +0000134039 00000 n +0000034884 00000 n +0000033661 00000 n +0000034747 00000 n +0000134238 00000 n +0000035887 00000 n +0000034948 00000 n +0000035750 00000 n +0000134346 00000 n +0000036713 00000 n +0000035951 00000 n +0000036643 00000 n +0000134454 00000 n +0000038022 00000 n +0000036777 00000 n +0000037885 00000 n +0000134751 00000 n +0000038659 00000 n +0000038086 00000 n +0000038589 00000 n +0000134859 00000 n +0000040087 00000 n +0000038723 00000 n +0000039950 00000 n +0000135050 00000 n +0000040644 00000 n +0000040151 00000 n +0000040598 00000 n +0000135158 00000 n +0000041658 00000 n +0000040708 00000 n +0000041521 00000 n +0000135266 00000 n +0000042803 00000 n +0000041722 00000 n +0000042666 00000 n +0000135465 00000 n +0000043962 00000 n +0000042867 00000 n +0000043825 00000 n +0000135573 00000 n +0000045195 00000 n +0000044026 00000 n +0000045058 00000 n +0000135764 00000 n +0000046500 00000 n +0000045259 00000 n +0000046363 00000 n +0000135872 00000 n +0000047059 00000 n +0000046564 00000 n +0000047013 00000 n +0000135980 00000 n +0000048429 00000 n +0000047123 00000 n +0000048292 00000 n +0000136277 00000 n +0000048925 00000 n +0000048493 00000 n +0000048879 00000 n +0000136385 00000 n +0000050313 00000 n +0000048989 00000 n +0000050176 00000 n +0000136576 00000 n +0000050880 00000 n +0000050377 00000 n +0000050834 00000 n +0000136684 00000 n +0000051891 00000 n +0000050944 00000 n +0000051743 00000 n +0000136792 00000 n +0000052615 00000 n +0000051955 00000 n +0000052545 00000 n +0000136991 00000 n +0000053898 00000 n +0000052679 00000 n +0000053750 00000 n +0000137099 00000 n +0000054496 00000 n +0000053962 00000 n +0000054450 00000 n +0000137207 00000 n +0000055924 00000 n +0000054560 00000 n +0000055776 00000 n +0000137406 00000 n +0000056687 00000 n +0000055988 00000 n +0000056641 00000 n +0000137514 00000 n +0000059023 00000 n +0000124348 00000 n +0000124152 00000 n +0000056751 00000 n +0000057763 00000 n +0000058862 00000 n +0000137622 00000 n +0000060408 00000 n +0000125766 00000 n +0000125571 00000 n +0000059087 00000 n +0000060010 00000 n +0000060350 00000 n +0000133021 00000 n +0000131844 00000 n +0000132239 00000 n +0000132537 00000 n +0000132933 00000 n +0000134653 00000 n +0000133329 00000 n +0000133733 00000 n +0000134147 00000 n +0000134562 00000 n +0000136179 00000 n +0000134967 00000 n +0000135374 00000 n +0000135681 00000 n +0000136088 00000 n +0000137821 00000 n +0000136493 00000 n +0000136900 00000 n +0000137315 00000 n +0000137730 00000 n +0000138206 00000 n +0000138229 00000 n +0000138251 00000 n +trailer +<< +/Size 248 +/Root 2 0 R +/Info 1 0 R +>> +startxref +138372 +%%EOF diff --git a/src/axiom-website/CATS/schaum10.input.pamphlet b/src/axiom-website/CATS/schaum10.input.pamphlet new file mode 100644 index 0000000..6149cc0 --- /dev/null +++ b/src/axiom-website/CATS/schaum10.input.pamphlet @@ -0,0 +1,2310 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/input schaum10.input} +\author{Timothy Daly} +\maketitle +\eject +\tableofcontents +\eject +\section{\cite{1}:14.210~~~~~$\displaystyle\int{\frac{dx}{\sqrt{x^2-a^2}}}$} +$$\int{\frac{1}{\sqrt{x^2-a^2}}}=\ln\left(x+\sqrt{x^2-a^2}\right)$$ +<<*>>= +)spool schaum10.output +)set message test on +)set message auto off +)clear all + +--S 1 +aa:=integrate(1/(sqrt(x^2-a^2)),x) +--R +--R +--R +-------+ +--R | 2 2 +--R (1) - log(\|x - a - x) +--R Type: Union(Expression Integer,...) +--E + +--S 2 +bb:=log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +--R | 2 2 +--R (2) log(\|x - a + x) +--R Type: Expression Integer +--E + +--S 3 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R (3) - log(\|x - a + x) - log(\|x - a - x) +--R Type: Expression Integer +--E + +--S 4 +logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b)) +--R +--I (4) c log(b) + c log(a) + %I == c log(a b) + %I +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E + +--S 5 14:210 Schaums and Axiom differ by a constant +dd:=logmul1 cc +--R +--R 2 +--R (5) - log(- a ) +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.xxx~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{x^2-a^2}}}$} +$$\int{\frac{x}{\sqrt{x^2-a^2}}}=\sqrt{x^2-a^2}$$ +<<*>>= +)clear all + +--S 6 +aa:=integrate(x/(sqrt(x^2-a^2)),x) +--R +--R +--R +-------+ +--R | 2 2 2 2 +--R - x\|x - a + x - a +--R (1) ----------------------- +--R +-------+ +--R | 2 2 +--R \|x - a - x +--R Type: Union(Expression Integer,...) +--E + +--S 7 +bb:=sqrt(x^2-a^2) +--R +--R +-------+ +--R | 2 2 +--R (2) \|x - a +--R Type: Expression Integer +--E + +--S 8 14:xxx Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.211~~~~~$\displaystyle +\int{\frac{x^2~dx}{\sqrt{x^2-a^2}}}$} +$$\int{\frac{x^2}{\sqrt{x^2-a^2}}}= +\frac{x\sqrt{x^2-a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 9 +aa:=integrate(x^2/sqrt(x^2-a^2),x) +--R +--R +--R (1) +--R +-------+ +-------+ +--R 2 | 2 2 2 2 4 | 2 2 +--R (- 2a x\|x - a + 2a x - a )log(\|x - a - x) +--R + +--R +-------+ +--R 3 2 | 2 2 4 2 2 +--R (- 2x + a x)\|x - a + 2x - 2a x +--R / +--R +-------+ +--R | 2 2 2 2 +--R 4x\|x - a - 4x + 2a +--R Type: Union(Expression Integer,...) +--E + +--S 10 +bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a log(\|x - a + x) + x\|x - a +--R (2) ----------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 11 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 +--R - a log(\|x - a + x) - a log(\|x - a - x) +--R (3) ----------------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 12 14:211 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 2 2 +--R a log(- a ) +--R (4) - ----------- +--R 2 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.212~~~~~$\displaystyle +\int{\frac{x^3~dx}{\sqrt{x^2-a^2}}}$} +$$\int{\frac{x^3}{\sqrt{x^2-a^2}}}= +\frac{(x^2-a^2)^{3/2}}{3}+a^2\sqrt{x^2-a^2} +$$ +<<*>>= +)clear all + +--S 13 +aa:=integrate(x^3/sqrt(x^2-a^2),x) +--R +--R +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (- 4x - 5a x + 6a x)\|x - a + 4x + 3a x - 9a x + 2a +--R (1) ------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 3 2 +--R (12x - 3a )\|x - a - 12x + 9a x +--R Type: Union(Expression Integer,...) +--E + +--S 14 +bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2) +--R +--R +-------+ +--R 2 2 | 2 2 +--R (x + 2a )\|x - a +--R (2) -------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 15 14:212 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.213~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{x^2-a^2}}}$} +$$\int{\frac{1}{x\sqrt{x^2-a^2}}}= +\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 16 +aa:=integrate(1/(x*sqrt(x^2-a^2)),x) +--R +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x +--R 2atan(--------------) +--R a +--R (1) --------------------- +--R a +--R Type: Union(Expression Integer,...) +--E + +--S 17 +bb:=1/a*asec(x/a) +--R +--R x +--R asec(-) +--R a +--R (2) ------- +--R a +--R Type: Expression Integer +--E + +--S 18 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R 2atan(--------------) - asec(-) +--R a a +--R (3) ------------------------------- +--R a +--R Type: Expression Integer +--E + +--S 19 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (4) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 20 +dd:=asecrule cc +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x \|x - a - x +--R - 2%i log(------------------) + 4atan(--------------) - %pi +--R x a +--R (5) ----------------------------------------------------------- +--R 2a +--R Type: Expression Complex Integer +--E + +--S 21 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 22 +ee:=atanrule dd +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R - 2%i log(------------------) - 2%i log(-----------------------) - %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R (7) ---------------------------------------------------------------------- +--R 2a +--R Type: Expression Complex Integer +--E + +--S 23 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 2%i log(\|x - a - x + %i a) - 2%i log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R - 2%i log(x |------- + %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R | 2 +--R \| x +--R / +--R 2a +--R Type: Expression Complex Integer +--E + +--S 24 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 2%i log(\|x - a + %i a) + 2%i log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R - 2%i log(\|x - a - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R / +--R 2a +--R Type: Expression Complex Integer +--E + +--S 25 14:213 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R %pi +--R (10) - --- +--R 2a +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.214~~~~~$\displaystyle +\int{\frac{dx}{x^2\sqrt{x^2-a^2}}}$} +$$\int{\frac{1}{x^2\sqrt{x^2-a^2}}}= +\frac{\sqrt{x^2-a^2}}{a^2x} +$$ +<<*>>= +)clear all + +--S 26 +aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x) +--R +--R +--R 1 +--R (1) - ---------------- +--R +-------+ +--R | 2 2 2 +--R x\|x - a - x +--R Type: Union(Expression Integer,...) +--E + +--S 27 +bb:=sqrt(x^2-a^2)/(a^2*x) +--R +--R +-------+ +--R | 2 2 +--R \|x - a +--R (2) ---------- +--R 2 +--R a x +--R Type: Expression Integer +--E + +--S 28 14:214 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 1 +--R (3) -- +--R 2 +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.215~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{x^2-a^2}}}$} +$$\int{\frac{1}{x^3\sqrt{x^2-a^2}}}= +-\frac{\sqrt{x^2-a^2}}{2a^2x^2}+\frac{1}{2a^3} +\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 29 +aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x) +--R +--R +--R (1) +--R +-------+ +--R +-------+ | 2 2 +--R 3 | 2 2 4 2 2 \|x - a - x +--R (4x \|x - a - 4x + 2a x )atan(--------------) +--R a +--R + +--R +-------+ +--R 2 3 | 2 2 3 3 +--R (- 2a x + a )\|x - a + 2a x - 2a x +--R / +--R +-------+ +--R 3 3 | 2 2 3 4 5 2 +--R 4a x \|x - a - 4a x + 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 30 +bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a) +--R +--R +-------+ +--R | 2 2 2 x +--R a\|x - a + x asec(-) +--R a +--R (2) ----------------------- +--R 3 2 +--R 2a x +--R Type: Expression Integer +--E + +--S 31 +cc:=aa-bb +--R +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R 2atan(--------------) - asec(-) +--R a a +--R (3) ------------------------------- +--R 3 +--R 2a +--R Type: Expression Integer +--E + +--S 32 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 33 +dd:=atanrule cc +--R +--R +-------+ +--R | 2 2 +--R - \|x - a + x + %i a x +--R - %i log(-----------------------) - asec(-) +--R +-------+ a +--R | 2 2 +--R \|x - a - x + %i a +--R (5) ------------------------------------------- +--R 3 +--R 2a +--R Type: Expression Complex Integer +--E + +--S 34 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (6) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 35 +ee:=asecrule dd +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R - 2%i log(------------------) - 2%i log(-----------------------) - %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R (7) ---------------------------------------------------------------------- +--R 3 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 36 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 2%i log(\|x - a - x + %i a) - 2%i log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R - 2%i log(x |------- + %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R | 2 +--R \| x +--R / +--R 3 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 37 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 2%i log(\|x - a + %i a) + 2%i log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R - 2%i log(\|x - a - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R / +--R 3 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 38 14:215 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R %pi +--R (10) - --- +--R 3 +--R 4a +--R Type: Expression Complex Integer +--E + +@ + +\section{\cite{1}:14.216~~~~~$\displaystyle\int{\sqrt{x^2-a^2}}~dx$} +$$\int{\sqrt{x^2-a^2}}= +\frac{x\sqrt{x^2-a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 39 +aa:=integrate(sqrt(x^2-a^2),x) +--R +--R +--R (1) +--R +-------+ +-------+ +--R 2 | 2 2 2 2 4 | 2 2 +--R (2a x\|x - a - 2a x + a )log(\|x - a - x) +--R + +--R +-------+ +--R 3 2 | 2 2 4 2 2 +--R (- 2x + a x)\|x - a + 2x - 2a x +--R / +--R +-------+ +--R | 2 2 2 2 +--R 4x\|x - a - 4x + 2a +--R Type: Union(Expression Integer,...) +--E + +--S 40 +bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 2 | 2 2 | 2 2 +--R - a log(\|x - a + x) + x\|x - a +--R (2) ------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 41 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 +--R a log(\|x - a + x) + a log(\|x - a - x) +--R (3) --------------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 42 14:216 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 2 2 +--R a log(- a ) +--R (4) ----------- +--R 2 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.217~~~~~$\displaystyle\int{x\sqrt{x^2-a^2}}~dx$} +$$\int{x\sqrt{x^2-a^2}}= +\frac{(x^2-a^2)^{3/2}}{3} +$$ +<<*>>= +)clear all + +--S 43 +aa:=integrate(x*sqrt(x^2-a^2),x) +--R +--R +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (- 4x + 7a x - 3a x)\|x - a + 4x - 9a x + 6a x - a +--R (1) ----------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 3 2 +--R (12x - 3a )\|x - a - 12x + 9a x +--R Type: Union(Expression Integer,...) +--E + +--S 44 +bb:=(x^2-a^2)^(3/2)/3 +--R +--R +-------+ +--R 2 2 | 2 2 +--R (x - a )\|x - a +--R (2) ------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 45 14:217 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.218~~~~~$\displaystyle +\int{x^2\sqrt{x^2-a^2}}~dx$} +$$\int{x^2\sqrt{x^2-a^2}}= +\frac{x(x^2-a^2)^{3/2}}{4}+\frac{a^2x\sqrt{x^2-a^2}}{8}- +\frac{a^4}{8}\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 46 +aa:=integrate(x^2*sqrt(x^2-a^2),x) +--R +--R +--R (1) +--R +-------+ +-------+ +--R 4 3 6 | 2 2 4 4 6 2 8 | 2 2 +--R ((8a x - 4a x)\|x - a - 8a x + 8a x - a )log(\|x - a - x) +--R + +--R +-------+ +--R 7 2 5 4 3 6 | 2 2 8 2 6 4 4 6 2 +--R (- 16x + 24a x - 10a x + a x)\|x - a + 16x - 32a x + 20a x - 4a x +--R / +--R +-------+ +--R 3 2 | 2 2 4 2 2 4 +--R (64x - 32a x)\|x - a - 64x + 64a x - 8a +--R Type: Union(Expression Integer,...) +--E + +--S 47 +bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 4 | 2 2 3 2 | 2 2 +--R - a log(\|x - a + x) + (2x - a x)\|x - a +--R (2) ----------------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 48 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 4 | 2 2 4 | 2 2 +--R a log(\|x - a + x) + a log(\|x - a - x) +--R (3) --------------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 49 14:218 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 4 2 +--R a log(- a ) +--R (4) ----------- +--R 8 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.219~~~~~$\displaystyle +\int{x^3\sqrt{x^2-a^2}}~dx$} +$$\int{x^3\sqrt{x^2-a^2}}= +\frac{(x^2-a^2)^{5/2}}{5}+\frac{a^2(x^2-a^2)^{3/2}}{3} +$$ +<<*>>= +)clear all + +--S 50 +aa:=integrate(x^3*sqrt(x^2-a^2),x) +--R +--R +--R (1) +--R +-------+ +--R 9 2 7 4 5 6 3 8 | 2 2 10 2 8 +--R (- 48x + 76a x - 3a x - 35a x + 10a x)\|x - a + 48x - 100a x +--R + +--R 4 6 6 4 8 2 10 +--R 35a x + 40a x - 25a x + 2a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 5 2 3 4 +--R (240x - 180a x + 15a )\|x - a - 240x + 300a x - 75a x +--R Type: Union(Expression Integer,...) +--E + +--S 51 +bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3 +--R +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3x - a x - 2a )\|x - a +--R (2) ---------------------------- +--R 15 +--R Type: Expression Integer +--E + +--S 52 14:219 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.220~~~~~$\displaystyle +\int{\frac{\sqrt{x^2-a^2}}{x}}~dx$} +$$\int{\frac{\sqrt{x^2-a^2}}{x}}= +\sqrt{x^2-a^2}-a\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 53 +aa:=integrate(sqrt(x^2-a^2)/x,x) +--R +--R +--R +-------+ +--R +-------+ | 2 2 +-------+ +--R | 2 2 \|x - a - x | 2 2 2 2 +--R (- 2a\|x - a + 2a x)atan(--------------) - x\|x - a + x - a +--R a +--R (1) ------------------------------------------------------------------- +--R +-------+ +--R | 2 2 +--R \|x - a - x +--R Type: Union(Expression Integer,...) +--E + +--S 54 +bb:=sqrt(x^2-a^2)-a*asec(x/a) +--R +--R +-------+ +--R | 2 2 x +--R (2) \|x - a - a asec(-) +--R a +--R Type: Expression Integer +--E + +--S 55 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R (3) - 2a atan(--------------) + a asec(-) +--R a a +--R Type: Expression Integer +--E + +--S 56 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 57 +dd:=atanrule cc +--R +--R +-------+ +--R | 2 2 +--R - \|x - a + x + %i a x +--R (5) %i a log(-----------------------) + a asec(-) +--R +-------+ a +--R | 2 2 +--R \|x - a - x + %i a +--R Type: Expression Complex Integer +--E + +--S 58 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (6) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 59 +ee:=asecrule dd +--R +--R (7) +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R 2%i a log(------------------) + 2%i a log(-----------------------) + a %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R -------------------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 60 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 2%i a log(\|x - a - x + %i a) + 2%i a log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R 2%i a log(x |------- + %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi +--R | 2 +--R \| x +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 61 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 2%i a log(\|x - a + %i a) - 2%i a log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R 2%i a log(\|x - a - x - %i a) - 2%i a log(x) + 2%i a log(- 1) + a %pi +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 62 14:220 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R a %pi +--R (10) ----- +--R 2 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.221~~~~~$\displaystyle +\int{\frac{\sqrt{x^2-a^2}}{x^2}}~dx$} +$$\int{\frac{\sqrt{x^2-a^2}}{x^2}}= +-\frac{\sqrt{x^2-a^2}}{x}+\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 63 +aa:=integrate(sqrt(x^2-a^2)/x^2,x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 2 | 2 2 2 +--R (- x\|x - a + x )log(\|x - a - x) + a +--R (1) -------------------------------------------- +--R +-------+ +--R | 2 2 2 +--R x\|x - a - x +--R Type: Union(Expression Integer,...) +--E + +--S 64 +bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R x log(\|x - a + x) - \|x - a +--R (2) ---------------------------------- +--R x +--R Type: Expression Integer +--E + +--S 65 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R (3) - log(\|x - a + x) - log(\|x - a - x) - 1 +--R Type: Expression Integer +--E + +--S 66 14:221 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 2 +--R (4) - log(- a ) - 1 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.222~~~~~$\displaystyle +\int{\frac{\sqrt{x^2-a^2}}{x^3}}~dx$} +$$\int{\frac{\sqrt{x^2-a^2}}{x^3}}= +-\frac{\sqrt{x^2-a^2}}{2x^2}+\frac{1}{2a} +\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 67 +aa:=integrate(sqrt(x^2-a^2)/x^3,x) +--R +--R +--R (1) +--R +-------+ +--R +-------+ | 2 2 +--R 3 | 2 2 4 2 2 \|x - a - x +--R (4x \|x - a - 4x + 2a x )atan(--------------) +--R a +--R + +--R +-------+ +--R 2 3 | 2 2 3 3 +--R (2a x - a )\|x - a - 2a x + 2a x +--R / +--R +-------+ +--R 3 | 2 2 4 3 2 +--R 4a x \|x - a - 4a x + 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 68 +bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a) +--R +--R +-------+ +--R | 2 2 2 x +--R - a\|x - a + x asec(-) +--R a +--R (2) ------------------------- +--R 2 +--R 2a x +--R Type: Expression Integer +--E + +--S 69 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R 2atan(--------------) - asec(-) +--R a a +--R (3) ------------------------------- +--R 2a +--R Type: Expression Integer +--E + +--S 70 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (4) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 71 +dd:=asecrule cc +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x \|x - a - x +--R - 2%i log(------------------) + 4atan(--------------) - %pi +--R x a +--R (5) ----------------------------------------------------------- +--R 4a +--R Type: Expression Complex Integer +--E + +--S 72 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 73 +ee:=atanrule dd +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R - 2%i log(------------------) - 2%i log(-----------------------) - %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R (7) ---------------------------------------------------------------------- +--R 4a +--R Type: Expression Complex Integer +--E + +--S 74 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 2%i log(\|x - a - x + %i a) - 2%i log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R - 2%i log(x |------- + %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R | 2 +--R \| x +--R / +--R 4a +--R Type: Expression Complex Integer +--E + +--S 75 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 2%i log(\|x - a + %i a) + 2%i log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R - 2%i log(\|x - a - x - %i a) + 2%i log(x) - 2%i log(- 1) - %pi +--R / +--R 4a +--R Type: Expression Complex Integer +--E + +--S 76 14:222 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R %pi +--R (10) - --- +--R 4a +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.223~~~~~$\displaystyle\int{\frac{dx}{(x^2-a^2)^{3/2}}}$} +$$\int{\frac{1}{(x^2-a^2)^{3/2}}}= +-\frac{x}{a^2\sqrt{x^2-a^2}} +$$ +<<*>>= +)clear all + +--S 77 +aa:=integrate(1/(x^2-a^2)^(3/2),x) +--R +--R +--R 1 +--R (1) - --------------------- +--R +-------+ +--R | 2 2 2 2 +--R x\|x - a - x + a +--R Type: Union(Expression Integer,...) +--E + +--S 78 +bb:=-x/(a^2*sqrt(x^2-a^2)) +--R +--R x +--R (2) - ------------ +--R +-------+ +--R 2 | 2 2 +--R a \|x - a +--R Type: Expression Integer +--E + +--S 79 14:223 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 1 +--R (3) - -- +--R 2 +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.224~~~~~$\displaystyle +\int{\frac{x~dx}{(x^2-a^2)^{3/2}}}$} +$$\int{\frac{x}{(x^2-a^2)^{3/2}}}= +\frac{-1}{\sqrt{x^2-a^2}} +$$ +<<*>>= +)clear all + +--S 80 +aa:=integrate(x/(x^2-a^2)^(3/2),x) +--R +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x +--R (1) --------------------- +--R +-------+ +--R | 2 2 2 2 +--R x\|x - a - x + a +--R Type: Union(Expression Integer,...) +--E + +--S 81 +bb:=-1/sqrt(x^2-a^2) +--R +--R 1 +--R (2) - ---------- +--R +-------+ +--R | 2 2 +--R \|x - a +--R Type: Expression Integer +--E + +--S 82 14:224 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.225~~~~~$\displaystyle +\int{\frac{x^2dx}{(x^2-a^2)^{3/2}}}$} +$$\int{\frac{x^2}{(x^2-a^2)^{3/2}}}= +\frac{-x}{\sqrt{x^2-a^2}}+\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 83 +aa:=integrate(x^2/(x^2-a^2)^(3/2),x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 2 2 | 2 2 2 +--R (- x\|x - a + x - a )log(\|x - a - x) - a +--R (1) ------------------------------------------------- +--R +-------+ +--R | 2 2 2 2 +--R x\|x - a - x + a +--R Type: Union(Expression Integer,...) +--E + +--S 84 +bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R \|x - a log(\|x - a + x) - x +--R (2) --------------------------------- +--R +-------+ +--R | 2 2 +--R \|x - a +--R Type: Expression Integer +--E + +--S 85 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R (3) - log(\|x - a + x) - log(\|x - a - x) - 1 +--R Type: Expression Integer +--E + +--S 86 14:225 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 2 +--R (4) - log(- a ) - 1 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.226~~~~~$\displaystyle +\int{\frac{x^3dx}{(x^2-a^2)^{3/2}}}$} +$$\int{\frac{x^3}{(x^2-a^2)^{3/2}}}= +\sqrt{x^2-a^2}-\frac{a^2}{\sqrt{x^2-a^2}} +$$ +<<*>>= +)clear all + +--S 87 +aa:=integrate(x^3/(x^2-a^2)^(3/2),x) +--R +--R +--R +-------+ +--R 3 2 | 2 2 4 2 2 4 +--R (- 2x + 4a x)\|x - a + 2x - 5a x + 2a +--R (1) -------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 3 2 +--R (2x - a )\|x - a - 2x + 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 88 +bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2) +--R +--R 2 2 +--R x - 2a +--R (2) ---------- +--R +-------+ +--R | 2 2 +--R \|x - a +--R Type: Expression Integer +--E + +--S 89 14:226 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.227~~~~~$\displaystyle +\int{\frac{dx}{x(x^2-a^2)^{3/2}}}$} +$$\int{\frac{1}{x(x^2-a^2)^{3/2}}}= +\frac{-1}{a^2\sqrt{x^2-a^2}}- +\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 90 +aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x) +--R +--R +--R +-------+ +--R +-------+ | 2 2 +-------+ +--R | 2 2 2 2 \|x - a - x | 2 2 +--R (- 2x\|x - a + 2x - 2a )atan(--------------) + a\|x - a - a x +--R a +--R (1) -------------------------------------------------------------------- +--R +-------+ +--R 3 | 2 2 3 2 5 +--R a x\|x - a - a x + a +--R Type: Union(Expression Integer,...) +--E + +--S 91 +bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a) +--R +--R +-------+ +--R x | 2 2 +--R - asec(-)\|x - a - a +--R a +--R (2) ----------------------- +--R +-------+ +--R 3 | 2 2 +--R a \|x - a +--R Type: Expression Integer +--E + +--S 92 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R - 2atan(--------------) + asec(-) +--R a a +--R (3) --------------------------------- +--R 3 +--R a +--R Type: Expression Integer +--E + +--S 93 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 94 +dd:=atanrule cc +--R +--R +-------+ +--R | 2 2 +--R - \|x - a + x + %i a x +--R %i log(-----------------------) + asec(-) +--R +-------+ a +--R | 2 2 +--R \|x - a - x + %i a +--R (5) ----------------------------------------- +--R 3 +--R a +--R Type: Expression Complex Integer +--E + +--S 95 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (6) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 96 +ee:=asecrule dd +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R 2%i log(------------------) + 2%i log(-----------------------) + %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R (7) -------------------------------------------------------------------- +--R 3 +--R 2a +--R Type: Expression Complex Integer +--E + +--S 97 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 2%i log(\|x - a - x + %i a) + 2%i log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R 2%i log(x |------- + %i a) - 2%i log(x) + 2%i log(- 1) + %pi +--R | 2 +--R \| x +--R / +--R 3 +--R 2a +--R Type: Expression Complex Integer +--E + +--S 98 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 2%i log(\|x - a + %i a) - 2%i log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R 2%i log(\|x - a - x - %i a) - 2%i log(x) + 2%i log(- 1) + %pi +--R / +--R 3 +--R 2a +--R Type: Expression Complex Integer +--E + +--S 99 14:227 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R %pi +--R (10) --- +--R 3 +--R 2a +--R Type: Expression Complex Integer +--E + +@ + +\section{\cite{1}:14.228~~~~~$\displaystyle +\int{\frac{dx}{x^2(x^2-a^2)^{3/2}}}$} +$$\int{\frac{1}{x^2(x^2-a^2)^{3/2}}}= +-\frac{\sqrt{x^2-a^2}}{a^4x}-\frac{x}{a^4\sqrt{x^2-a^2}} +$$ +<<*>>= +)clear all + +--S 100 +aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x) +--R +--R +--R 1 +--R (1) - ----------------------------------- +--R +-------+ +--R 3 2 | 2 2 4 2 2 +--R (2x - a x)\|x - a - 2x + 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 101 +bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2)) +--R +--R 2 2 +--R - 2x + a +--R (2) ------------- +--R +-------+ +--R 4 | 2 2 +--R a x\|x - a +--R Type: Expression Integer +--E + +--S 102 14:228 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 2 +--R (3) - -- +--R 4 +--R a +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.229~~~~~$\displaystyle +\int{\frac{dx}{x^3(x^2-a^2)^{3/2}}}$} +$$\int{\frac{1}{x^3(x^2-a^2)^{3/2}}}= +\frac{1}{2a^2x^2\sqrt{x^2-a^2}}- +\frac{3}{2a^4\sqrt{x^2-a^2}}- +\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 103 +aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x) +--R +--R +--R (1) +--R +-------+ +--R +-------+ | 2 2 +--R 5 2 3 | 2 2 6 2 4 4 2 \|x - a - x +--R ((- 24x + 18a x )\|x - a + 24x - 30a x + 6a x )atan(--------------) +--R a +--R + +--R +-------+ +--R 4 3 2 5 | 2 2 5 3 3 5 +--R (12a x - 7a x + a )\|x - a - 12a x + 13a x - 3a x +--R / +--R +-------+ +--R 5 5 7 3 | 2 2 5 6 7 4 9 2 +--R (8a x - 6a x )\|x - a - 8a x + 10a x - 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 104 +bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a) +--R +--R +-------+ +--R 2 x | 2 2 2 3 +--R - 3x asec(-)\|x - a - 3a x + a +--R a +--R (2) ----------------------------------- +--R +-------+ +--R 5 2 | 2 2 +--R 2a x \|x - a +--R Type: Expression Integer +--E + +--S 105 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R - 6atan(--------------) + 3asec(-) +--R a a +--R (3) ---------------------------------- +--R 5 +--R 2a +--R Type: Expression Integer +--E + +--S 106 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 107 +dd:=atanrule cc +--R +--R +-------+ +--R | 2 2 +--R - \|x - a + x + %i a x +--R 3%i log(-----------------------) + 3asec(-) +--R +-------+ a +--R | 2 2 +--R \|x - a - x + %i a +--R (5) ------------------------------------------- +--R 5 +--R 2a +--R Type: Expression Complex Integer +--E + +--S 108 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (6) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 109 +ee:=asecrule dd +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R 6%i log(------------------) + 6%i log(-----------------------) + 3%pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R (7) --------------------------------------------------------------------- +--R 5 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 110 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 6%i log(\|x - a - x + %i a) + 6%i log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R 6%i log(x |------- + %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi +--R | 2 +--R \| x +--R / +--R 5 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 111 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 6%i log(\|x - a + %i a) - 6%i log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R 6%i log(\|x - a - x - %i a) - 6%i log(x) + 6%i log(- 1) + 3%pi +--R / +--R 5 +--R 4a +--R Type: Expression Complex Integer +--E + +--S 112 14:229 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R 3%pi +--R (10) ---- +--R 5 +--R 4a +--R Type: Expression Complex Integer +--E +@ +\section{\cite{1}:14.230~~~~~$\displaystyle\int{(x^2-a^2)^{3/2}}~dx$} +$$\int{(x^2-a^2)^{3/2}}= +\frac{x(x^2-a^2)^{3/2}}{4}-\frac{3a^2x\sqrt{x^2-a^2}}{8}+ +\frac{3}{8}a^4\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 113 +aa:=integrate((x^2-a^2)^(3/2),x) +--R +--R +--R (1) +--R +-------+ +-------+ +--R 4 3 6 | 2 2 4 4 6 2 8 | 2 2 +--R ((- 24a x + 12a x)\|x - a + 24a x - 24a x + 3a )log(\|x - a - x) +--R + +--R +-------+ +--R 7 2 5 4 3 6 | 2 2 8 2 6 4 4 +--R (- 16x + 56a x - 42a x + 5a x)\|x - a + 16x - 64a x + 68a x +--R + +--R 6 2 +--R - 20a x +--R / +--R +-------+ +--R 3 2 | 2 2 4 2 2 4 +--R (64x - 32a x)\|x - a - 64x + 64a x - 8a +--R Type: Union(Expression Integer,...) +--E + +--S 114 +bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 4 | 2 2 3 2 | 2 2 +--R 3a log(\|x - a + x) + (2x - 5a x)\|x - a +--R (2) ----------------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 115 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 4 | 2 2 4 | 2 2 +--R - 3a log(\|x - a + x) - 3a log(\|x - a - x) +--R (3) ------------------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 116 14:230 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 4 2 +--R 3a log(- a ) +--R (4) - ------------ +--R 8 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.231~~~~~$\displaystyle\int{x(x^2-a^2)^{3/2}}~dx$} +$$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$ +<<*>>= +)clear all + +--S 117 +aa:=integrate(x*(x^2-a^2)^(3/2),x) +--R +--R +--R (1) +--R +-------+ +--R 9 2 7 4 5 6 3 8 | 2 2 10 2 8 +--R (- 16x + 52a x - 61a x + 30a x - 5a x)\|x - a + 16x - 60a x +--R + +--R 4 6 6 4 8 2 10 +--R 85a x - 55a x + 15a x - a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 5 2 3 4 +--R (80x - 60a x + 5a )\|x - a - 80x + 100a x - 25a x +--R Type: Union(Expression Integer,...) +--E + +--S 118 +bb:=(x^2-a^2)^(5/2)/5 +--R +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (x - 2a x + a )\|x - a +--R (2) --------------------------- +--R 5 +--R Type: Expression Integer +--E + +--S 119 14:231 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.232~~~~~$\displaystyle\int{x^2(x^2-a^2)^{3/2}}~dx$} +$$\int{x^2(x^2-a^2)^{3/2}}= +\frac{x(x^2-a^2)^{5/2}}{6}+\frac{a^2x(x^2-a^2)^{3/2}}{24}- +\frac{a^4x\sqrt{x^2-a^2}}{16}+ +\frac{a^6}{16}\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 120 +aa:=integrate(x^2*(x^2-a^2)^(3/2),x) +--R +--R +--R (1) +--R +-------+ +--R 6 5 8 3 10 | 2 2 6 6 8 4 10 2 +--R (- 96a x + 96a x - 18a x)\|x - a + 96a x - 144a x + 54a x +--R + +--R 12 +--R - 3a +--R * +--R +-------+ +--R | 2 2 +--R log(\|x - a - x) +--R + +--R +-------+ +--R 11 2 9 4 7 6 5 8 3 10 | 2 2 +--R (- 256x + 832a x - 912a x + 404a x - 68a x + 3a x)\|x - a +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R 256x - 960a x + 1296a x - 772a x + 198a x - 18a x +--R / +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (1536x - 1536a x + 288a x)\|x - a - 1536x + 2304a x - 864a x + 48a +--R Type: Union(Expression Integer,...) +--E + +--S 121 +bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 6 | 2 2 5 2 3 4 | 2 2 +--R 3a log(\|x - a + x) + (8x - 14a x + 3a x)\|x - a +--R (2) -------------------------------------------------------- +--R 48 +--R Type: Expression Integer +--E + +--S 122 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 6 | 2 2 6 | 2 2 +--R - a log(\|x - a + x) - a log(\|x - a - x) +--R (3) ----------------------------------------------- +--R 16 +--R Type: Expression Integer +--E + +--S 123 14:232 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 6 2 +--R a log(- a ) +--R (4) - ----------- +--R 16 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.233~~~~~$\displaystyle\int{x^3(x^2-a^2)^{3/2}}~dx$} +$$\int{x^3(x^2-a^2)^{3/2}}= +\frac{(x^2-a^2)^{7/2}}{7}+\frac{a^2(x^2-a^2)^{5/2}}{5} +$$ +<<*>>= +)clear all + +--S 124 +aa:=integrate(x^3*(x^2-a^2)^(3/2),x) +--R +--R +--R (1) +--R 13 2 11 4 9 6 7 8 5 10 3 +--R - 320x + 1072a x - 1240a x + 467a x + 112a x - 105a x +--R + +--R 12 +--R 14a x +--R * +--R +-------+ +--R | 2 2 +--R \|x - a +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 12 2 +--R 320x - 1232a x + 1736a x - 973a x + 21a x + 175a x - 49a x +--R + +--R 14 +--R 2a +--R / +--R +-------+ +--R 6 2 4 4 2 6 | 2 2 7 2 5 +--R (2240x - 2800a x + 840a x - 35a )\|x - a - 2240x + 3920a x +--R + +--R 4 3 6 +--R - 1960a x + 245a x +--R Type: Union(Expression Integer,...) +--E + +--S 125 +bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5 +--R +--R +-------+ +--R 6 2 4 4 2 6 | 2 2 +--R (5x - 8a x + a x + 2a )\|x - a +--R (2) ------------------------------------ +--R 35 +--R Type: Expression Integer +--E + +--S 126 14:233 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.234~~~~~$\displaystyle +\int{\frac{(x^2-a^2)^{3/2}}{x}}~dx$} +$$\int{\frac{(x^2-a^2)^{3/2}}{x}}= +\frac{(x^2-a^2)^{3/2}}{3}-a^2\sqrt{x^2-a^2}+ +a^3\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 127 +aa:=integrate((x^2-a^2)^(3/2)/x,x) +--R +--R +--R (1) +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 5 | 2 2 3 3 5 \|x - a - x +--R ((24a x - 6a )\|x - a - 24a x + 18a x)atan(--------------) +--R a +--R + +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (- 4x + 19a x - 12a x)\|x - a + 4x - 21a x + 21a x - 4a +--R / +--R +-------+ +--R 2 2 | 2 2 3 2 +--R (12x - 3a )\|x - a - 12x + 9a x +--R Type: Union(Expression Integer,...) +--E + +--S 128 +bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a) +--R +--R +-------+ +--R 2 2 | 2 2 3 x +--R (x - 4a )\|x - a + 3a asec(-) +--R a +--R (2) --------------------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 129 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R 3 \|x - a - x 3 x +--R (3) 2a atan(--------------) - a asec(-) +--R a a +--R Type: Expression Integer +--E + +--S 130 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (4) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 131 +dd:=asecrule cc +--R +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R 3 \| x 3 \|x - a - x 3 +--R - 2%i a log(------------------) + 4a atan(--------------) - a %pi +--R x a +--R (5) ----------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 132 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 133 +ee:=atanrule dd +--R +--R (7) +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R 3 \| x 3 - \|x - a + x + %i a 3 +--R - 2%i a log(------------------) - 2%i a log(-----------------------) - a %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R ---------------------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 134 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R 3 | 2 2 3 | 2 2 +--R 2%i a log(\|x - a - x + %i a) - 2%i a log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R 3 |x - a 3 3 3 +--R - 2%i a log(x |------- + %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi +--R | 2 +--R \| x +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 135 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 3 | 2 2 3 | 2 2 +--R - 2%i a log(\|x - a + %i a) + 2%i a log(\|x - a - x + %i a) +--R + +--R +-------+ +--R 3 | 2 2 3 3 3 +--R - 2%i a log(\|x - a - x - %i a) + 2%i a log(x) - 2%i a log(- 1) - a %pi +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 136 14:234 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R 3 +--R a %pi +--R (10) - ----- +--R 2 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.235~~~~~$\displaystyle +\int{\frac{(x^2-a^2)^{3/2}}{x^2}}~dx$} +$$\int{\frac{(x^2-a^2)^{3/2}}{x^2}}= +-\frac{(x^2-a^2)^{3/2}}{x}+\frac{3x\sqrt{x^2-a^2}}{2}- +\frac{3}{2}a^2\ln\left(x+\sqrt{x^2-a^2}\right) +$$ +<<*>>= +)clear all + +--S 137 +aa:=integrate((x^2-a^2)^{3/2}/x^2,x) +--R +--R +--R (1) +--R +-------+ +-------+ +--R 2 3 4 | 2 2 2 4 4 2 | 2 2 +--R ((12a x - 3a x)\|x - a - 12a x + 9a x )log(\|x - a - x) +--R + +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (- 4x + 3a x + 4a x)\|x - a + 4x - 5a x - 3a x + 2a +--R / +--R +-------+ +--R 3 2 | 2 2 4 2 2 +--R (8x - 2a x)\|x - a - 8x + 6a x +--R Type: Union(Expression Integer,...) +--E + +--S 138 +bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2)) +--R +--R +-------+ +-------+ +--R 2 | 2 2 2 2 | 2 2 +--R - 3a x log(\|x - a + x) + (x + 2a )\|x - a +--R (2) ------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E + +--S 139 +cc:=aa-bb +--R +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 2 +--R 3a log(\|x - a + x) + 3a log(\|x - a - x) + 2a +--R (3) ----------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 140 14:235 Schaums and Axiom differ by a constant +dd:=complexNormalize cc +--R +--R 2 2 2 +--R 3a log(- a ) + 2a +--R (4) ------------------ +--R 2 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.236~~~~~$\displaystyle +\int{\frac{(x^2-a^2)^{3/2}}{x^3}}~dx$} +$$\int{\frac{(x^2-a^2)^{3/2}}{x^3}}= +-\frac{(x^2-a^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{x^2-a^2}- +\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 141 +aa:=integrate((x^2-a^2)^(3/2)/x^3,x) +--R +--R +--R (1) +--R +-------+ +--R +-------+ | 2 2 +--R 4 3 2 | 2 2 5 3 3 \|x - a - x +--R ((- 24a x + 6a x )\|x - a + 24a x - 18a x )atan(--------------) +--R a +--R + +--R +-------+ +--R 5 2 3 4 | 2 2 6 2 4 4 2 6 +--R (- 8x + 2a x + 3a x)\|x - a + 8x - 6a x - 3a x + a +--R / +--R +-------+ +--R 4 2 2 | 2 2 5 2 3 +--R (8x - 2a x )\|x - a - 8x + 6a x +--R Type: Union(Expression Integer,...) +--E + +--S 142 +bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a) +--R +--R +-------+ +--R 2 2 | 2 2 2 x +--R (2x + a )\|x - a - 3a x asec(-) +--R a +--R (2) ----------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E + +--S 143 +cc:=aa-bb +--R +--R +-------+ +--R | 2 2 +--R \|x - a - x x +--R - 6a atan(--------------) + 3a asec(-) +--R a a +--R (3) -------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 144 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 145 +dd:=atanrule cc +--R +--R +-------+ +--R | 2 2 +--R - \|x - a + x + %i a x +--R 3%i a log(-----------------------) + 3a asec(-) +--R +-------+ a +--R | 2 2 +--R \|x - a - x + %i a +--R (5) ----------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 146 +asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) +--R +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ + %i +--R | 2 +--R \| x +--R 2%i log(---------------) + %pi +--R x +--R (6) asec(x) == ------------------------------ +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 147 +ee:=asecrule dd +--R +--R (7) +--R +-------+ +--R | 2 2 +--R |x - a +--R x |------- + %i a +-------+ +--R | 2 | 2 2 +--R \| x - \|x - a + x + %i a +--R 6%i a log(------------------) + 6%i a log(-----------------------) + 3a %pi +--R x +-------+ +--R | 2 2 +--R \|x - a - x + %i a +--R --------------------------------------------------------------------------- +--R 4 +--R Type: Expression Complex Integer +--E + +--S 148 +ff:=expandLog ee +--R +--R (8) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R - 6%i a log(\|x - a - x + %i a) + 6%i a log(\|x - a - x - %i a) +--R + +--R +-------+ +--R | 2 2 +--R |x - a +--R 6%i a log(x |------- + %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi +--R | 2 +--R \| x +--R / +--R 4 +--R Type: Expression Complex Integer +--E + +--S 149 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R 6%i a log(\|x - a + %i a) - 6%i a log(\|x - a - x + %i a) +--R + +--R +-------+ +--R | 2 2 +--R 6%i a log(\|x - a - x - %i a) - 6%i a log(x) + 6%i a log(- 1) + 3a %pi +--R / +--R 4 +--R Type: Expression Complex Integer +--E + +--S 150 14:236 Schaums and Axiom differ by a constant +hh:=complexNormalize gg +--R +--R 3a %pi +--R (10) ------ +--R 4 +--R Type: Expression Complex Integer +--E + +)spool +)lisp (bye) +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} Spiegel, Murray R. +{\sl Mathematical Handbook of Formulas and Tables}\\ +Schaum's Outline Series McGraw-Hill 1968 pp68-69 +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/schaum10.input.pdf b/src/axiom-website/CATS/schaum10.input.pdf new file mode 100644 index 0000000..8271532 --- /dev/null +++ b/src/axiom-website/CATS/schaum10.input.pdf @@ -0,0 +1,3941 @@ +%PDF-1.2 +7 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +10 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F1 +/FontDescriptor 9 0 R +/BaseFont/XGVGVP+CMR17 +/FirstChar 33 +/LastChar 196 +/Widths[249.6 458.6 772.1 458.6 772.1 719.8 249.6 354.1 354.1 458.6 719.8 249.6 301.9 +249.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 249.6 249.6 +249.6 719.8 432.5 432.5 719.8 693.3 654.3 667.6 706.6 628.2 602.1 726.3 693.3 327.6 +471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 +693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 +458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 +510.9 484.7 667.6 484.7 484.7 406.4 458.6 917.2 458.6 458.6 458.6 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 576 772.1 719.8 641.1 615.3 693.3 +667.6 719.8 667.6 719.8 0 0 667.6 525.4 499.3 499.3 748.9 748.9 249.6 275.8 458.6 +458.6 458.6 458.6 458.6 693.3 406.4 458.6 667.6 719.8 458.6 837.2 941.7 719.8 249.6 +458.6] +>> +endobj +13 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F2 +/FontDescriptor 12 0 R +/BaseFont/EEFPIB+CMR12 +/FirstChar 33 +/LastChar 196 +/Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 +462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 +734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 +272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 +544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 +489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 +761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 +299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 +761.6 272 489.6] +>> +endobj +16 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F3 +/FontDescriptor 15 0 R +/BaseFont/TAMYWG+CMR10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +18 0 obj +<< +/Filter[/FlateDecode] +/Length 180 +>> +stream +x%=@ wE#1j&o3Ĩ^86> +endobj +6 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 20 0 R +>> +endobj +25 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F4 +/FontDescriptor 24 0 R +/BaseFont/IJTCAF+CMBX12 +/FirstChar 33 +/LastChar 196 +/Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 +562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 +875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 +675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 +687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 +343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 +593.7 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 +656.2 625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 +812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] +>> +endobj +28 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F5 +/FontDescriptor 27 0 R +/BaseFont/EBENTK+CMBX10 +/FirstChar 33 +/LastChar 196 +/Widths[350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 +575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 +869.4 818.1 830.6 881.9 755.6 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 +863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 +319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 +319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 +511.1 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 691.7 958.3 894.4 805.6 766.7 900 830.6 894.4 830.6 894.4 0 0 830.6 670.8 +638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 +575 1041.7 1169.4 894.4 319.4 575] +>> +endobj +31 0 obj +<< +/Type/Font +/Subtype/Type1 +/Name/F6 +/FontDescriptor 30 0 R +/BaseFont/CSSXYP+CMEX10 +/FirstChar 33 +/LastChar 196 +/Widths[791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 +1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 +888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 +1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 +833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 +1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 +1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 458.3 458.3 416.7 416.7 +472.2 472.2 472.2 472.2 583.3 583.3 0 0 472.2 472.2 333.3 555.6 577.8 577.8 597.2 +597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 +791.7 777.8] +>> +endobj +32 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/omega/epsilon/theta1/pi1/rho1/sigma1/phi1/arrowlefttophalf/arrowleftbothalf/arrowrighttophalf/arrowrightbothalf/arrowhookleft/arrowhookright/triangleright/triangleleft/zerooldstyle/oneoldstyle/twooldstyle/threeoldstyle/fouroldstyle/fiveoldstyle/sixoldstyle/sevenoldstyle/eightoldstyle/nineoldstyle/period/comma/less/slash/greater/star/partialdiff/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/flat/natural/sharp/slurbelow/slurabove/lscript/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/dotlessi/dotlessj/weierstrass/vector/tie/psi +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/tie] +>> +endobj +35 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F7 +/FontDescriptor 34 0 R +/BaseFont/PFTUWD+CMMI10 +/FirstChar 33 +/LastChar 196 +/Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 +750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 +762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 +388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 +298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 +465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 +639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 +570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] +>> +endobj +36 0 obj +<< +/Type/Encoding +/Differences[0/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/arrowright/arrowup/arrowdown/arrowboth/arrownortheast/arrowsoutheast/similarequal/arrowdblleft/arrowdblright/arrowdblup/arrowdbldown/arrowdblboth/arrownorthwest/arrowsouthwest/proportional/prime/infinity/element/owner/triangle/triangleinv/negationslash/mapsto/universal/existential/logicalnot/emptyset/Rfractur/Ifractur/latticetop/perpendicular/aleph/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/union/intersection/unionmulti/logicaland/logicalor/turnstileleft/turnstileright/floorleft/floorright/ceilingleft/ceilingright/braceleft/braceright/angbracketleft/angbracketright/bar/bardbl/arrowbothv/arrowdblbothv/backslash/wreathproduct/radical/coproduct/nabla/integral/unionsq/intersectionsq/subsetsqequal/supersetsqequal/section/dagger/daggerdbl/paragraph/club/diamond/heart/spade/arrowleft +161/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus +173/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/spade] +>> +endobj +39 0 obj +<< +/Encoding 36 0 R +/Type/Font +/Subtype/Type1 +/Name/F8 +/FontDescriptor 38 0 R +/BaseFont/XQGLQC+CMSY10 +/FirstChar 33 +/LastChar 196 +/Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 +275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 +611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 +820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 +666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 +500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 +444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 +777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 +777.8 777.8 1000 1000 777.8 777.8 1000 777.8] +>> +endobj +42 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F9 +/FontDescriptor 41 0 R +/BaseFont/TAMMEO+CMR7 +/FirstChar 33 +/LastChar 196 +/Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 +323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 +323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 +874 706.4 1027.8 843.3 877 767.9 877 829.4 631 815.5 843.3 843.3 1150.8 843.3 843.3 +692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 +323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 +600.2 600.2 507.9 569.4 1138.9 569.4 569.4 569.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 +877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 +843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] +>> +endobj +45 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F10 +/FontDescriptor 44 0 R +/BaseFont/RJRYYM+CMMI7 +/FirstChar 33 +/LastChar 196 +/Widths[719.7 539.7 689.9 950 592.7 439.2 751.4 1138.9 1138.9 1138.9 1138.9 339.3 +339.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 339.3 +339.3 892.9 585.3 892.9 585.3 610.1 859.1 863.2 819.4 934.1 838.7 724.5 889.4 935.6 +506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 +1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 +594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 +530.4 539.2 431.6 675.4 571.4 826.4 647.8 579.4 545.8 398.6 442 730.1 585.3 339.3 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 693.8 954.4 868.9 +797.6 844.5 935.6 886.3 677.6 769.8 716.9 0 0 880 742.7 647.8 600.1 519.2 476.1 519.8 +588.6 544.1 422.8 668.8 677.6 694.6 572.8 519.8 668 592.7 662 526.8 632.9 686.9 713.8 +756 339.3] +>> +endobj +46 0 obj +<< +/Filter[/FlateDecode] +/Length 1122 +>> +stream +x՘K5 +wXU\x*̉$p!@T1?X{iYle1W__&-G@{VC9;YxCë׬N5 iYNCD~xLLvv jvyOE +t"s + jWD OϿloڔOtVGQHt<\#k[ ^r:zQa[,o\g~ __5nc}&DY, +6vWTF֨.jQ%/Bu9 6biƤ=iبFGOt5 =`zh{\|RdװO 61ٯjQ9;{;J%PnQ_>`i53;\koѪVٮZDNWgQ?k'> +endobj +22 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 47 0 R +>> +endobj +50 0 obj +<< +/Filter[/FlateDecode] +/Length 821 +>> +stream +x=o0 + yǏc.E]IAsId)˲% Ox䑺:!AJC'~w{go +[kAkpQfKFn[Q<>a+P(1i X#9vwa%Zx#~ KZ* n@6Bv&0 vɌ%`@Z陽{G7^AM;>|S6+Y3A_M\V^Ee}$D*, P5›%ǯ  ,kuu\XQo{> +ܕ11yc+nس C Q +3]ht] @ëhx497Koq'CCWLngN Y1(WYj^ +KQ.BBeCN]?OJljsih(@<).EN4MrN8 i}Inh9)sBWNΉq";NoNHIuI n@ ;f}k*kf +Rd+@歄N#Ae;,-Ji7rRZHgvfM!?Ec'4姫Z~/jtl=:1VK=qʼnLރ}ũ^NVKiJ٣k[6+ +1MDތ++5E2_p8bg2 ^!`\=8<'@(^dhd/2g8FİS 1Xm uxa& w +endstream +endobj +51 0 obj +<< +/F5 28 0 R +/F6 31 0 R +/F7 35 0 R +/F3 16 0 R +/F9 42 0 R +/F8 39 0 R +/F10 45 0 R +>> +endobj +49 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 51 0 R +>> +endobj +56 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F11 +/FontDescriptor 55 0 R +/BaseFont/IAEDAF+CMMI12 +/FirstChar 33 +/LastChar 196 +/Widths[609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 +761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.9 772.4 811.3 431.9 541.2 833 666.2 +947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 +380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 +334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 +699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 +652.8 598 0 0 757.6 622.8 552.8 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 +589.1 483.8 427.7 555.4 505 556.5 425.2 527.8 579.5 613.4 636.6 272] +>> +endobj +57 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +60 0 obj +<< +/Encoding 57 0 R +/Type/Font +/Subtype/Type1 +/Name/F12 +/FontDescriptor 59 0 R +/BaseFont/SPMOLI+CMTI10 +/FirstChar 33 +/LastChar 196 +/Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 +306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 +306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 +525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 +743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 +460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 +460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 +766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 +511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] +>> +endobj +61 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/dieresis/visiblespace +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/dieresis] +>> +endobj +64 0 obj +<< +/Encoding 61 0 R +/Type/Font +/Subtype/Type1 +/Name/F13 +/FontDescriptor 63 0 R +/BaseFont/RKAXVR+CMTT10 +/FirstChar 33 +/LastChar 196 +/Widths[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 525 525 525 525 525 525 525 525 525 0 0 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525] +>> +endobj +65 0 obj +<< +/Filter[/FlateDecode] +/Length 879 +>> +stream +xڭn:} +n +Hq9!)4=HiPlזQ_^%Y79 e!?wQG{$(aɀhsBSL)˓Ԩ%wiºP*g6..lBVn& ~ HPzB+iKSu񢃤 "҄d䣜^H?!9Fc.$k*A+ārgfKKAP0N,qrC&G;t260axtX(1j@D\(CVk`zG4ڠ ([1e/f0>jMB#J!5ޑvq~t&F;6tnŚg)fR&jX fH@DBd,r[(iN iNQT3IZz۲=uԻrKS7mXAzc%CW* hW ljW/j6uܼwoX;q ^GuxSە4.,WUu?嶬ru,-eV:.qT۲^)W˯H͡HǞ]y27OF hM&79IER?eӳGdzzU$7֔<[Kھӱn8.ĉ3-әK0B9;8#ά I1>CBX\NgegjYl\,3Jq.nRॊ4xIi_l+hyr/tljqm!򲇫'0ʁ ?/.g*τ鋖5OǦs<{&g +q 3h!~Y~ л +endstream +endobj +66 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +53 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 66 0 R +>> +endobj +69 0 obj +<< +/Filter[/FlateDecode] +/Length 239 +>> +stream +xmOo0 >!H;؁oHB/#L4N~~Y/.40gؙ͞\G`jP+0O %$0I8P|ntMޗNl9Yu]-+ЏSOއyHĵ#2y<Mw9҂!ķucmW>$$˘<=]~@*Cfn*qdz=ql/T5MR  Gy15p^e +endstream +endobj +70 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +68 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 70 0 R +>> +endobj +73 0 obj +<< +/Filter[/FlateDecode] +/Length 756 +>> +stream +xVn0+xpBR\ ТI(dM 8Nj +;\زP{3oƴ- \.dhFjHE.3S΅.Qu]Wϧ8pS8`Б-"8d."iaTvN3j V{"4_t yP~AI40A'Na "E*ڔ 8K$p, +۽,hMRH>$X@T +38jq4nZHc%5^}9Rppʹs-r w ܾQMaHd"pv2(hЖv;$w< =PJ`AѾɠ8Ό=P +Ls^rtEf?^tTAE]huXCZ[y_G,e:RqqDajQmr֪VP"nf˓㯨ƓiqeV GׂVע.!/E}hCR]0h|F/cx SiΜ:4r|3.U8UxbhGsn +u$i$} 5a ˦^>~,[O!8\~&3Cl6uիԯAZ'^rQ*ڪr +ٷwks9ab~Wߦx7q^>ܧb1OfL%_пrPueu Q785 +endstream +endobj +74 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +72 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 74 0 R +>> +endobj +77 0 obj +<< +/Filter[/FlateDecode] +/Length 1041 +>> +stream +xVKo6W(G+3|ȥhh]參]@I4Muzz1z.Ǚo .gq}]W mgլ +P`ya{Xd0:5Y@XO&d"{˽cc) :"R#H~ %s\C7߳1Nu$6B> $ + +|dr8 lO8ŝ?&q837&Ԩ`"E3A C*@Q鲽 D(<3`LrY*\("HLN C2z'dS魅GqbOPZ LLf?b%GNЇ> +endobj +76 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 78 0 R +>> +endobj +81 0 obj +<< +/Filter[/FlateDecode] +/Length 285 +>> +stream +xڥRMO0+z,v 5zrs= _% 믷lv{7y3o*`=M6[$%P+ +dX ܽ@=D%S25y JqxvT8L}yH0qun*bX qvE)-.ӏvtN̵n4,~;,yduH3ϣL}SOzhӦ,N>&R¬ ILFW{~{xT{MXxt~Of*Cο_o=}*BK8㘹 ,1N68 +endstream +endobj +82 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +80 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 82 0 R +>> +endobj +85 0 obj +<< +/Filter[/FlateDecode] +/Length 964 +>> +stream +xWKoFW쑊[-V/ cvTǀ@~|g_$E6@uY7ofI1k;ńfXj@}ÚP;OB޼mכ}5B?' loi UղNi8R/b +ZmxktJyeToU8VHPMUgMk/qh/#6nT2[Ӟ;h*A eo_N\g 9Źn!Q}JSIGv9 :)v#='aZvpz0Ά#8@5rES+0bkCEŻ٩6눣T49Rv:ky,Pg" +ϯ>=L?7zM+pu޴m}yrsdW1_U`ڃO?׎| +endstream +endobj +86 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +84 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 86 0 R +>> +endobj +91 0 obj +<< +/Encoding 36 0 R +/Type/Font +/Subtype/Type1 +/Name/F14 +/FontDescriptor 90 0 R +/BaseFont/CQTQCY+CMSY7 +/FirstChar 33 +/LastChar 196 +/Widths[1138.9 585.3 585.3 1138.9 1138.9 1138.9 892.9 1138.9 1138.9 708.3 708.3 1138.9 +1138.9 1138.9 892.9 329.4 1138.9 769.8 769.8 1015.9 1015.9 0 0 646.8 646.8 769.8 +585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.6 +646.5 782.1 871.7 791.7 1342.7 935.6 905.8 809.2 935.9 981 702.2 647.8 717.8 719.9 +1135.1 818.9 764.4 823.1 769.8 769.8 769.8 769.8 769.8 708.3 708.3 523.8 523.8 523.8 +523.8 585.3 585.3 462.3 462.3 339.3 585.3 585.3 708.3 585.3 339.3 938.5 859.1 954.4 +493.6 769.8 769.8 892.9 892.9 523.8 523.8 523.8 708.3 892.9 892.9 892.9 892.9 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 892.9 339.3 892.9 585.3 +892.9 585.3 892.9 892.9 892.9 892.9 0 0 892.9 892.9 892.9 1138.9 585.3 585.3 892.9 +892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 1138.9 892.9 +892.9 1138.9 892.9] +>> +endobj +92 0 obj +<< +/Filter[/FlateDecode] +/Length 842 +>> +stream +xڭVMo@+dg;R.ҚJnP)V"Hxƻv8͛^ŋh@,BzcN%"~3PO?.^9!уѕ M3u=(!vF-9 #~ +tY&6xyAAQrˑBCBmXq :q:9̼{RLh1 r +P!CJrA#>$b5=h "HTE3!Y7 {oa/ϥ~rc.Hb0 +. +иp m>A;P̀TT/R-;fs2 RC +xnq*e֫Zhf_'-aRk/5+96R>z6Ⱦȴ>*2*9 #݄g'gJHt? &IkN>LhkwڷUPULXKF6r;riH>k*|}|q}s-gdwrc{K%b|WLRnWSӿ~|i* 8VM5^X\M1ϱZyѢsP|ƞ#a!2qu>\voF`8?/pV| f?Ƞ w=h >G2]phVb/R^]=3=#gf4ECw#U`j=8mH?kuн쑿;٣U=}*O +endstream +endobj +93 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F14 91 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +88 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 93 0 R +>> +endobj +96 0 obj +<< +/Filter[/FlateDecode] +/Length 576 +>> +stream +xVM0Wdub'H\ڲU{dst%^4P5'&3a 6\Y@@D" $ "O!Jh~Ͼ !HA[9<·vlnPAqorxQsHgU8J~g]|i>HǑhZ6z:6]:V^a!YȈbz@ fDv綠 +(uM:R-!چ>um寅W*" q!9L_ږarwW[VAƤgпP +Ti➮!7診ÔYAѡ }(HO{ôسlM9Pb|B]KЖAzibtw^ +K)8L,j֨$i4jEM&fbg; +endstream +endobj +97 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +95 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 97 0 R +>> +endobj +100 0 obj +<< +/Filter[/FlateDecode] +/Length 537 +>> +stream +xڵVn0+|2krip+=D*mrHb\7ÛǼ"Sj߾%H:EyC$屒( "c~$JJqDyQ+"|E8^Ѭ01Q9@cn@Tlj!܁-K;VUW֡ x2) C) N%# L&W2ᶘvhA]iL)+RnG# +MO\r +r8iˍa=iocP˺{;>4w֠Nll^SgÈEYBg/\։NC--NLnZ[N&8S:βf*_S +endstream +endobj +101 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +99 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 101 0 R +>> +endobj +104 0 obj +<< +/Filter[/FlateDecode] +/Length 275 +>> +stream +xڽRn0+R v<.j=45=Pb),*~})&JkO> +endobj +103 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 105 0 R +>> +endobj +108 0 obj +<< +/Filter[/FlateDecode] +/Length 824 +>> +stream +xڵVKS0WhZY/g&v +XK18!@f $~|W9vmjb0:=$$ (B`RD@%@W/,.0#t<ⱒ3*Y\n*CFC_r T[f5y$qY? ĹvSLa%f6PLZt۟#ea` Z(:جx$еC!$ =~2D}jpr&@L1#̆"Ռx24Ӱh1'LjMhǩBD0k7iLJ .R|pŷ>ψ0%tmJ,~ܐ}0ӣ]"͙X![.G +zr _Н[(m[]~Zw >l[K#1n羾"#g + Cƒmֻ1g\a&Yׯ/Xw~aZ.R.<+Xރҋ`1 gnQEER]hy-HO"GS^o\*^?7 +ʨ`ש<5v9Zʸt1˓(^M\e ^V;Ey2zyi^$gb\.k7a==vZ˺0y/W|1 eI,Z2;fm{nj:y mk +endstream +endobj +109 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +107 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 109 0 R +>> +endobj +112 0 obj +<< +/Filter[/FlateDecode] +/Length 1067 +>> +stream +xWKo7WBR/E=6X;Jju]@U ?×}YnNe3曏sˏ"Td`VjSx z>Kn>޾51g˔!L\[(agZ.Nއ\"pYAiYkD g=y8NdB0IXZ` B[D!e0-0Q +^ IL  =;tBxÃG? $CtxuLȺC%LamFQB;&[dL-+0ikkf1 `m;lVabܫh&Z|byk1" 8KJp.$zAwJqr@B +3W3H1nu\&={)E~r8RagBYzҰ-5`[ 23Zj}U H܄b0.0UsPbyÐUɶLQP?nӴRc:<i0~Rb=E8ڣrX**lJ*6%ŌٔBz@1}3䲃Cx {XyGXo=݂:n2˺x'/F>G|K?džj@s}XNh.jiwWwχ/Э`ۭN㳿(kޜ^S_K +&Y +lsV)e$PHh )Ї~ +%TZ>(뾞?&SIRP:EqT6o>ǏVt[TsqY F, age^Q1=^QL^gU %YqIe/-Yt:Fzy 9/m?]tOxxz'?>7y^/$ɧ nnvWSIn}OHϲk=~퇹ͅQ.iBDj{AE*71hU\.ֽF1EbrQ$0R LW,@<]*s +endstream +endobj +113 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F14 91 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +111 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 113 0 R +>> +endobj +116 0 obj +<< +/Filter[/FlateDecode] +/Length 566 +>> +stream +xڕV0+|lcc)٪=f]))MRTaC[$D3=3HHZ#YDcB4ᄅRw}CaJCu2 y1@tƂxy~}L 4WUWq*5K,mBWP z{K!JY!ڗ[˽)nv=ʰF͡LHw_L*r5_b]TλN{6b Q M15gp;hgIn64AfO) 1:M不LK L 6ܨ6ӋOU&~Sk–d c(m:dbV(Uc1Y=g! j6ͷ. lGhoFJ VmJ:{u{p+~uݠ q)t-$Wn687He*p[,gr/Ԓ9WҨ~eQ}cj \"th;}P'Trj)53~=]>:HT*LS]&<: +endstream +endobj +117 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +115 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 117 0 R +>> +endobj +120 0 obj +<< +/Filter[/FlateDecode] +/Length 575 +>> +stream +xڭVˎ +،a"e6S*"jHd)MdR>`ֱ ㌆ \p=]6$ P IbI4dA"RCrHg"$V]+&yn0ǰ)e<iGno榇)S@u9]j/nFu.}X01zBs׿:Ozoߟ~]9vqUg}[32]4U՝K +K 䬶j<D15(͂VWFbG1Bs$me-qdӓ&[G6{ൣ%b) +sM-鋑 kOzS-p5}mRSo3 +ݣfA)c:4}==ard^ oKW=?y$tr8Uo"x_ :` +endstream +endobj +121 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +119 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 121 0 R +>> +endobj +124 0 obj +<< +/Filter[/FlateDecode] +/Length 426 +>> +stream +xڵTn0+|B&frT[&@" )@rxPM0׽8]0 f4,ן-ֿ*Lֵrf*^#W E> +endstream +endobj +125 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +123 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 125 0 R +>> +endobj +128 0 obj +<< +/Filter[/FlateDecode] +/Length 987 +>> +stream +xڵWKo6W(K3|ȥhh].nͦNIzI"Q7L +)=Kٷ{@ 7fA8øuB/9#| +?[D*RXL~߱ +E()"͖0P*=8P;]ه&[c>Ur"xm8ujȘ9F&D==A k)q,%@.G5W¹d1B) Iu+r ! +ړ+0+" wCZl;Cu U݄$p@dNK{BIBX\ +lSZx%R,R*eG콴k X򲍥!H/wNz]RL|rU[#HleKMeRcc/!t~ǭ4M V1"fnf4yY\)]?*d7_Nػ`Ў z|>GGDM#fae\M7{gg۹~#@jz$7~U~WJn5V)sPCTzs?/xRXUٷ OSŇ3EU[[;NFRk4cy},C(tx+:ÏU؜ ٠V'TT}U,vy\ miIeVdJϩ\ēLSPF9"B4R$Hi? }(HOMF*nO3?n !+?`8ZnF_tƫT)ð R9s4Q_)|PgT8;02dk~Kdʒb<~,͛ ww混oɿnZ/ ~?&E*b7šV`lo78\j +endstream +endobj +129 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +127 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 129 0 R +>> +endobj +132 0 obj +<< +/Filter[/FlateDecode] +/Length 276 +>> +stream +xڭRn0.6>)EQRȺ[R0K@$6_椋7o4<>F\ݞx @* IIсхT9Ѕr'^C6kF]}RH +V{CQ3Z@XH!}I^6IYp5mmaVjϧEgK6Ø4Y^mUzzh:7xүjq>G17؞uCD1^#Um;[n3H0dž= m K'ewª +endstream +endobj +133 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +131 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 133 0 R +>> +endobj +136 0 obj +<< +/Filter[/FlateDecode] +/Length 864 +>> +stream +xڥVMs6WHEOB3>Sk0;Ug RTطow.H1[wffh-ZDaE(va;8] ,=@,(@m"+ 8>yXSڲ@eXZ{v +CfRJ) +0$e GJ < ii'9tq7uc M:F+-$*$켴y%Bx?OUxo.vO3=Mlkqq꼺lW}#h=ޮ*y|2u/o?lXqjbg\;3 ^վ}m 7SvL#ܬ·>^I^0> +'eb~/^bK +endstream +endobj +137 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +135 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 137 0 R +>> +endobj +140 0 obj +<< +/Filter[/FlateDecode] +/Length 1192 +>> +stream +xڵWKo6WhY+\f^Jl wHEH<8}3Cr7"1^m~$AJTT/ *_5Q믛WeeHXR8_![B밣2ԉу@\UI/zYU]QpHU\qDb4GBHʪ=*tL;~~0H)-1fRW#AĊZoP<@HxJ= + pof0a &r<i5>:Аqȏ;U31+Eޯ2p*׍ -RcYQ;ryS{QΆbő8liR=ТD\;Ca -m@j#XV&#kJRrw\Pk-mCy}-Rq~LGPiHؐL0*P1!L2\=q=5ǓeL㵳F{L{BX iH⨓sV{Ε h3-;1!,gޓG# +XQdĂjfmIy"̤ȮIBI\E72eyv~_Q<Nm?y!A6Ze{_pC_[Юp:/sg͖%"SWŠѴ'Gy3XR O9)lcc6kNiIWн78ᔰ]!ah2Dջo9"8"Ԁnȱ@fz(ԉ<ى9 "8O%6>Ah'gć] +Yp.-1t^" +h݄?ûνB(,%0UsLe4=o[W<dJ/]3[f6t:I s$uA—˱UKN1N֙ՌC˽ nAI]]Dsm[Ict&d\W}޾j޿.\2%墁hxc~^ʄLN~!7aKQcݿA +endstream +endobj +141 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +139 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 141 0 R +>> +endobj +144 0 obj +<< +/Filter[/FlateDecode] +/Length 279 +>> +stream +xڥRMO0+zCmx=xp- +% 믷RX5.'{뼶#A ƻ=@H$PP$9.ҧ̉O +])w0TC;RK0`G+I=,X`Z  )-yfELn,̫0Gvv#L7]'7i]}œTF17WnzBrn(kZL i0#slڰ4/Og@ D٬O +endstream +endobj +145 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +143 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 145 0 R +>> +endobj +148 0 obj +<< +/Filter[/FlateDecode] +/Length 1018 +>> +stream +xWKo7WB)c\:lǕ]T3|ܗ9D]΋3|gkkE@1obYML +`AÇ5 h6oW iXcjv!.6샍<fju0NO6X?"0jfJ[r,3Jjf V(ܿpoэwzޜպ~>bX]*8Ídڔ6hcq@~D9W= g8&Ѐ@#ND{2GzЧWqg.ك.(z!觾\FpCrrgcFeyEg~B^3ryL g]'Ѻ#1!։9M!5&gB`~_tjjɟV.*aoE&qI6bb'cuJfSYw➲DuWnփñDPz's֧7O]m4(_bz&MoV4Xza9_\L^<cI.":ѫ,$&<غZ(ё'0MLԈCkHŧA3!7ZoW5X3G |꾗+' F=./קh+J/ +%'}t:G +zΧ~p<+xīi +&;n 8HG~s1{x B0a +ͳ#a+WcwQvnlj^]O^^>r !@_?B߾@X3 +endstream +endobj +149 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +147 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 149 0 R +>> +endobj +152 0 obj +<< +/Filter[/FlateDecode] +/Length 928 +>> +stream +xWKo@+4twDApp-T*?];~7.|3c ]t{ɞ_h&5(֟ ΀6lR)!Ň6ڐLta[R̂wI6*5a0`(fܨ+Cc|&R k"s=*3 R'10yBZfnC$jAA9 .P%e̺)'sB ЦĔT9̧ݰD G)h)LC"V(xU hl Vz "9cFQ} o{]h;X覓SP!*MvRޫ$?2Ʌ#S+xOc4{])cUǜrϲE=rz<v[xoY@U{C,HjI3#4)U¥4!TdIj"y=冣!b.헺ĸWRqɥ%eWC:vˡBԸcΒBecSQ..7v \&?e8F5hmsr[o,vW\E.> +endobj +151 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 153 0 R +>> +endobj +156 0 obj +<< +/Filter[/FlateDecode] +/Length 566 +>> +stream +xVˎ0+AJ&6#%ͮJ\J||afUG׏s= +@1B` t<3 c9BH ( _q,V7r2m~ "4)өLf."Ѩ|P!zyC8wB2!hMnTr02:Lv9ʡoހr6Lj"/4g6%߽EOU\e{kY=~oE;8<֌ܤA2h3VɴՉZ.E)QNfBB|eCQjKYX.5 yA5гV1M *W)Pg &*y +.%Ru~?Np'7_dTΕt"Ȼr1s8BƱ4"ʯF*:6~)B5]bK9rt&f0%gzNmL}OD_i;VC#N v+_1;RqŊ,6ȝߖZާc.:nh e@kSg\]LYs +% ; +endstream +endobj +157 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +155 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 157 0 R +>> +endobj +160 0 obj +<< +/Filter[/FlateDecode] +/Length 549 +>> +stream +xVMo0WR(2k#-6r+;THm@iLꏟJk5_HyhL)}|A$HZD +bH+7QPA1`F?o"끱L<zϕ۽#T3WѥJ138(mtA}sb繱laIwaތr}}'ҧYO6h{UhыЁ^SE%e0 v2"pgp$ƑNAy@c4<~7mC+ƾ8Le7Y~yI:v(e6_ʙt385,c|m@ jѳ(BgNLRL +clll2a u'# Z@m['Q#sgi /lG&C2ĘȻx=w^y{GUm.uxoUYN8] P@D_Bï ?5Ɨ$tx$ E;s3-g?SeFPijc3emuo +endstream +endobj +161 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +159 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 161 0 R +>> +endobj +164 0 obj +<< +/Filter[/FlateDecode] +/Length 264 +>> +stream +xuQN0{AJvm'H=H8P(:y( Rce Eeg3^ 2bh9TK0o!nN'RHO c!۬L?I<=ɇ%kaL%4{eں;P}Y7!E+Pv(RKoqa9٭+n[\gk2um㫐<5-\8kbs.5P1%s217ߓu +endstream +endobj +165 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +163 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 165 0 R +>> +endobj +168 0 obj +<< +/Filter[/FlateDecode] +/Length 1008 +>> +stream +xWK6W(!çh{ic7[T)gHJnP_D3fd8'$<~&?o*IEPdӻdJN) 7o qL& &*H1,9-*B!vDhtV.d =eTeD1PXrʘ r*`{"(1qάJG`AL|`i&1d%.UfF*uVC'0$SY, T8+#!z[òM8`ʡ6>]3$`Kvpa:`8!;Z`vƶ@d,c`i Hb-fcK +K E5j J4a]jfqtF{.I T.L :8 )vH!+UɅ&$ 9RqJ"I@fxڒLj.U߷\NgEAt#V~9UeS v7LqL5@McT%_氋~]cy؟S?j:[vu+וrT8 +wL}AU +endstream +endobj +169 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +167 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 169 0 R +>> +endobj +172 0 obj +<< +/Filter[/FlateDecode] +/Length 171 +>> +stream +xu;0 w~dp͋"Q6*$V-{ӝY2H!%T0V!)(/pKQjCst^i1@ $m5+YVK-rmOȨ\T֩G3.y[b_| i#) g&*S3'= +endstream +endobj +173 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +171 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 173 0 R +>> +endobj +176 0 obj +<< +/Filter[/FlateDecode] +/Length 1042 +>> +stream +xڵWMo6W\r/A=6KMbqݵ@~|j^,Ùy d3~%wŤ"Of5V3Jt^|b>~߼53o\e:0i_) YdZÜ!\mɿ02J@]'bB C!gʾ+˼# a֓cԠDI> +endobj +175 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 177 0 R +>> +endobj +180 0 obj +<< +/Filter[/FlateDecode] +/Length 594 +>> +stream +xڝVM0W 5`)٪=J+EY6B&*;a̛̒ A[/c<I_(}B"3_D(xb٦ȧvMlżGX`F _3|pWА$)h\xOI֙3c|n.^ ~k 쀹@5BC׿n ^ih#I?IМd~ +endstream +endobj +181 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +179 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 181 0 R +>> +endobj +184 0 obj +<< +/Filter[/FlateDecode] +/Length 577 +>> +stream +xڵV0+|Y(5q$.mU"ŠHـTe|l6`V[_&1o3319hw%YޓH_ ɀ $~C6"SRk0FGp) u4D0p{SX786Ys&Sb RLЍ[OjRxR>-ʃUt뺬81[^B{ۤ/ރ0OVqDs2n6J u6PQ,5 = :Вi%]񼴄D$d)VgK/'Dʦҳ + dPAlHҏ+0+9. +endstream +endobj +185 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +183 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 185 0 R +>> +endobj +188 0 obj +<< +/Filter[/FlateDecode] +/Length 395 +>> +stream +xڵTn0+|KCj=4J4!), +D|| 6 i jy3o0p '.r@$ "ɁwjAbyOHrNHo2@0sݖjgCNEmH Jߝ46VY[++&9L'mVm IÚmyn'm1{TѿN9jaIO O ɂ(u*mp|Ez%*4M>0 +]ƍ:5FIaX6jt >¨εqSYyXRZfYZltsr9i: Vg1Qԭ@,\ʓNpuEPѾd"\+ CrX{_# +endstream +endobj +189 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +187 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 189 0 R +>> +endobj +192 0 obj +<< +/Filter[/FlateDecode] +/Length 833 +>> +stream +xڽO0+|La~Vi0m]F@JKJPXiA⏟;eHzq{)"@E}8r7HRPaŀ 4tQ1”2]ˉUc,]N$2`R΅&?-s0^~]9t:9p1B@-biNEofLȆ1pH-4oSV`4@}B̋u 8(a#D`tawPCU+>I4>,L mCS ¤}.f;'bnWTF 9h%dAe!ԘJ6b+zI35>>NJQ]:іщ5ASxjJ@`9u"AXdj"*wik_+=lBBkZ>>" m?Wm1ONf•}Ci/W/]Xz>fjӍ +endstream +endobj +193 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +191 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 193 0 R +>> +endobj +196 0 obj +<< +/Filter[/FlateDecode] +/Length 812 +>> +stream +xVMo0 Wh/orذv؎kvYNҴK:,GY%] -=zlD Ubz&DH4#F!l8 +->\$L1 v97ez<=(#v(|Z7aI2rH0*>8Wtl$8dkKFwJyΫtymUy2Ԉց+h7$Hlm\C%7>B1 dgiJ o6Y +|yx_6 $j {A.fa;X'0D湑+d3ؓZQHbmW i:C9tjh oA^];: "2oLFvvt +XIhO)" 2Wu܁N8=E +BO(W0gn0CNY{dƔB4iЈv̹q&Z]mazQw&M8bZs,f1;לyڔ. +NbP4<0>VKcl>7̓WW> +endobj +195 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 197 0 R +>> +endobj +200 0 obj +<< +/Filter[/FlateDecode] +/Length 1040 +>> +stream +xWKo8QZ4ߔ 䰋MƽjqR] +DJ@>of8 J(E [$B=Ҍ1cL*>-@s~Z5QNrm1 %ʚA>x0К4K{ʫֆ!yNʇã%B¦D G&yޡwL5L4Eщ!K28 ،hwZ P=3) Ҿ~+^lZ'Htc&)a0$31"IHt,xd2A}Fm-ˁFn4th[wb"Y% +2&2;D֡\MwGF#9"V#28Έ>D f 9zjcrw&\D$r$FZ'wԳ j *6!^Opodby; nX@3Bzd8\(g}n̉.]PaSp=t"Fô&&n~ruq&sx)\rjݯ}""ܬ:*Dtr2[+]61 +rsQ87^Ffڧ\\mño2)/&ܯGLAL6t*82O_6 }<utܜN0Beڐ}=r|Z\j~xzaxf4F\s.q@׼o/֨]Nph^ W%_^£D_5LԠɠ~)KSUY5L 9аvlOr,} j +e#(tݯL.nf?jӻ~W_;Op:s)m0o~SbƆ +endstream +endobj +201 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +199 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 201 0 R +>> +endobj +204 0 obj +<< +/Filter[/FlateDecode] +/Length 198 +>> +stream +xuP=0o,Ck[(#L7q0X _ Lwݻ%B +#a' HjwA{IuwgomaJ몎@3F|_ĞG’ )P9aSWi<2ल\zAUîntfUiCԩn~q}„K< XP9ޘ PlO +endstream +endobj +205 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +203 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 205 0 R +>> +endobj +208 0 obj +<< +/Filter[/FlateDecode] +/Length 926 +>> +stream +xڵWMo6W(K~ȡEE{lKW@ɺI6uRw!diB3of 8'7$.?7Ť"߉jBbBTqnfq!y0he:0:B~K`+h U'}rC ˼#Ai͔#w|P/3lδ$w"Jd_Q&5(YR +1ZPb = 4 0dX{&fNr rS3gkKlj=O 6f<̈RZQSh8…QN|P0lzrDPϪP-?Q0졆z1K(YGGF1^`遼Wvo,XHɒ1%CZ5N7>fgU!d`Js°ѫT(BB a&3,:ZuBꡱaD=iRQAjVXT3n#@A@AЙT{iyqWg<ɨS7_,"q#ݶ-/dwwxpJ/f=of)W7eF8Rˋf 7͒<+ J#k:>Rhި֛ë:Z'/ecezW]Zm7f.aYذ$j89S +PV"8G-*gR>aUXN_DhO]'_n:zuurЂÿAMPgzJϟoUb +endstream +endobj +209 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +207 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 209 0 R +>> +endobj +212 0 obj +<< +/Filter[/FlateDecode] +/Length 1051 +>> +stream +xڵVKo7W(!E|)Q/US>v}IJ +yrofI8|$q|ۼUD(&F`Vj)Mv߽_ B^`v?n7L&(nbʯCw"YT09C `{ 0^R$(,(lV<4S&M)CHbWl36!+44@zHii'`#b\&ŪjlZ`  +aW:}a>$I sx1P #e.! :^_`Q^2g@zbe:C` L 3X^^p,:v⽮>f3Wro [1%7dmZN-N&<\P|%|l&|fc8,Tbhڬ= ~Gfv^oS,f2$DM1oº%@^Ȝ㈭n)$J&&şD8O|N?F?aS =|k ioEߴԫA.tJǺƌs ~"G28i8sAW3+gV3_`uuX#^LU|Aҙ)~V s86y{Ƙ(9$j/0ҥx|/L +endstream +endobj +213 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 91 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +211 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 213 0 R +>> +endobj +216 0 obj +<< +/Filter[/FlateDecode] +/Length 574 +>> +stream +xڕV0+|1Gʥmj)J(FH$%J||۰YbB{x(mYD"$|qspB}㕋 y.)g0̾aB|qCPD a˶QD(s"*MZ)f1esݩܔezӗ$|羫,a8϶/\>NӾ~XϪ>l!ެznm1ؾ?KpڼQYeÌjYZ:lzD!FALʿuu*W Ma[6jdeL":yd{ 4H%tVSPK,4pOBSLz@r|(iCV5Z6Bjz`F z"()E;xц^4)Fɸ)^  sHI)١jQ>H]]Rw +U24Axgͨʼ:jV h7Axʄ ,V}!BO9Mi*c +e?% +endstream +endobj +217 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +215 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 217 0 R +>> +endobj +220 0 obj +<< +/Filter[/FlateDecode] +/Length 535 +>> +stream +xڵVMo0(kb)ծr[5!TM5TC]_7y +h~m\D#'@biDR-|H ʏjScT~+ʝ:D::bo@?v$a ۽'Y?5J-ztMݎ(#4kćkYb o"ҙZU"șٽɻ M.hjBjPh4օa- }2em-A"jWdK7I?%XM[*0Ԝ0Am%V.F&2x$FPM b#BIq:˜.;tTr*2Sbܜ'ꦸA>7!{ospm9> +endobj +219 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 221 0 R +>> +endobj +224 0 obj +<< +/Filter[/FlateDecode] +/Length 396 +>> +stream +xڵTn0+|dK.IzhhBRXRT m2ߌ߼Tܺ1uZwŊ$V Q,} J 8!FµKZH0-RJ?ͷpdI"^=o[(I _S95wmxƴ4md; +^"s8D9NE+vs39 +V2K|GS +m̋PVs_gTH> +endobj +223 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 225 0 R +>> +endobj +228 0 obj +<< +/Filter[/FlateDecode] +/Length 981 +>> +stream +xڭWn6+ ߤ dѢ]6 ;ΌIm)z%u,"yx/€1ԏ_OpR1& +P~, ?/M}^vѐrc +ڧ0!yVYPypYaCc`sBgN#>[''@u*Tm+rG{0 6C.3һ.ցiz@x qi v̶5+ Ծ&61raiٔ$Fxc$ {B 9 Am@kr"|cI)" `\n;JHƥ[s\3φu=Ybm.VfӅ(#5REm cLDShK(2s3hOn'pD2xfe,+tP fJ ҠU][tTTC@3>QbJ* WlzamDKN^aF`_aSSbܞnnxXaxsPMdpxs'q[2/kn"S;PzMؙry۟_i[,UEwg}Dk23FVKfªƁϱ%lAC1kLs.gEdFn!=O?%\ +MXhcET}$exV.?]Ǫ8`*_l!y_,nx{{ӄޤ"CMp^/) *SV}q&Rʦl_99inNV`${[UbY&jz ¿;LHd{P 3Ok3闫'^|-~:Ǝj^w8z<rleI7U?Y9&skz;ZͯTs*j +endstream +endobj +229 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +227 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 229 0 R +>> +endobj +232 0 obj +<< +/Filter[/FlateDecode] +/Length 1219 +>> +stream +xVn7+xp_%$x|Z($ M6{Ɂ1Y{"%O(|~Dvo%b#͈QNB>8[cƸZ}`ƹ[<{#N{]hkT`,$.v:iH֖XDJ@Zߡwgd9.9HOg$,FQsHH +j*hD_GͶhS璍?bvAQֵ~Wc_ԦcB +Y\Isaψ4<(!J5L֑2N$%iL,U;ĉee99 .}'DusH.s=>ׅ3Zȝm%9%Rԓj%X9)3@ˤrIUCRN:|/a:&#.9س\a0,0l۶ž6]0 Qyn grQAX=(:LYp[rf93˜1M(L Mu$LY7EM/M[w81zeU9t&OY}Ei?L'2 +M;֩827C&-4O(7@g sS=D0f 2GO]yq Hvqs‹t:LO)$:ݱ}\c2w{E)f_??=fvt%6+ެY9s_^2 +lJPe#BKWb9KkN$ep̀w啂 + P[XoҦ|J~p(AB%=.;?Ħm;>\Q_\uC*R/}jŽvY8U-CUlXXwD-x[T۞s q&y{?2ꡟG򈢊hx I +'AqtrAY{?-45>q;,^qGx|zO~Bc|ySzs1;L5M OW)O<ͶdqXj®1yܱNIi/ y7k>He3 +Qksx-Z|vufѶzW?SV?N\ +endstream +endobj +233 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 91 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +231 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 233 0 R +>> +endobj +236 0 obj +<< +/Filter[/FlateDecode] +/Length 562 +>> +stream +xڝVQ0~߯ \n-R_yeĩCC J mO Ak'> ^h/9J A}A1J?~u0^/ L/ϓ8,v<:8\(!` T8Xo[0q;jI^"F|y\n3_<=m!_{!eD(PJǪ3'>&O!ŦU`"aS}y/ámrvl^.Jurߛ|:3G'j;i'E6uޤxHX֟8ЯIa%zYT,r01 :Mh̃B`JQ1_(2?~7yuAuQ Z#6з鬭 [Ɛ-/2 +4FdZG~ C +)_4cـ82KB¯tA͇'x!M21vmjM %z!m }Q+*ïX$ ,sa>FR?UtU HxN ) ^=hD@V$UupH +endstream +endobj +237 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +235 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 237 0 R +>> +endobj +240 0 obj +<< +/Filter[/FlateDecode] +/Length 569 +>> +stream +xڭVM WpY + DʥmjS[hC"Kib%[Օ D#x{<c3Id(Hw &aL49H?D8 ^͏C<_PQLH 0ǰt4Aqz7"w&j3(LE=gl/O;vi(0SMVZ: ~9:xYTi,rOG>FҮE^n,4Z,"g]mtȴZti(ѺP// C æ*̵*{i$fKkD$"ԞH oΐX'Y/-﷗p;yFRǐ"|BPN9l-eBK ݣY?7@oRp׮6TR r)0&fKUioqJb Iנ3pm½}杯~PAM!TUQ@ؙ׊vO3Fk)UtjyJf'p&z&IUU/˘9 +endstream +endobj +241 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +239 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 241 0 R +>> +endobj +244 0 obj +<< +/Filter[/FlateDecode] +/Length 429 +>> +stream +xڵTM0WRr8C8PJn=HC@P폯$[vg͛8| GsH)P]_ѡt6x +F(ܠ-Tr@pȲt[UE^KK?O%HA҉ ثX0 )>C]DT=#!>-2n)MMTYDss C1# бZڈmXکrevED.;eMp yoCotm(#W}{J u2A&]^WEIZ $K^W/_.wk,WxUU]𲙣YVnK"dD?mo? d] .cxWߎ~zӳ˞~F?Pz_B JM,aB, +endstream +endobj +245 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +243 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 245 0 R +>> +endobj +248 0 obj +<< +/Filter[/FlateDecode] +/Length 1185 +>> +stream +xڥWn6+!À7E3E츛&qn&u|H(N2H}^Tw\[jg(ֲBJc>/L.>/pc_v?b\ Xt)!R9dM."P$"| +Vޗp,)M5X + t\ +W`B]& ޖM,`#_O%'V, ՠԙX)HK!R;ea]T'Svggz=ae_yoS٭b&( +o=B&ͧe+qWh{.hhCA'տw)ƒUWhLM7>T|E(p?F@ T)#WO:U`Vj'6' 5;+Lu*}RfUKPp؝Inw>S$&[͔ܸ4NW%H$r)z^o{X] q#9j 3V8u:b'cS=z9ހ}ID*"źhE*q|Gfaͨ}e (PPQЀ(9" 8[Jil&N^M$®fԠL?Z2)N2ٞA P/m}x +@vWџ<6> +endobj +247 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 249 0 R +>> +endobj +252 0 obj +<< +/Filter[/FlateDecode] +/Length 327 +>> +stream +xڵSN@bf:wL[ @@SjB>b p FC3ԙt Vh PhNB+&% 3I@WX$Y 0-*(8%hnobPǨc\8 Gb7MQW>~V,_~\P }ra weC.NҏlTwnۢ.ө[ 7&fTLlxbLWc}Z82 B;)~5Ptr@r'p0ؿ)8P +u)!G +endstream +endobj +253 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +251 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 253 0 R +>> +endobj +256 0 obj +<< +/Filter[/FlateDecode] +/Length 922 +>> +stream +xڥWN@}WCwV},K1HR. +TM%>{׎ ޙ33{ J(E7_>ىDL!Ҍ6Ddz f⌝ 69_|hTR; Xr!q" l\ )-X:#Vx"%MXKFud% v3Nu&0]i2ml|lJR_o|H0D\19x +0NJ'O bMWiR( jgƭ=ikG<:;s.) 4]aV&o.X6 FGA8N:>ģMx_<L'~!.-;$(#lԏT&7(}LJIDaGWL7>\>$.Ӫ)w)M8&kаh7);W-7ztԬWr5oFc2͋p MtkULG ˥=ʖCnYVlQ SF둖>ʼ6S3d}C˲6Dc*,&"ANHG!vorݯxY>=}X&rsH>8by4p./GWa4}%ݩ0*HpTÒUt"XFlX8ϙ#JQyS6#B~y|noWwqf\Vzu5?k|yh# +:m-p&ϖwQ +endstream +endobj +257 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +255 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 257 0 R +>> +endobj +260 0 obj +<< +/Filter[/FlateDecode] +/Length 1328 +>> +stream +xڵWKoFWHYzgmN(Vu k +wArXR[L.;}38㼺˷Ʉn40F&i݇@UWWo|+ǜ6$eʻ*LAguD0g+]IS5¦oT `kֹ{Ex;9wXM(6XSL " jfxșa/j@05U9ЎB[g ~o3sm{Kʹ] s] _M{yBx&wf `+wcrJ6^y2b~fEDŽB{Yٞzf{^NP[j}41 +eBw].t`t* = B)y$s=͌eN.9͙SOa1`/#,p}8›F$O_qToO ҧq;EPRB!׭3$}'}˴N\M/?6czhJ pL?HK9TqՓk`vJ S&)eq8q:Ó&W)zv:Kzѽc.QKR)Qsi):٭9-5uftճRoup|V1R˽0![O팿ɹ`m)tݶ}^5n|~7 ?}~[:7順ɧOW4'YY]oMrWL흦EhL1o%[GMȜ|ʻ)O돁"dr^zS<^b9]%VJ%K'8^ ^ J{?W~} +endstream +endobj +261 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +259 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 261 0 R +>> +endobj +264 0 obj +<< +/Filter[/FlateDecode] +/Length 377 +>> +stream +xڥTo0b^m mÖvHU'hzyx+`B = ]9K@0,9 Ym|S8e:#Qlvxk;ůW @ ґvD.%7 Ln)nf*nŲXF*((@U`jd`KG>XTu*z`aoWWuRik9$d݅~q]fŴw}_Y &r_E8UZmOy y#q썢"[-Xg2N/%$KN?]kGvJz6@D`Q%oqw? +endstream +endobj +265 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +263 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 265 0 R +>> +endobj +268 0 obj +<< +/Filter[/FlateDecode] +/Length 1029 +>> +stream +xVn6+<|SfiJ;M n!H%i +t#Q}J||{:> [Ѳ&߽jAv=c W5ӏ窱*V"] +%}%-1s >|N5$9ր%$B70"ޅ~NzfT+LoBq[M& AmгY B<4AmJL:ܯ)RɉT)ƶQ0 +NHt '&㯖{o +UΜ[UKdw|rFkXAh])Ia õ8r8Hg{Gc}Jp4K*q}4etCoKn0p TcACarak)k7b~ b`* "V@ ma= 7jڽqJyv/(kdZ_SK<LJ M/K8^?~8}?rǯ? #^]S&>֩kсZ9tp "ms~*,u\qhXJ)eG!֤p;YCXSP:5H:'c\Tɥ n/o< + (VH8CUň]}>3`TcXI +{lQ=bx-'rQ\D43橠n&hʊt#Z`=D6+[@srjLZUNO V؄H7 3u7`(-o-\CWҷ\铊1/$.ӳ2h.ϒߙ{RUIARC)඿C{{yt~r~zF)oC@ߛ77SJSCOL:ZV#aE,j\4VQl0)ɔɪP+C?W7#bRO `"~}R:a +endstream +endobj +269 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +267 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 269 0 R +>> +endobj +272 0 obj +<< +/Filter[/FlateDecode] +/Length 218 +>> +stream +xڥP=o07:͝IP;o!n@@IPZNwx +j xJ2YH9ir y!|Kv +܅> +endobj +271 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 273 0 R +>> +endobj +276 0 obj +<< +/Filter[/FlateDecode] +/Length 1119 +>> +stream +xWn#7+xT[C" 9f4LL ؎#ǧtEpYUE +QB)Gn^"&h;ҌQiӊ37.dyF8cJ*xFe($.zXQDjDbgnjPKA\)|)0c|^f fR"Z`>88io)%Ɓ(7}ʕ+p*s" ee83# `Ή|ЗXK!Mhhvg2zxVʕLK~ALJ{ҎJ+ ]1ȥ֗b^F& +jD"ژ66?B36\9mr+iĘ),Ґ25S79o~5 + iZcSi P;R 8QM1FKS)L(ٟ ז'p X0 =9D+qfnVѡ`B,P=F(nTKMSvsi`_?QT<Ht1-oݻI qq7Dqq)01\C}whMw߯Cg FƇx5ˡ{ٷzw׼mەss|w}T oLl +(έ8~T# 42Uxq`]NW`?  +0%Dx + S%ox^* c +ĉz\H!F]Y46g@Ҷo{lWS/Ba&yKzk +9 *q [ɴ؉[Q2Z]}ZDa<κjy&}Ri`t#^8ISPħYHn#ll>J_sl$ӿ+u~?> e~u|:쟟{w!dNK;^H/:uw-.:8al 3ҹ;A52˸DkOjZ`穄{<&~sMu IeY@ sfظh4v{u[KJ[1  +endstream +endobj +277 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F2 13 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 91 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +275 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 277 0 R +>> +endobj +280 0 obj +<< +/Filter[/FlateDecode] +/Length 619 +>> +stream +xڥVˎ0+1a)]fؕV24BJJRJ^? $$,"!h O ?J?~u0^8,rN.`a.fX_AROt!NYv]L lam׈GkakP[* 2׸c+e>$C启 -! + aG1oϴE]VPwokEOWmErPf\泹sc볧IYL'vɜï9S2}'OUoǜzN"A-/AW46tHy(Y!A'XN椸 +,4^mB:`*+gYWiM'e3v5!>PycTd3<~Ynפ]al􁆭ףL#| +Q8"e3 FCbo)m\8z4['`motKWW2ضV~mp4RZ+Ld-ݍQۍSk]bߊ L9yˡ7JF)i{Q߰ Y-h9kEK8܄DEH+ +endstream +endobj +281 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +279 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 281 0 R +>> +endobj +284 0 obj +<< +/Filter[/FlateDecode] +/Length 584 +>> +stream +xڵVM0WpY(578R.mUJbPl@TMtb;trAߌ߼?pqTEc._D(/$)I* A)[9"$Q]N1^ΐ"Yot:uOo׏A_ _\_~zG3ױ~DٵGFnWj{O@v;w9HE\ĩ 29<jΧ3D GdXЂ`cdinWKFݾf擩Zp A0`p$\W_W WjmUi",y[ٸMHAPWEF(Wk*An*@["@J(,kHȃ͆2 !O/J_q N"Gy-DDC2|Fh zy9L=ڙrPt07̊x8|ȆbdK=FIqy_ $42M={7 }N8 Jr|*> +endobj +283 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 285 0 R +>> +endobj +288 0 obj +<< +/Filter[/FlateDecode] +/Length 412 +>> +stream +xڵTn0+|B&^H=tICí@B¢J&P\f<~> +endobj +287 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 289 0 R +>> +endobj +292 0 obj +<< +/Filter[/FlateDecode] +/Length 1209 +>> +stream +xWnF+(ӭ1\28cL= f,c\j^WSJ +ѷ{$BoH3bF n1٧ qv?k>DZ_2ADX=EtaQDjD[gNJhpkd&o)Ai6˿,CYDޖ-,v@D!N)1`DY=Ї\!Γ:$L] $̡~=TόfvgD2g@4(޽h[dF`W8$Pa[ݎhFb>'a-#9W9Xu"#IjNl5Erߌ~V*ɘ7ѱ>PcILX#iGЏ#wCzןL /@~Դ7Aٳfe|v +>zǨb|Lmώ*rAYɊzQ-&Cپit`lNCy+4CujUtyȫ&;M(Q(8JQ6i-<@1fNוbl8w+A)P@S\=M&>u vߏHWq Ң.b8 ,_vþyZb hd´FE4yp9nyGkx~wcT)OL\*LSp jdbT{xP,1pi/5X9u_6wL>|5ϥ+6\S$4\T1Z=iSJL#(_BY!vof3M9Y%60cqwCr1?%zaefIDǟ??ԋ8?# ubzuj77-'[V/J?^2c~v۱*.Xs4?fZ3A tns=Pڗ%ƏYQ 5/֡/x{6 9L Vc;?|&|ZݼM0aG3oP+'5MZ` +endstream +endobj +293 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F2 13 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +291 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 293 0 R +>> +endobj +296 0 obj +<< +/Filter[/FlateDecode] +/Length 294 +>> +stream +xڵR=O0!>'H RFB/%AJvPF{wg#J(E%2f DHHpHݿ:DKo Q:IYvƚYUZ%Bڵ㔴y#Ͳ&횾nhN>*4=a/ =gz6oʽw-^[`ukjA|q.'6P׳n< @zf0fմ +endstream +endobj +297 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +295 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 297 0 R +>> +endobj +300 0 obj +<< +/Filter[/FlateDecode] +/Length 1189 +>> +stream +xWKo7WhY! R)c^lו T;$}IA<8}3CI!%gv^3BiY0˶?}§ RCeWn[DцD$?^A "d,:FhdTu;8<)`(K}ou +5L=?B<ފUNcy˱e!K۲-ٿ . g {gse!ƽ90KvF%χ1O1 +JUQ 6~Lp(ݐ.Hnaski%:ys<=$NThWz_SOm?n]4H#dܜ=V`fxWmh nnO ,.2>Re*/R3Citr:Jt_ 87;ϧdږsWحv.^qnu*Nv mu{+nW߷! ,\QD˻Ǘݗ}8\#Z]WgjCZ; ښo߰8C1WJiϟ%ĈEVo*~L/qpul̙K>7X3> +endobj +299 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 301 0 R +>> +endobj +304 0 obj +<< +/Filter[/FlateDecode] +/Length 586 +>> +stream +xڭVQϚ0}߯ ||"&l[G S.c?~8Z4&蹷E'm>iBC@wS? 8]$1w<.~BaJ303JlĉeŔ-Va9> +endobj +303 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 305 0 R +>> +endobj +308 0 obj +<< +/Filter[/FlateDecode] +/Length 563 +>> +stream +xڵV͎0)|YQjq$.mUJQcR6 T`+j{rн>@x${ĈC|.YH =1 yS҅>ܝ60>]ib٥ak]b+Ynd +2kuF􋛦TG>R&nEx)H[IjՕ|f+G +4:.-Y:E' DRbsH,`M#ܥ?LԫOEEPVMSlC1U8M/FDUQBxii0>s6l@}<>ԎQS y +[_8T [$Ⅎ; +߀v!BXBAm&e'..q#ZD4-ֱlq5N<">(0V0z0t`0~t]br%Vdgsqn4U!9jV =?zΝUdcfo[l,ͼ&glW=ĸz,/kaY֢VO42/*𢨋b&y@3 +endstream +endobj +309 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +307 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 309 0 R +>> +endobj +312 0 obj +<< +/Filter[/FlateDecode] +/Length 421 +>> +stream +xڵTn0+|B&6&DKRnĦJx@T/3޼y6F$EHGtFF +͐CM",,{x0~߽gDtwAL5_s}2N42d Z[\tlQBjK-x;-dk:t&#_u%Ɉ_$lIr,4f[ik\BOg*)vL?Vm@F!?vCt]]wJ^֥-duoU(2EXq>O$l&ʖa.ڸen7pҜ eYm%bzWj: +endstream +endobj +313 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +311 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 313 0 R +>> +endobj +318 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F15 +/FontDescriptor 317 0 R +/BaseFont/EVJXTH+CMSL10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 808.6 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +319 0 obj +<< +/Filter[/FlateDecode] +/Length 266 +>> +stream +xePn +V +cVU*%ܢ~Uq{aݙQ lxJE +6"匎tk 7y42T+ /g~$c \a8٢ȏ4 +O3Ntwqboۏ+&^BgweXy24d C`ٵJ scSDvnWyE*7]EUʵTR]I k$j~d. +endstream +endobj +320 0 obj +<< +/F4 25 0 R +/F3 16 0 R +/F15 318 0 R +>> +endobj +315 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 320 0 R +>> +endobj +9 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-33 -250 945 749] +/FontName/XGVGVP+CMR17 +/ItalicAngle 0 +/StemV 53 +/FontFile 8 0 R +/Flags 4 +>> +endobj +8 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 3986 +/Length3 533 +/Length 4538 +>> +stream +xg8kːH-H:Dm1D'z {g !D I!jt(_}?{_\ͩ',rF8c`PQ܊84q*!h) XR w`=)1 Ba@>E.P @-$+s P7#F`0v,@7KFƹD9c @ 4/1CpwGGms6 H;j98߭ش(߻jx#Fk0n*/4J"h,'_\g xp/)H2Z|3aXgk#($/ߡ|ŁbPRIHWquG)! & SqX텶deY + Ycev:8aʑLdqD:1i|uZ - yۡvOGRUkctM&Ģ;VK<>*ұsDc`aɗ+R6SʞI9ǵE V)X<q 'h|uV7ƣ!u+Q{??H'Og|&˳7%J(kf~!pq炄mST߱^j`(+ S>pnP#j& dVf$ [Q&ӽ._x?gkr+S{Ddqݳ*mculSdleBSeQ`@v +OX~eï./ erd>Oh}o1[̏问oՅY+d)?&3٭,^NБwoE#)*HH gRn22jjkֺ.ԇܩ9yŗ\^l(eomvy"7\zZbX7ٯ{"zK^C$!.ST 4@Ɋ,ib#h]BNNcBQ ?PȸQLEB_[ LSiST;YV#d+7K{9A5ݳ-ب[ݥ79UiTl;V_g - ܽ)OS?KI3k%KǦ&szKc?XV3(u'5=W]዇N=.}КDqPbkfޡ  Cx\!8KO#YJE?RˆHrv9V! y lȤV{u0&Ź[\Է5?GWqU N˥3;ˑŏViq\%YPO `ڧP|~(D*;ZeS'W -q"0/\>nנ&nt\d|giDdz֖Ǥ J k$O/ּX 2*K7 S;-"%闘GZ[4 bX汕ls!A^`y,usq;-< V`nNliUߢqs8yިvF1v< 5H:cXC<1|'$Q1m,҉wQ;Ԑ =d|j}@i԰uM,Ǔ»TGo0e4+S/d烔R),/22

r+9K1X!ݙJ!D'O/tET-E)$%{9Eᤵ¨rdXؚN%}P{ `z%E]}jdDO_ KWiإ֣632;2 @X>% RϮ 8s_ͥœk Rr+OxY[p5akVN(b+%̦|&ʲjϯ|aXHv"W#)4Xkv5lPxлT-*zZkwU$J(?h;ź 1!$m,w3 !ٻ#1&"Ɗ>9l+W{n+^[J|anΰ)W]`(.?XHK!fsn +)qMpqɰ6v{cSu`j9x~=V|GR,ԗnS,I{ W+ a}kR,K:vuOkO3w5+sL(M_-gZBX39^@#%|HA *9KG )) _^{4_-?:\lIl # 2o<&1.GKQBKKB-Fk@DLo#`UA>6V`?'{֩aԗ5/BU,~1Ϛ02L.΁"c<".nnڮFCjY|*8yqIKvJT#2x2({bu.ZͲuZf&RZig^٥ +ZJJta3.~]ށ^57'=$rkY)"$1O?ECoZLfT67ߺ* c67UR1RP##>qfWb=Y ͂{~8wZ)Jm2Og|c}9$<)yOa_KuZLkgBFN07skVg;- #+3E@GyPԮܣu'plLmIVͶVB J;vGⷩr͗D)s%׿n7Opko I#2RSɋ'Ug/+_z,GVB'1 jvsg$!Gi(ǀ:Z"<÷f +>[GALFŌgQPծjR{IQك 7Z/G^iG/RjmZz̛݄]n;An0ؐ+u'tWs5=iEa޷7iꨅ[1C\699W ݆Jx V5Jh#gGWOI[KT߯JPG/3-*V +ҥs Rη0܂0DEJ܁&VDL%EgIƩ OSb> +endobj +11 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 4273 +/Length3 533 +/Length 4821 +>> +stream +xgXۚ*EZ6%ҋ@ M4 %$B )R7E H w*HwADzU:s\k5g>[F*p7; +# +ȁt ! O bnP BT@`9%%HF:8b@jBA*4EtGdC"0X1HdO!~QRB 8!(J?Qn d?[Oh_\ _B_p7 GS: P=\EGs6h߭ftp߻ rpAIHO 7APOğ:;į *'E0Xgk }$e%Ta^h4/u_A 0T<6w nI}ʖ$#}T.bSNa4[Q\JU1?X`<`wWcDmw6"R>֤7փ[lu3R /kMr g:"i6?*PJ F?נ;&Gʢ&/>h9ͭx%7s]Kn~JRZ5&6'Մ⢜we/Q ufC2+_]U<-\D0P`@>,Ѿ1*O9?,sLge;!8MQvuImT]:3-'=~0S:/zB(SdfVoQٙ]ux\dzLa`.W-m!rl:]$iGk:֙>i!s(kG.n)EzVbnyW5|=ks@01 оSbމ_6aɹ[ؒ0oUiQp}Aa +T`\7''Xk9hKlh< R2y$gMMlX[7+s:|fl2⛎{ ժS"@DcKχY*foTs()|wޙ73R_.'(#|`˿h6`@MP:w߲֊ngyl*IW8,?_r5pL_UN)--M1(ERN^vn +F"o`FvϘgGىWNiZr-藿q6瘞RX F͜2  +$`|j!BU˯}BTX}u/K: QW"gׁ;>qÎ] UV]*9W8 hĝZl"|Tpڤ:z8{qn(qBu7fsƆiKCBvT2#w2A]`e-lEurgWH쮪 EonqNPO-I§-?)p>$Ϛ<hc{p@ٖ&5/x5 1[wI)8~^W sAmCR,+ +Т;$qr H_yMɒ%, 7Ѐ[NRM~1B]s cY6~v ʘß*Y]7NKhC/TS~"D=|[= +F{NUI}"@ӽ /a{V6\פ0jFzWGaZBqm) G˨۩e≮I{:lq?}$2:ĕL}v|7T4"RN/w;)37߱/n7# r}|7ёZ"nЈ^tc0a>tT<x#|o7ԲW,b zdɚvmᥐK&.uzΙ#zN.lzHKFUၰnL<.v!7;(ӑݜxa=̔ +D3O=AAf,N.VX;٬ka w'=lOT7](fpVW4V  jWnu/>'K(Yt+x\kdÇ}͡b8JVɪ x˥S +-: B6pڱbc3FyP 2WR00|`(f~|0D͐{9uv)h`qx 2K<}A\DtSkKfm0ؑy&NgnH~Tp*ѯػn+lkyܕGt$jKQUB3&e+Gz]_h]Zj ob4SMdύ:;Fw1/H7{^> x^EE~,ήWh{W úwk]'E~ghD+#7|"oq,3s>$oGi>_ 8zKP)\TiGW)smaEu6o. БyT0d;0aqh\WLzskE/4i#'N(BlͬS9+|-+8U=/q3@B+gTH]_|%V"3FUJ@7 sDQ XAd}+Q(0+E2CgZX4"dL8ekƫk§; &@}F LFUnQ]iH13kY?[:gyA Ǽ^̨u+aV'4!E&']!:N2\m|TL.$*/=co~$oW0#'+*ZzmRiLZ;49TabW~d̮tdGfʏeaor3r-Pފbuke-䙓`ey(TϮ<7ǻ]ZC?PpfH/hԠ =0`k ۥ#DӫNTa)|]Y~|EPBMQ;Mg&079 j[OO4gzR—Ҫ q!z ,SK%.i(1'aI L89j%Z0u3Q-;ø_5p2~nzQk_p$9lL:44Oezmw'G_ɬ:"fi@ SW|@D<xh!NU:wea)M^|6YVqS]!G[b[4Aw.ZB3{~bcu֑:Q9u4ACQÄSl_ e0ǿ\m!]B6&r)i[.V1k}KZɮ4$מ<}d=ZJacP +sNryNsJ^A9ƍ G1(rF +/?sA@7W(ڙ +endstream +endobj +15 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-251 -250 1009 969] +/FontName/TAMYWG+CMR10 +/ItalicAngle 0 +/StemV 69 +/FontFile 14 0 R +/Flags 4 +>> +endobj +14 0 obj +<< +/Filter[/FlateDecode] +/Length1 720 +/Length2 8955 +/Length3 533 +/Length 9509 +>> +stream +xeT\݂44 8k&hڸww<[p'rf}e|5:_*zj5Mv))D-QpspqI8B@Ζv g[X 1;d=-X8dHB-@P2b dд38{pR66Ѐ8A]!`44nn` +b E 4?KG\2r60Sz4`7sQoeڻ8Cv`#ߥ:)C.^UpXIA@\JY:YCjfsy;ONG뿊j K3lg?qt|_¿?g,l tA G%;;qq W%(Ϭ#ϛw[1CTWf:aZ&"2.c` +}. +|yהUx3(RoȄWo|x]:(63-v>y.rWubmlHqQQa +mT#T[l.4SO n`2Dd}'$Ab,c=cy·m,jvMr)nCBфdu;5ƒ +A |=~_C%3eI߶=vX4pCW$~zTGЖlNxxlM{Y~TY_A }mtWRiRVꇌ<%a{[c=]͒G0C=؆ k叙Rj3&憶B]TzkJ3ˑIԀ}-|4敐=TL +\S^$Å|?y%˫ fFě >v/EI5׸N_(9>pUz*cy%7eVʒEo.Ia/߶W+ |b,'$g%#_)UASO%i6.U+M5R>5ˮhP\8a(C$_[9qȳzpoX)n S~t\Fx8%\/q͐oE HtdEV=g32[dͫ63<2r' + T2 6H)"YnyyU,"\;_1t;B*aBUq" +o^/wrG; MED^zޑY;F\㈱+}/æ 7v:#D`)cc1Mԥ5~tWr :DtzP)7+ݐқ64٢^ͅEX.og%Ƹ5S\gaD[v䄷E%WQA~-#~:s$LLiczgZv^߾R+sI)>WJ줛2289̭>| {N^LmE8PSdd,.19 ;jgm&ʞZsr9-vzu20d@AІZ-#p=`=$7(t‰3Y$<}Qh7 +B9wF.c:Ϣdjs?6m% cly4u |`__UNiT? rhxz}h'&},2zc`. I`b nk9!5Cpߞ@٪9/IMYڎsh,ߖ1b}q?v?qTe)òa_~>ܶ\LDoucD;)iwȚoP1B˥#Y{-4Wu17y̖+xC!|vGD5Q&];b\hC^ic[ƿYӂcV\ 嶃xQNRl^,5+H)nFs,|C"G&nnJϵml˫#UyYI zqfňMA/]}O$d6b6Տr0~F=nˈ8.QY-U>BUi.6oqJ|Ol(07]oLf~9oH@BPeMR^6L4j.7ׄy_{>X`B/;y5^9dCֹ6j}8o)QeWBYCRte턣%0dic)U!s㴡 'M$EvוhRObf?P9ӊ3Q8TjQύxꓝcPha( Y#*?Rg]X`VZx5v]ý%6_NAتi2i-G"/zG1sЏS~!@l룰~pswY鯕z۟^ ;=,3f+e"^&\GK|dYhG|"3y)zʪ`K +f%Ԩ4IX?%[n\b;/6NPg63>Ŋu&钗<++K]L3bFq0+՚~ +ɏ4z{W^J .6߈xQZ[~=y$i2@2UZEetRE;8etAlKmig}j7 8CDNςFI +cJ0&FUszF1p/>ӎs!^ ާ(l4a*v~M5Fpw~?Ix+3獃W/*ߜ\;ϝo b 7كXHљr]^黫Nl6ʞYc$s +]YsdR\ i6Y%. +]Dhӊ^&$Gt-Uf߼efzGu8'BC^0l%BmY)*R)Y]QaG5Az@G޼^r0?eZجsܩCM'5R. RC!7ÁRiD¥v=(97<8X9_0n'U5=H9=yd_ m/M]>:qi_ng^ +-2E Omq F7Yc ْ=[I1rjt$8LO +E򦼐i[\aTw3+ CK[f-{qy9qVyӵm'UZrP82+ kq}$@mҁB "{(y}W\Ԧ=qa1pGqiWͥ b1"Жmj8Ӎq瓙) 7C$GM, $ =[d-: )7 uGNK&cqp> ӎ%xx>M~ıM!/үrˇAH)wr'AV enRAb3>G7|&Y-z[7&BY|{h"E#g쵋!YEwݙiz^)gr0$M]&2#_>~VkFo6;.#o]RΣh zCw5R;W E5HH׭4: ,ԕ̄8P~K09yjW7v6D u@XEOXKZyN"Zd'Ǹ)|$Shf.Es69Em1f^P;w$1! +_;hZ{Gygn#2 +w$Q!0÷pXiK;鐠0Fqsu2}|:Jؐ[v|ȭg<20DI/J + ݀]xgkm񘥒RRQ+ɁǬxto 3O2k8͠heF™Ȕv^~K FzZoXM;O9#ulRYT1``mEE ck.| +!ZAz +3 nG ~GDc`κʡޜ)ل_qo&#Ti11Yծ'e Une1V<\od# L]HRi0#RX\!Ԇ?^lZdfgF۾o(3{m|/YWc0q -ࡨ{Yy߰[I4Vݗvxg{wrE" <W SҼ'%̶@~}'GaY!GN*v2=Ҽ O tPyOR̼kbj*#iW4d +M1BU= JyQϦV;yoY23F"(7t޴>(%[CRS)\Ge9ŚO6avniji驏"qa+Djt7ٯ<~%MR'%f|jQ]uɌF&}XLT6\~WP`kN؊.=wL۸NφMSuo%">'yzkS'r֢Q$fbC:1z\g 'gfp|{uDJNJZluOo)K#Gui +h~!\@vXo9_RgÊ\)~1n94φS1*Ncab"k `:.6F[WԞ#@XotUpӬ҂D#KTr]'Z_I +[oi.6^ NS~QA\p4Ky'Nj~zd _"vk\ڲG:xm4+"`nZ6VK +ѧpSOs t #zVmЕa NIyxi[tTÿonm9E>G_J9*dwP ((ǰ޲~Җn7R"HKLl&2 j4'G^vl)~6b>I[='*L̴CKɎYtlk%Pr!'4ZLy "=Oڔ_"ktEXvIzRd^]wkT!SQK + $+ J_t GJ@[GFzTݞE'V=]# 7\, p|ZW7l+}?"~4{8T}OXttdK+y3ꅆ}lyIIAQS!dqx^XBʅ_':/47RKQզ*^$Q`mhu0~Gڌ\n13W|δ]^2d0o`nҵжQޚc=}En鳮D*d=ߩ/Բ;hgF eޮaUI Z=SRE%wgZ^ ND3F֍ܚ:Wܳ>O$NA&{= +lɜcv G7TDM]"6Yi|Y҉6EԻ9L!|> V>)w\-̱iգl~0TJxw_j6}u9th1-Vvͻ +mfY-ߠ81g5c1šW.9kw&ŸŌ`> +endobj +23 0 obj +<< +/Filter[/FlateDecode] +/Length1 716 +/Length2 4612 +/Length3 533 +/Length 5158 +>> +stream +xeXT}%őAf(NI``QchDQ[@BR<+)qA0b60{8 + & | usgq\s)h t`,cjnG> GxÁF:aa6 +àn5FM,UD#`@_U ±@;CAp?4(+ՅQX/ag} hOEC({>B0 N +`$5.n0Mz(.jP?7gm dd?2v߸o\X;]{Da!N?'ζtSOxX_hKǵ[yy1g`|$.f]`)P,ʬ%ֹi|E)SdŷRc?4^i#EB~*Tj8Q 5,ˇnq'=J 5ܞק7c꧜u5| qƖ`1CWњe7,jӊ25˜. $HZ8iwtf1xGfl)&\0p5@` DM[7%g0xϽ7խh&/xIxSV s \o-oe \Rkܜ!֣ h֒覑ZۮPn:Qe.:Tl;͖%wăuR}{Si)Y~+V}ȯx=`J CGc_EjH}{=L4DG<*n$9#JR pzV™1 K:<S87LJD#Egc$sv0l!فS(ʽsGΩyO8nx&Ilg#Jp_Jtg uK36ls8͹oWtgΞRÑf̗l.FP˝3(X8MX6ϪG]R)r3nv{!*q7:rknʏ%2ny1Q/SNRs %SWo*ɿ/{4JYp= Qf ʹDd]s|r@ӶbfGE!wUg1cY2o}1]ܘ{Nk9C @zLVSb6R\ +L+ʜ`:5M|JsVW +ǝm" +qcJ Ο0r ۊ3H(W6׶JӧةjX PTf1srp,8 jF1=mgN&,=! Fg =[gtU3Mq쭞㔛y7NwS\T;B7xui\ݚrY[wN;zWd!JKgtx<޼>?EU)'?rQ瑒էҗ=e +aOpsd٠mVWK=-ª #4׾*%h՚xۺm:dPa.6!)~}H° ͶW1%92̋禦C #lLPJ~ 89_(oy-ЪjȀP;ܸޔdߘ+ +~[YHdÍ̹vA xG +iM{oq)bѪgHnCXmTiϾa@:29]Pa_6V5NKXmXDOI$17wC]'倵eP~J"䙟b"t—} }4廉G-DA ިf>Ev4I)N65f01W 2YKm.do؟C]%*>`4+޻e`y-^WD<N=:J.9i2h4 ~ݛY˦4M6 +yx{hYLpbh.By RȚ9Sð:g%zo7;(=rw +mwx$yhi?C 󍒴rY<3t_Zo$J빭WqĎV] / HɃYkEd+/p]O B$O}ҽ3>!ByP%K3 "&${h|bYUYk_޶+3KȡSj]ukm.,+`fii_8~gmr-՗ ڱKrhGUʾa0t,3{\IKTh8[yw ?)*2| RuWKG#ߝA2B5!?u^g<ۢ_OCʺEHX2]6|@pT꫸UpvfP$'X llf+~jA4g[%9xӲ0R)P֜1LOGouvlt'& 襛4UBw M}d+Q *a4W)ڞ6v).| v@71Wwak'7wHE +1UtJ|D tZ^v?R Q+Vށ TNyn35-<~CD8W0]ZVֻ*/9M1=ًŢ փ}3Ԕ#ki`e.\#Gj؄sz!E|I~h~Z)N+9X.8[Xf43;ndxtP?򦵾ٌZicU2_o--x +"}Bt5NM;6Y)4Wy*ô{<kwlR,l)'GrH(jsQpd$%Ʉ'$K>ϫYU}Z>> +̼KZq|dg7*:<]'ɏϔ&6f3U?g gyAg[-sR*Ol e(p`Ig9$K*/e[K%iYv 2prGj&8Hb6,+oo~n4:CKd2+yX;ӲY뵩QE;&O=8RaG%ț>a  zǍ`r"b[P+ A%BblP[\Hx{tƜ;w*BG8B֩%Uɗ +TL-y=ӏ$^ZĈF7ˀAs 7kŒV"!,Ue>v|?@:Z"hAB +r>| TfɬiobMb;|/Wz&sn3Egw;ybEv`߈G $9 '\T ,fڀl0k&3yꐠ_n &CG|Q\|BG;h 2G6D&64ㅽETMkƧNj/`12DϟaM{RI>$ׁ;ћ߮=3!i&: F٣)šݵVV]L]m-XRT!Qr)ӀDZ9eQIVI/-9,ʟA@>%Ylfr?Ԏ~W?IL`(yw,7 zI]Cu ҹt .X@gn#E}Ji/?VѲJd*$jGh_Wǭe蟈X!K|ɸk`M@\C\nѮNBk7>0tRYxAPy?D-`H T +endstream +endobj +27 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-301 -250 1164 946] +/FontName/EBENTK+CMBX10 +/ItalicAngle 0 +/StemV 114 +/FontFile 26 0 R +/Flags 4 +>> +endobj +26 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 4645 +/Length3 533 +/Length 5199 +>> +stream +xgTSkQ H/J@)^J I@ +4&bC(#]D@:itHΚΗYm֜s><{Y]7SC\8,ALR\Ran# JHP8&TJK.GAVF,8/<͝CaxH̹ Z($_TC 4Gz#H8 ) D Hu!>^,"\@?ID ]Ƹ~s1wsm4a[Aa|H<@Z#SǡFհnh$W +孍C"LQ;FGbG8ܟZZƷ D[PXm!3|5!*MR(wUC;epduOk41=/Ϣ# =o%_բrǃluכ~Mcwc $tNbxbE )|z~o6kc1̹3CI'S]o#u Yc:ڤí ֙$½l( ﻐgfK] + {KfՂj +5 +.c-@aG"'-\:5+t*9>Đ8c/ BYUrDxGo⺳Cm\ J);z,WB0GhWyb2CMo1,O:UI\Bwjv-zmM Okw;R/w"n^Jɾ?\A>nFH]ҰlŤ0 w|Z)oV8doK+ףv ׏\rd:Yddnfc>^`FvVLDkv~?̈́)vARS;dVG}T`fcK{-(ʅwvWCs,v^ґ(/LԏM14o94'\Z(ICYvqk lfrQxYSGl 7Yj_Ӽ_[ x~:|{*~a6aIsGXi 4e]-Aq]'Ĝ/+D]&c^}C\ibtLjRn͛> +Z1t=T*ߪ.?mb-ۇGk4$Rwjƅ*R805Ҥu]2 W7 Wȶ5?8q* c|XEn 聒hZ_fQ#ˮS^5gO?FXUSr=vviR}S#aLs" 3@L30,~lAyZzg{e;Fo1`E\RoF`aziݣб[5@ _*MVD$k6KB-ibv-TBhDmo%AW܍VRZߕ׌(EZ'{%> IGl+Zɽy%PhNde˛ՈOբW;|cMj[Dwa{f97c0@g]-GSvIc3@(q$6(.V'ĻBCw1=5|貆;FLIPPD*CQZPϳ: d*`Xi_,zg5 +z귮G-{ȃF~T}j`M = EM [!(p]Tq(1vAّRLYLeO@b_+qug;$!p,yבL/RǾj*=/aAPk*?͏jBr\z1^S-]$> ~SY2kí.:AJ;D- lFh:@d*/sظуR:3e\-ΛgOedcyR~%UJ)Zi(l3`+7rxMrsTLv:2g!ъ¡k _CMEkQG~3RYQ*fv_\jPr_EdSR,7Rr<]{AVg_gaƯt-|a}daVkK݄T L8ݰwdI=Ά C# %ܦGAՕP $g_.mW ) E=vNì_j|D`_w}S<njf+g{$ϯxj> }5Bn&As_h )җYuȕ )`-+UWÛU%4B,(4{Ez)ܞ?X(>@;kxXP90s*ԙtCnbv.+fFl77H&z<:ihaqp'M*gE&]HP"m-m!̍x-_ށ}0;)R ٻ^ˌ;mdCdDu58v .Wx{XI&ByW"ߘL+!O,d+$׹ Gd 7^2-"5%Q{7[G7 QэiOb!nKmӇ5ˏp OX5KG!%2.8 8wtIcjj3.h < LS?NEd`^rx%p۹'Xo`;rIUbs#&Щ1Y9|DA(%1%of ;)loB(\9-Ջ,&qj::e4,9Y41;FKBז8&|"9Pr;#3KgT9FH4Zo}DQJgMkڶk\s5n86=,@dSM:x̛8'2]ƍ +bƈH1dqȎ,{1L;{{-4%Tu:bF}\{W0Gr]g#WobxX6u$%ؘ/eȳxP쎈9ZףGTxM'U_?)XFNȘt;GysԻ=݃_v{δ +$ZQ^̲ )h(:ZZzv6A&PVjwM+Ggb8? O(ߏ]n6Lq5s[ V5c׈]gQA,.=ˈD7Wf4)$`s!UAEKc 2jS„͔ +pCmj}z[܂l`RŒPtw{ ݩ+Zķ~tq)gք'x}S*RNΠB@poytEgv}pcJS ~/'T`ֲ.LTg-DMOm%IGK[+Y[`(Wt)؉t<ܐ;WJF]˱Ax;#*PC>[^ӿ{@cbY֛XS:',GIJzBM-SCf)p,`wtKj*!+)+,wǕq@YFgk׏*&Pԩf4M [A(z7.ΡEy1I9f)z)~aCWfEۊ3.Y (ح)ooO\Pһ7+vK^%lܜ-tN4!1B ]Zjl^/qÈbtFκf K{P|Iݑ:$ͳI"g=YItleݓ<_TC(e_׽ =d> >( u) 0,Nؾ[Nz#${t6иDh,izV|5g5|V #Bρ nfG,эy.<=m;cVY{719=H766<j;'t/|3.3x0σ OHOXW +endstream +endobj +30 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-24 -2960 1454 772] +/FontName/CSSXYP+CMEX10 +/ItalicAngle 0 +/StemV 47 +/FontFile 29 0 R +/Flags 4 +>> +endobj +29 0 obj +<< +/Filter[/FlateDecode] +/Length1 886 +/Length2 1710 +/Length3 534 +/Length 2349 +>> +stream +xRy<?edk,%o5dXkeRY;,̌p&J +1i%IRIȒJd~s?|>秵 @b, ` h iG l X#b-`0- +!Z0!.p!2 CԄLn,2rӁ]K%`@! @ĄT93,%M .@gI. Ia1|Ra("Kt(7~lNIV'1 :+ lEq.  +g:sItg 8B\r0@%9rdR~!rnYu_PWCwc"A ƈdb)@bI|" +@L +@H2ʐJ+bÖV98"+dBIlI\[1CE7ϐ $:Ie,b(KkZWlmY($@bME8VL&:&h43^Β"M*[LDS $bm{ϡrrN㟐J^YjGRkcPU=n[%LqO)>F=A\]t99h#ss&輒81Zރmէf4T ѫI#̩u҇[/9؇k1%R1l˩e +iۙj+ȿe& %^]wSvr }Kkiٱ[>(%L \R2z~EA 4uM?GP}i<~:ixb=~㧚0B:u*b `JӋ (rJرCf +N0 S)T}͟&;Xqx%2 5 +ߨ܇^6N볦XH_k5{ݷj~x`WZ!/itũ/OӀG VE/n4$_y\ {̬-Q+VP bQcҁīC*3JbE6MͶ??g$8$*$^!IGvtqwJ^6As= +jQYdŠV:Tv +30gNM35s{W[%AWn{Mـi8xV6io%,?+'>aF/J:0];Y{NS7C>(W+zCOyy#ƗI +aw* (ߩ¸/rJIҸ#Dmg]+K +~IL gjҳOO8beZ2>ad3q9ɒᶸ8ae"pS3g왦)=f B[iS5S7>_ +7]*nw9 g3]yccI'?0ZTZ{ 'zUUꎸƜ53<9=~~xmT4(x@"OT{")X`J@ >-ss袢~JsR}B|ze!(tڛmgn}g DKV͈dȲV[k(eTI| Z8βt3a7/4B*pfϐwQDܬmkx\#0 ҚٶN~D~KhV|֜74U`ƺΝ[pβ;'~4ۄ҂ԕtkql2% +Kû== mY{WknqkMe?U%C#~ (4neJm6EL)~q9@$\~y[Ӂ)DX̤'/T.Ӽmٷ&mni3+xG;!P/3r eg90a +d7몊M:7MfaN/,ݻ<#A | ѕ0s]Z ޼'|ԅw =~UFWGSqe,a- +?Z{ nYy%wY Co4 Ab{a +endstream +endobj +34 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-32 -250 1048 750] +/FontName/PFTUWD+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/FontFile 33 0 R +/Flags 68 +>> +endobj +33 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 1752 +/Length3 533 +/Length 2293 +>> +stream +xk8DZF2(#3 `r% K2f^ c13T4Q!B2m-b"*CQRjMZum_}!cU`Cngu`PQ\/Om{=pdoLAU .K,yLR_\],I')PwJj? )>y62sK{T.[SK(_a,笡(ϖiїG,r% +Ćez>zKMn -R~NZ"{c+l|m˥6R7Qir57E> $/vB_*ˇh.i> +P4z~/!NvដBTiٍU{R6egߑ?3x`NSZ)>꼅[QW>ksuy"UCk#UFw?USLl ^jih? r䣈OYND\M"n*&y|L2<͗[r[7S˯ V!$m'̼#GDX2Y^dx!-`j!G`NHE؞ځuT +?)`$uF +[+v{\ww5hgTryrkKV+޹-vmjb-^-Ֆomv3rfG/͒a"gLH>y ѽVL:ht*[8 0':,dt㊴EKrԻ HtyZ5'窿Os{"=GB8ğ8#/6{(=9jN1_Qo3ꨭAY;'XɶƜ+(;U٭VЊ) vL4Wx^Uf쾾[QILܛ*LoLaf,~Rl3!'/h+Ѣ B%g䏁7|!T&>!5+?K{A|@6wZxX6fR!ZW$%~OxᓱfVcLۦP$AꈊQp^WwM*(pbf #EY6tm2'cbP]瓡Z%+1'c9Cɢ!C~ǹN> +endobj +37 0 obj +<< +/Filter[/FlateDecode] +/Length1 724 +/Length2 1132 +/Length3 533 +/Length 1671 +>> +stream +xSU uLOJu+53Rp 44P03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ !S U[PZZZ4<8Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D?"'Yـ̼ʂTr0SQfB!P!Xh%d+$$0]_QkdkiLjf +榵 +C2 KS=]L , L.-*J+'aL`(V&s͞##5ˁJNaz&CIMXǞ;w\[Žg40њ3;nY($ǝg0eXWҞ1Jԗ]aKuz]XU- ݣ%6 t6,`N|+Kgdq;)yAWpq3z]K&j؟u~x?˰ *wO٭\vwv%|3:YY}|v߿Xd?/ya^:-w^fys[Ӟ|g;} +[ף~m7 {?hr=<ɩ qKݮ<:w}Լ8wÛK3?'lqf>H~I9qŧϞM69}o=[,_JqUl9Y&˩H)n;AۍvCNǏy2`R\=#cGeIC6Xp0zm%2pz,+`-4rˇ6I7o|qmG/gl\_}ªzmSV=(|5p9}T= +SvnQ[).46p0, HIM,*M, +endstream +endobj +41 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-27 -250 1122 750] +/FontName/TAMMEO+CMR7 +/ItalicAngle 0 +/StemV 79 +/FontFile 40 0 R +/Flags 4 +>> +endobj +40 0 obj +<< +/Filter[/FlateDecode] +/Length1 712 +/Length2 2182 +/Length3 533 +/Length 2721 +>> +stream +xy<E!-28ˈ4d/3Mfa%6(ٲJXDD, T-C9u;}y>(8`4MЊBiµH`s*(d , Dp8`.rR:w@վSH%dI[!8,PpFS"pKS ^ <G|@?ɖKJ@jT(2A_=ek5p?7T?[X1MŒD?t +) R4R?Z]hhO&ҰDΔG!Ȋ +4 K A2G}C>bF[v5,L;B+[ g5*!i`-ױֲ$(xаd"%Tjw07GIɸ 9XS+ty}Kb~e*%)yA9ǟշmT=A9ߦNX{fA6VXA[k8md>*;f +whrzB`^v~KXu>iB/4_m0TnG  Xeݱ.-YЀ/\󟢒Rݘ_[Mnʽ/Vx+%A#HRgNW!Mw t46M*['1W$S. 6KZ5f{@(>9*FX4\W>z]ϼ5>^۳l[콐LQ+W)Nn; JyՈ+Z +<˹t/^WOY͹GQx겑.l=D'LzҤܔvM^<y1HZP̻2+ZqLI#TFĬƷ]Vt}6h)Z|:1VgPfH9'iC u[H<3hLsé2)\wLk&yog]7\ߦ2x3㓛/}2m'M".?׍-=Qzdʌt;2V]}nrWM*}1q gzwئ*isヤ,-8{:?]m}|4[FsW0 ϟ/(np9pX$hXE34ìL&?VCEw F[vYPV:KzEMuva=ArS* +w#dЂM\L#0 g*ìX4ODAԗsR oCJ "ly쪑1U,zH=]>?h-=Q4<1~ ~4}+DJ@ ]p:+2{5UfṇⴘGVuvbgInFwDbZC:8$xI?q6iCVMQ7>f<80g9ZsiFp?~lX2 iDip*%cw;W×&MmKC!aDb4 + K@D +endstream +endobj +44 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[0 -250 1171 750] +/FontName/RJRYYM+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/FontFile 43 0 R +/Flags 68 +>> +endobj +43 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 1103 +/Length3 533 +/Length 1639 +>> +stream +xSU uLOJu+53Rp4W2 TURK2\KR --Js ̭LKU9(3=DAY\17(391O7$#5hHrbBp~rfjIcNBHKBPjqjQYjBJfrBRjzf>Uyi +TYjQ1] +`j*ݙSƥ/]膻%悌tbnfN%TA~nAiIjo~JjQT|SS2Kse=Ks2sRt M L n)% +i9ũ`Լt H_mHB$3JB* R |CFE +z@@cŢY暗\XtS~EA-мTOS sc #hriQQj^ 8- eC(5"5iMyy= eye~/ț1gFɡ&+Uq)Ңcs}`b <*1 7NĤgw-E-$xUaë,-Yv可UEӽDv4N;vR>ͯkO/LΓq™c}˲Y.'iKh:$EQfqQ %f(qRqR?n q;U^}Q;gw3u*;a@:"-f,O6}vBχyݿ< V#x|+?4U#+߳ ZU;| =ed_ lV3_-t*Ǧ)._=_bg7=])u[nZpmLvӓ^l=]|rA26eU߿D ǀB5j0 9'5$?7( 5uxJ +endstream +endobj +55 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-30 -250 1026 750] +/FontName/IAEDAF+CMMI12 +/ItalicAngle -14.04 +/StemV 65 +/FontFile 54 0 R +/Flags 68 +>> +endobj +54 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 2695 +/Length3 533 +/Length 3246 +>> +stream +xy<[&Kd+Kw3AXFv!˘1̢19I!K%'%d߷$EB#L@H&`@d" LB$P[: 2C`@6|؀ #$P$ L&Ӡ`Ҽ2)V~*{$:@/%}o?p?7\?c)K>JA2A@g#'$?wM +h@ #P,LE?tFdo~?8TM N`OvZ4]? aQ#QMAf.83\4H'iހ-@#А +D05uDiꈋlƀ:yC%2 ;_yoH pTȕB-÷qHi[Tv\GKLg>R|Q寸j7>6hql[GZ`@Hv;f}/ D / K3>Mwz*iS)vE-֒/-%^(gw ƗtNJڊV*6 ۚguY"7MR60qK-Hk;"i 2QX 1!?2T9=S};W(E$5<,2iA!)_xx*2k:/]@7iSK3KIP~!2PuEo)s{Fjx50nNr=M5.ژέ<S0a$?bދ6m4H/\@:%t-Vf*m_߬S'5]QB ڏMSo̮L`q{(h8au&o4puz^2rnؾH 4XRDqzNbZU['= 5r48Qts|11VLj9r]xizAdгOǹ?V'LQ=/$ϙq vlEhU$RS0=WO |}握ZWUxsajѫ$.3w5Ğ8J $do69 +e6=ZڍӍն%cKiFxîb.sNlRh;&эmʍ$>(ss {t71 \^__-~+w8r!ʴǵ]'4L+qx >ZzvʁG~s97.wSh^/ˢNwźB≑NwC  +{mvg_sB^TFXAy#eEXs;Jx~z2%WU턀UuoL|y7W{kݶ1H5 +<sJh`Og#jпrL $/_V2{>JmP;"TN 0+w~QN1zRnwʪRjnJHes3ˮXУGNeseڠ#L.FMfXC,j"} uQ$t|Ϯ|߾ +Uq a꬚Иak>#g"ܧMgj37 l^j X!ͯ"lGuQ}IruZ'd[dK[~E Nآjf^{]#ӎԙwM7خJV#)۴ tYթՠapn|'s8M[]Tk~!|@܈xs +*5 iu.4}搠n>31UȻ>hv|ڢd2x]B:# +7<N=[ڥ92e3q@Or#i!gsgϏ~H|P;qVE/ o +`.7=tQǘx7>yS&-r]y3*49{Ӈ^i;GNX2SO}wUT-A{tj򰄕C(LPY230L^6_ +t ׳jBUP-̘hL1b4Zp\Ez.hw!{BLHVw87V3 aɸ؊G,o_[ă8mߺ_b/ +/]**pq? =VhxIiۂOrZwc"[*K0S>-/fqDLy{Y ڤ9;GB1,^zO> +endobj +58 0 obj +<< +/Filter[/FlateDecode] +/Length1 728 +/Length2 1814 +/Length3 533 +/Length 2357 +>> +stream +x{8T%)tr2"F*RƬ5c1fD3B&r'Q)Юv))&JI{<~hz@F Ġ(%{`1#ttpLȆt"ƀ(^KS3KLqo b$"AMYf$8_wymVF-\/׌Gc+|,',1'Ts=7 {AfrYyً_]5ZQves< X+ _IAxa}ltZm/Ty!Deɶ+VԨE ) dt%&4ⲣ'Y䮉/DR~лm_>.J.y־C6XU Ϯn\Su`]372;4#{ӿk^e<™1[k2.rDr(EEN +n9_^| ?>>g+.]{uў{'?]֟ײwM~8xhsSnhjC=%MȡU Gfnpa2, +_^@BD&A#2Cu +endstream +endobj +63 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-4 -235 731 800] +/FontName/RKAXVR+CMTT10 +/ItalicAngle 0 +/StemV 69 +/FontFile 62 0 R +/Flags 4 +>> +endobj +62 0 obj +<< +/Filter[/FlateDecode] +/Length1 719 +/Length2 10301 +/Length3 533 +/Length 10859 +>> +stream +xUTѶq܃q qwܝl4wwwIpkpws=~o=V=Ԝ}5kꡨɿ2ٛ휘ؘ +jjl6fVV1$jjqN `D DB;C,,tPqDmA+Sc;% @ + Tq#@̘fVN?dJ9;gq')=/; dĢhw>_c ׿K9(ouc[+P:8; {3ߥ)̬m*dlce*jga+e(e2jdj p8ٙ;EE^TKCU[9;?g?+7.yoIڙڛYYŤ!fTbbnL& ;' 9d%<fM!?os@ 7) 2+a9 ]Kq:r^sW5J5 'V1_9o# d{LtLdE#fdFprKڃ7SK-]XҖ*S41q ە%ܕaAn_y`$QȝЎR'e㈩KFz6BgF{ɐ,,xd0# RjL^RytgP?(;l.$sc'BkФǒ_N%¼h!{UoI/u$;f6TW4z|$Ep-[Mp>vmS_5CYՍgv,]aXnM9[C07flTZFSz^j3Ź&jcDQ À'va0|ƚ` 1KRP3- lvO⣊=6lpPY"`ʪu8?S +;;r931 t-) ʛȷBc,1{꩗ A xmוS#(+l:3\ =]@Հ`VܝNdŇm(ܐ{Ŷc8w2uX9WU,~^U![oX{X8) +.X%{E:O s [SHxmԬV~St$շpjOFaya kYt}(¦bM<سLILYE +$dIKt n Sfd6ZcͤۅOiRiF_ܿ㕦bH8! jŭ'``^HRferAe'+ŷ h|'/QUXs V{xQ`lǁXgD2T]F*/Ī=k4P3Ի" +4 +A:*䗦;6?/}oT&`aggT!^T zIqm9OC_{rC*pЎ‚B}(z(>4XkS;sfH Q}p˄*,:+$`̤EEx1KB1ލBαT  4Zbƞp +WD==)4]I}IACCU"EmRES(6H/GU@"Ćƭ̈́V)dm4H\d xi,קPP{y ٘/=$19E~4kXoQŧlΟF,YFI̓wJ@y=p''4FGd4tw_0h^յKyMʞYZee!~tEG{*y@p-*OlK?aPLYܙylP#Br-ƮZh<@LZ6 #:=O I@w TKLMi8[ĆToKd*d%qVNO8U^{>~[܊4^ؘ> [2xaK%ܪKf/4ᛅr(b*llS>K˛0 >$4fh.(ExwhAHGqһ/C7Fᬺ mޠ]8nsH3]4Xi>zi[6vl@#R '@+GbGy@ `WFȼ!/h +k[vV R-BP/!E8ja޽9Vj>X#9$t: r%:y;m-ƞH/pFY:I#Aď,;WWs^*tЊ=&>[޻SQ8=cPҒMA +\Rc,ڳ&p Yc$4G婀i`-H &F=DGA!9:_ K-A]2wo c]rpl'#_1d&|&b:DCnqq~ <ۺZ轱PcD!Q5KlC1Јf]*sĿK@/)"FuZ_ T<HZtXTG">$ZHr+}Fb3N_T`H|0\q;<&hB`f٩C'2Av[T"T6\n TK1fLN399mnnqgCGz*0aע+P)3dtSuy _(' wV<}{K`pÄROXWwV ].6umA +/ 9Ԟώ/+):^MMSBʭw-dZ}1q_L,-U9';5d.`毲ب9'6D& ! h7,ˆE"~WZ-EW3^ik_l1vÉ/M ?,`kArNqFt5 ڢּIf2??:E78$qBb\7[AsYo7 rXmV MoVy'-d3( gg.U;K/V' nzo٘/W7䵗X?HlnYZSŒ2tb?2 Ѩ`< E'GnKn'RjG`Ќ{V+ۺH?|Z%?)~bN;xJZ񲗥|]("1=j4"*jtVlgڪpYU&N"ÉzDe: )=p$ 'n=L+36#RLŵkĶduS?Yۗ 5_uޮ5? *܌Un`{h<G*(uz%'Z'T]  + 0sh=xQpR2CJy$h 㤓K +[?4rJ3І'K<6R'>K)T@umFif)mkxޤ徢etfQZD<>^ԃ#fB&^dCfM%z{mo[mWV"sISp +q%2s(\1EN9ч^hO*'XM6(4VLG>~Wʊ\4o~6,''a?;/RfPHpRuj.5xҤ;-}"3j؊njԞUqW^yLp Ӭ?]Ӝ a8`UXF CT$(=q0t> VQ qX6#4] ˝n_tĞI |%͕뾄 h>=mP2-B*\"90{#ȶV% q{Ah!.16ʞJℽI^wfnX ekv0n]nГ',3a4zgNAdm3fЊo6̡ZRz]9ӳ&~BIg?0 0O{j~AԿ3ރ[y]ф^QsS +ͣ:%_;~C)`ԠFeзm!eVOi3A3z -!sr54]QgMTB5+ VY&y%3GظJYqqȂO?0ͭ'P(kzM3 |Zo BptJO'6d:."`Pr8Z@:3q1ϚfS(^ܯ:@ҘMV:1(Ϙ{n˪|nU9NiKokB-5pY9P4 qlc?eK\:9Y.Xz3¦a˕ "ȹF$7,81ΣtB2VRlDGR.>-=tJ*OuSF*:$*6Rŧ YBUZIlN:v&@sx9G[ b" yna&WPevw՞8Oo!YO :=d'v<2axZ}iן2Rn̹5\nkdӈԯ|[:Li,b RYt)]Q$6Gz$Nsip Of+#k(`.wg |ǩ 2:YJBR%mSуr` RMhfP _}c>TaO]aKSNxNw)"fԽoE<.GB`PQET e 4ػ6PYiA.4~JM`褤hOtw tΜ n?sZ64z?'9HȨnG21!Ҧ-?UOQ D@&JK[tlIL"M3la nF_-[3GRm|r#V@KD`rFV%sMq]5P$XRBquVtE "KIӧ,r \CͶr"8a1RW^3Ud Mpwn/0a)Kdwék9Iy՜D6̘ҟ8e{Q5)(<9J0!?a!kVf$`QRXuǯ1f+d (,[Kۜ~NxOǐ[r0Ek/[^Ų>:氮;K5$n2JRaQ Qp:,#ѥ'kŜ/FbЦv@~Q@@Ft r?jC6C.zZL,z^7QVVhZ}Yԟ"< pqĎ}#|381y -vX{}$Vy-q(3I1OơW.L orD4/)PyjcƱWF EXdf!T ?ù}ޟwzԞ̉\Ú*4;(y J7sN/{ zEC(<`C8M/tdȪ/KEmpPw + 3l@d!]"9{襮ye_Γo[}x pLt |!`A9L|a o nDqH$ܨh?3,6`+R9 IM"6FF6o1D'O'Hcڌ0lI :6}$Hc%9a,i9 6Iݫx)s'qN{c~] lRg 昮 :Vr=_ahB(48*t}:餠} =H'B15,0F,c=+opw~Ɗa+}VpYͬ,NnRRÆucWNv#kd,Wk~s|Qar)^!H THR"uiM +W&P>gyh|AE``l(qmru5cj3i[' |qC7vqSv%{ŜCxy6\ ``,EZ[t:8q'e-8T3*A%9ZcE~ښO59R +g.).k bSn%aģ|&%x"Y%AbQFg:(zS pgH|jw+'ρdA@>k7B++dLheh獆 +<-MѮnzZA嵪kDIxE">fV9l[U(0|.v+m9 s[5 t~w.hrfE>đeE$*5kt ހ& eBc#S$M*%Vry7LL T#4Cgr̯܎ MkFdM+8l T $'mAGH2"(3ЗlW ##Hb_M}FuƄaJ2"H7/t2Z?~h+tVN ,СT4Gy^W1TpL$UvO8>NJܩ}),>iw| XFmxoᏞp؇tgTgq:s^; )97WuB?cW|K@lNpUfqO%0D[H +3=!Ci8"AQÓ, ]Wކ&U7אHnM{BcJCͅ+ +uJaDԊfc˺g|4O +LgY`jSŰf!O*p(>[)[ugr[9֝r yw'Si +O2cD"4M\]qC>]^P톄@E %ph]Zmtۗ+`SkͯmEZ5xPSZt=y!Vi ƎI"><-H$h voo 5"&o+ZܧNW71W=g奞tusϦ^:@PR`DǙ| "ݢlUXÕK^ImɉBl\OQU +ç46B=kE< p ,1Dۦ]v +aF^(Ә8oyK^ ˻}d"FcAaYPxzNԓό=n)?Um oi1[n~w2?T=2j1`iv_޸1 +VsWCK]DUU4Kz>$A/~4GPPPՔCAzvz@Oڀ!Nk$_ +endstream +endobj +90 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-15 -951 1252 782] +/FontName/CQTQCY+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/FontFile 89 0 R +/Flags 68 +>> +endobj +89 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 599 +/Length3 533 +/Length 1109 +>> +stream +xSU uLOJu+53Rp 4W03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ A!S U[PZZZ4<6Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D90$9Rɀ̼ʂTj0RQfB!P!Xh%d+$$0_Q LC +FF +F +C2 KS=]L , ɥEEy%0 ԊdsD3ud&|9pU)|׉s77Rd(wirkSsk|^1=6Zsas_y2-3%^ Jړ}9_+l5_ ?ܛ%a{TĆ6ႮԦ,؉v3k02<[RZlez_ 6n? qܸs)_Ǵ3٩F&dL淖g2)D^c]Q,'$'Z㛾 l>uy;Mwָhl49"K]9h\8?Lj#oY~8qo{ jVf4HOc_s&z򏲫۽;|]}xNezesC&Ꝧ[֭fS!ES:ZK8sJhOOʝv2+ìRZޖ(ynY҇3 +=m^un)[TZbeQ9E%E\\w +endstream +endobj +317 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-62 -250 1123 750] +/FontName/EVJXTH+CMSL10 +/ItalicAngle -9.46 +/StemV 79 +/FontFile 316 0 R +/Flags 68 +>> +endobj +316 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 5038 +/Length3 533 +/Length 5592 +>> +stream +xUT\ۖqw N + +wwww¥@p 4@pNsoK~{s@!vȻ8@@0@FMG0d< V0 " R^v>0/07@jg0˰H9C<6V.5+=9 j@W<O7 ` ` `pb +K{ |0?s).N~0Sy53뿡{VP'8\ݼ`+w/85 j#bpyP_X +Z9yB!.࿃<O N9}eC]EؿVP/5_<. |oɹظ.v ¿SIKps87 _z.Pw/,K@HOs3<?k[ _ lb(;ۥEKaBBLAX4E+9Ee㝻6R$pЉQj#(J 1t6ښr }xE!߸];'|BYEBH}U:p,ϐ:DmVK0d +cz;®!X8ʶq.f3 Ϫ\3H#3 I=+OEFԬ^4\T@vt Iu{}z.ԮlWp"v4`wsجIZet汝Wl$uzIȎt5۞ۨ^G%}Trg_™o 2Dv>}Bu| ѽJ(j2Lҭ1Ѩ8,Wv;w8]1^e|Y?kъ=(`WuI5n\vo%#b]@򵍡SC::99R+k3"$؋/C$1ƯM{ +d +?dnw@2ƪ fŊswY&Iuxe9Hx" P_AC| P_rv;߿i8sCI[&eW7;$ 2hOuƧ%#h r +A_: K0M1M0?6"7_4haݟgT=A[lڈc.ޫMvգ3<=*+t0rdL!.6*Φhك/AΘ6!",xgEztW޸ptӶ?'ffb U`δh0$Z#ۓa^ =09m.r[ʠ@4:FɕmU/6ihҺ&ϓZ~u-O6O*GrKlgVR8ȿh)?L.vp)1FY"Kk{'Dr_= qbi\.PO%r,u8߁mI7u=~2͗n)gP"qiKκ[]uw1{962I HWܛ*z@ih|?,>$@ qΩ24wT$\Sd#$Bȭ7\/u-ƨsO͸j7|:}ڤ [DO EqN|m[X9dxl]45K&$`}!k:mAkŒ Cܺ^`zQs%8T y}0*7EoH؆V5ᅆ cKZ1Pr—:a݅SPK9<.)nۗn+JG}~g=ϼf+{ELAy3qX2·F,pStajߝ3Eɉc9"61AkWėyX{$GG/+>)g}["መu?J)dM^җ6_U$ :\a^6U?IylOtͤ6SI$R&s>-͌c{LITB}NVx}Jh?TvK%c +Qm`!7gjKZW@P B,{A!Չatd9Jo$G>:9S1PgrRiYVJg/BdLfl- d}u+y);JN: :JוG"Bu|=ƩBvxj >0TcokDiۣ>1Vi-_w7L5TB֬Dfp"^e]Wģ~=q?,^i ^a=et+\1Jb7HGpjfUJ|1m6viŐ.iG} +#)ם?cM,9ԣY{u,(Et:ԋւ*&VXE4b4}S] g5(u-~NQ:ap >O7Zq'J,Xׅ-ɟh"kz0p36w}CXAf!parCD7}ůęRIO霬^Q­H㚇NA`og*~Qᒭ3FaT):bԤ<*=R{cF-S8%@3`YgX\㣨`~I>ƃzyTɋDLtFcc O>7 ym*~a@2˽7R@Z嚟8d>X ŏ,o?xum_՛Z2"p{f!5J㖪\#ߋ4Q؎6AGbg4(Bp176vE.>H-0mΔDrJ6κ V27rDd;uó?֛Z!<̠baտ'Oa U]t`QMyOS$;, ָ?7(ZAn<Ǭ{>-&w"ۃAd JOz/],VJM7 +i_)у~t6Ouֆ3l_.ߌwܥ|';SgM6i"-H%(.w'3uhr*F?dVxCЇZH (|6]A۬A;FSj\@Tû +_oeH +ʲсsurZ֮BJ TZ +Es+wqa-nFx|TArMtIQH _φy)7hNo z-tu +aLy:Ä!{,״Z.?0mB<)N?Ҵt O48b,jRݞ+dDJSTYC0tR\ʾMckQB)as".j-8|q3ʭ 4WZGe:;%H+F弼["eOPmfQ'M<Fa)FUfJecɚ~ d]m +AW󠍁W:ǰڗL#jLˆYs| hwKI('=+ :(QyJ#I'8JE't8~QOJ*|)O +-XS<+A@LҜtW?v8涝/qцL|q0FG>bq" mJz=dX%$ZCC`X}L!i>劉ҫeM15M@W +VoQaB F%RloD%SDǾjJ2|fM4i1̠lhVZ4rQQ>emQBԈ_>@A.ā!*5^X oUx^~.6-L;xvJxB~%[LM uX_G@bdG\щyz 9>ث:M;H=J2ub8džC$x_s,^Ĵ=5fztogU(pkqRL#ˢ m-F ~'圕^vDVj4B42O2rFɮt?os:Ǵ6bVZf\6<|냍 jզ0>tG݂о߁Ң鱿[OzM |,aQ|Kqw,xB]PRp֚2kf](Ϣ6GyQe j$?a@T­R0&, $p|FW +?P qhEJ|^>6ؾ2 m;{.bo=\kMh,ص!ǣ< 9s6-nL,]bEii=ٺY/N" 7Ł:_p{ |cY,4?TD3N K>vO|)X呣F yc.=h|B+v8Ҟn6G'[1HMҜ;?F5v}̽]Z.G<%-CSo[/{R:U_Ci,q78p]P8ͲUn@lYL,ʪd ߅yV׾ O +F̈#( "Ň -gb3՞C*.kذsy ?Vw.5l62 2 +3;@N/}wz +2_i@~n/KG rE` +*;GR 9Pu VΈ&aL!Ĕeڑzhsgr~tczEm _`4K5dw@cO`D04o!`Bj7>dņRc.dmn.XEQO>U͑-#@X¬;FYT>hGn?fGgH7\69]_J +ILBB)j P>>,krژ|ڧ54 TnO$/AI;ْ?D_iyjIh͚ǟj1[1hFw@_6ͥeG(^80 >KzVTr//?`:[y8b` +endstream +endobj +1 0 obj +<< +/Creator( TeX output 2008.06.15:1852) +/Producer(dvipdfm 0.13.2c, Copyright \251 1998, by Mark A. Wicks) +/CreationDate(D:20080615185349-05'00') +>> +endobj +5 0 obj +<< +/Type/Page +/Resources 6 0 R +/Contents[17 0 R 4 0 R 18 0 R 19 0 R] +/Parent 322 0 R +>> +endobj +21 0 obj +<< +/Type/Page +/Resources 22 0 R +/Contents[17 0 R 4 0 R 46 0 R 19 0 R] +/Parent 322 0 R +>> +endobj +48 0 obj +<< +/Type/Page +/Resources 49 0 R +/Contents[17 0 R 4 0 R 50 0 R 19 0 R] +/Parent 322 0 R +>> +endobj +52 0 obj +<< +/Type/Page +/Resources 53 0 R +/Contents[17 0 R 4 0 R 65 0 R 19 0 R] +/Parent 322 0 R +>> +endobj +322 0 obj +<< +/Type/Pages +/Count 4 +/Kids[5 0 R 21 0 R 48 0 R 52 0 R] +/Parent 321 0 R +>> +endobj +67 0 obj +<< +/Type/Page +/Resources 68 0 R +/Contents[17 0 R 4 0 R 69 0 R 19 0 R] +/Parent 323 0 R +>> +endobj +71 0 obj +<< +/Type/Page +/Resources 72 0 R +/Contents[17 0 R 4 0 R 73 0 R 19 0 R] +/Parent 323 0 R +>> +endobj +75 0 obj +<< +/Type/Page +/Resources 76 0 R +/Contents[17 0 R 4 0 R 77 0 R 19 0 R] +/Parent 323 0 R +>> +endobj +79 0 obj +<< +/Type/Page +/Resources 80 0 R +/Contents[17 0 R 4 0 R 81 0 R 19 0 R] +/Parent 323 0 R +>> +endobj +323 0 obj +<< +/Type/Pages +/Count 4 +/Kids[67 0 R 71 0 R 75 0 R 79 0 R] +/Parent 321 0 R +>> +endobj +83 0 obj +<< +/Type/Page +/Resources 84 0 R +/Contents[17 0 R 4 0 R 85 0 R 19 0 R] +/Parent 324 0 R +>> +endobj +87 0 obj +<< +/Type/Page +/Resources 88 0 R +/Contents[17 0 R 4 0 R 92 0 R 19 0 R] +/Parent 324 0 R +>> +endobj +94 0 obj +<< +/Type/Page +/Resources 95 0 R +/Contents[17 0 R 4 0 R 96 0 R 19 0 R] +/Parent 324 0 R +>> +endobj +98 0 obj +<< +/Type/Page +/Resources 99 0 R +/Contents[17 0 R 4 0 R 100 0 R 19 0 R] +/Parent 324 0 R +>> +endobj +324 0 obj +<< +/Type/Pages +/Count 4 +/Kids[83 0 R 87 0 R 94 0 R 98 0 R] +/Parent 321 0 R +>> +endobj +102 0 obj +<< +/Type/Page +/Resources 103 0 R +/Contents[17 0 R 4 0 R 104 0 R 19 0 R] +/Parent 325 0 R +>> +endobj +106 0 obj +<< +/Type/Page +/Resources 107 0 R +/Contents[17 0 R 4 0 R 108 0 R 19 0 R] +/Parent 325 0 R +>> +endobj +110 0 obj +<< +/Type/Page +/Resources 111 0 R +/Contents[17 0 R 4 0 R 112 0 R 19 0 R] +/Parent 325 0 R +>> +endobj +114 0 obj +<< +/Type/Page +/Resources 115 0 R +/Contents[17 0 R 4 0 R 116 0 R 19 0 R] +/Parent 325 0 R +>> +endobj +325 0 obj +<< +/Type/Pages +/Count 4 +/Kids[102 0 R 106 0 R 110 0 R 114 0 R] +/Parent 321 0 R +>> +endobj +321 0 obj +<< +/Type/Pages +/Count 16 +/Kids[322 0 R 323 0 R 324 0 R 325 0 R] +/Parent 3 0 R +>> +endobj +118 0 obj +<< +/Type/Page +/Resources 119 0 R +/Contents[17 0 R 4 0 R 120 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +122 0 obj +<< +/Type/Page +/Resources 123 0 R +/Contents[17 0 R 4 0 R 124 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +126 0 obj +<< +/Type/Page +/Resources 127 0 R +/Contents[17 0 R 4 0 R 128 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +130 0 obj +<< +/Type/Page +/Resources 131 0 R +/Contents[17 0 R 4 0 R 132 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +327 0 obj +<< +/Type/Pages +/Count 4 +/Kids[118 0 R 122 0 R 126 0 R 130 0 R] +/Parent 326 0 R +>> +endobj +134 0 obj +<< +/Type/Page +/Resources 135 0 R +/Contents[17 0 R 4 0 R 136 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +138 0 obj +<< +/Type/Page +/Resources 139 0 R +/Contents[17 0 R 4 0 R 140 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +142 0 obj +<< +/Type/Page +/Resources 143 0 R +/Contents[17 0 R 4 0 R 144 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +146 0 obj +<< +/Type/Page +/Resources 147 0 R +/Contents[17 0 R 4 0 R 148 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +328 0 obj +<< +/Type/Pages +/Count 4 +/Kids[134 0 R 138 0 R 142 0 R 146 0 R] +/Parent 326 0 R +>> +endobj +150 0 obj +<< +/Type/Page +/Resources 151 0 R +/Contents[17 0 R 4 0 R 152 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +154 0 obj +<< +/Type/Page +/Resources 155 0 R +/Contents[17 0 R 4 0 R 156 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +158 0 obj +<< +/Type/Page +/Resources 159 0 R +/Contents[17 0 R 4 0 R 160 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +162 0 obj +<< +/Type/Page +/Resources 163 0 R +/Contents[17 0 R 4 0 R 164 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +329 0 obj +<< +/Type/Pages +/Count 4 +/Kids[150 0 R 154 0 R 158 0 R 162 0 R] +/Parent 326 0 R +>> +endobj +166 0 obj +<< +/Type/Page +/Resources 167 0 R +/Contents[17 0 R 4 0 R 168 0 R 19 0 R] +/Parent 330 0 R +>> +endobj +170 0 obj +<< +/Type/Page +/Resources 171 0 R +/Contents[17 0 R 4 0 R 172 0 R 19 0 R] +/Parent 330 0 R +>> +endobj +174 0 obj +<< +/Type/Page +/Resources 175 0 R +/Contents[17 0 R 4 0 R 176 0 R 19 0 R] +/Parent 330 0 R +>> +endobj +178 0 obj +<< +/Type/Page +/Resources 179 0 R +/Contents[17 0 R 4 0 R 180 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +182 0 obj +<< +/Type/Page +/Resources 183 0 R +/Contents[17 0 R 4 0 R 184 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +331 0 obj +<< +/Type/Pages +/Count 2 +/Kids[178 0 R 182 0 R] +/Parent 330 0 R +>> +endobj +330 0 obj +<< +/Type/Pages +/Count 5 +/Kids[166 0 R 170 0 R 174 0 R 331 0 R] +/Parent 326 0 R +>> +endobj +326 0 obj +<< +/Type/Pages +/Count 17 +/Kids[327 0 R 328 0 R 329 0 R 330 0 R] +/Parent 3 0 R +>> +endobj +186 0 obj +<< +/Type/Page +/Resources 187 0 R +/Contents[17 0 R 4 0 R 188 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +190 0 obj +<< +/Type/Page +/Resources 191 0 R +/Contents[17 0 R 4 0 R 192 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +194 0 obj +<< +/Type/Page +/Resources 195 0 R +/Contents[17 0 R 4 0 R 196 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +198 0 obj +<< +/Type/Page +/Resources 199 0 R +/Contents[17 0 R 4 0 R 200 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +333 0 obj +<< +/Type/Pages +/Count 4 +/Kids[186 0 R 190 0 R 194 0 R 198 0 R] +/Parent 332 0 R +>> +endobj +202 0 obj +<< +/Type/Page +/Resources 203 0 R +/Contents[17 0 R 4 0 R 204 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +206 0 obj +<< +/Type/Page +/Resources 207 0 R +/Contents[17 0 R 4 0 R 208 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +210 0 obj +<< +/Type/Page +/Resources 211 0 R +/Contents[17 0 R 4 0 R 212 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +214 0 obj +<< +/Type/Page +/Resources 215 0 R +/Contents[17 0 R 4 0 R 216 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +334 0 obj +<< +/Type/Pages +/Count 4 +/Kids[202 0 R 206 0 R 210 0 R 214 0 R] +/Parent 332 0 R +>> +endobj +218 0 obj +<< +/Type/Page +/Resources 219 0 R +/Contents[17 0 R 4 0 R 220 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +222 0 obj +<< +/Type/Page +/Resources 223 0 R +/Contents[17 0 R 4 0 R 224 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +226 0 obj +<< +/Type/Page +/Resources 227 0 R +/Contents[17 0 R 4 0 R 228 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +230 0 obj +<< +/Type/Page +/Resources 231 0 R +/Contents[17 0 R 4 0 R 232 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +335 0 obj +<< +/Type/Pages +/Count 4 +/Kids[218 0 R 222 0 R 226 0 R 230 0 R] +/Parent 332 0 R +>> +endobj +234 0 obj +<< +/Type/Page +/Resources 235 0 R +/Contents[17 0 R 4 0 R 236 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +238 0 obj +<< +/Type/Page +/Resources 239 0 R +/Contents[17 0 R 4 0 R 240 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +242 0 obj +<< +/Type/Page +/Resources 243 0 R +/Contents[17 0 R 4 0 R 244 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +246 0 obj +<< +/Type/Page +/Resources 247 0 R +/Contents[17 0 R 4 0 R 248 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +336 0 obj +<< +/Type/Pages +/Count 4 +/Kids[234 0 R 238 0 R 242 0 R 246 0 R] +/Parent 332 0 R +>> +endobj +332 0 obj +<< +/Type/Pages +/Count 16 +/Kids[333 0 R 334 0 R 335 0 R 336 0 R] +/Parent 3 0 R +>> +endobj +250 0 obj +<< +/Type/Page +/Resources 251 0 R +/Contents[17 0 R 4 0 R 252 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +254 0 obj +<< +/Type/Page +/Resources 255 0 R +/Contents[17 0 R 4 0 R 256 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +258 0 obj +<< +/Type/Page +/Resources 259 0 R +/Contents[17 0 R 4 0 R 260 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +262 0 obj +<< +/Type/Page +/Resources 263 0 R +/Contents[17 0 R 4 0 R 264 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +338 0 obj +<< +/Type/Pages +/Count 4 +/Kids[250 0 R 254 0 R 258 0 R 262 0 R] +/Parent 337 0 R +>> +endobj +266 0 obj +<< +/Type/Page +/Resources 267 0 R +/Contents[17 0 R 4 0 R 268 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +270 0 obj +<< +/Type/Page +/Resources 271 0 R +/Contents[17 0 R 4 0 R 272 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +274 0 obj +<< +/Type/Page +/Resources 275 0 R +/Contents[17 0 R 4 0 R 276 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +278 0 obj +<< +/Type/Page +/Resources 279 0 R +/Contents[17 0 R 4 0 R 280 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +339 0 obj +<< +/Type/Pages +/Count 4 +/Kids[266 0 R 270 0 R 274 0 R 278 0 R] +/Parent 337 0 R +>> +endobj +282 0 obj +<< +/Type/Page +/Resources 283 0 R +/Contents[17 0 R 4 0 R 284 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +286 0 obj +<< +/Type/Page +/Resources 287 0 R +/Contents[17 0 R 4 0 R 288 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +290 0 obj +<< +/Type/Page +/Resources 291 0 R +/Contents[17 0 R 4 0 R 292 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +294 0 obj +<< +/Type/Page +/Resources 295 0 R +/Contents[17 0 R 4 0 R 296 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +340 0 obj +<< +/Type/Pages +/Count 4 +/Kids[282 0 R 286 0 R 290 0 R 294 0 R] +/Parent 337 0 R +>> +endobj +298 0 obj +<< +/Type/Page +/Resources 299 0 R +/Contents[17 0 R 4 0 R 300 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +302 0 obj +<< +/Type/Page +/Resources 303 0 R +/Contents[17 0 R 4 0 R 304 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +306 0 obj +<< +/Type/Page +/Resources 307 0 R +/Contents[17 0 R 4 0 R 308 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +310 0 obj +<< +/Type/Page +/Resources 311 0 R +/Contents[17 0 R 4 0 R 312 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +314 0 obj +<< +/Type/Page +/Resources 315 0 R +/Contents[17 0 R 4 0 R 319 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +342 0 obj +<< +/Type/Pages +/Count 2 +/Kids[310 0 R 314 0 R] +/Parent 341 0 R +>> +endobj +341 0 obj +<< +/Type/Pages +/Count 5 +/Kids[298 0 R 302 0 R 306 0 R 342 0 R] +/Parent 337 0 R +>> +endobj +337 0 obj +<< +/Type/Pages +/Count 17 +/Kids[338 0 R 339 0 R 340 0 R 341 0 R] +/Parent 3 0 R +>> +endobj +3 0 obj +<< +/Type/Pages +/Count 66 +/Kids[321 0 R 326 0 R 332 0 R 337 0 R] +/MediaBox[0 0 595 842] +>> +endobj +17 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +19 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +4 0 obj +<< +/Length 33 +>> +stream +1.00028 0 0 1.00028 72 769.82 cm +endstream +endobj +343 0 obj +<< +>> +endobj +344 0 obj +null +endobj +345 0 obj +<< +>> +endobj +2 0 obj +<< +/Type/Catalog +/Pages 3 0 R +/Outlines 343 0 R +/Threads 344 0 R +/Names 345 0 R +>> +endobj +xref +0 346 +0000000000 65535 f +0000147560 00000 n +0000157299 00000 n +0000156944 00000 n +0000157149 00000 n +0000147724 00000 n +0000004048 00000 n +0000000009 00000 n +0000080116 00000 n +0000079932 00000 n +0000000913 00000 n +0000084953 00000 n +0000084767 00000 n +0000001906 00000 n +0000090076 00000 n +0000089888 00000 n +0000002823 00000 n +0000157049 00000 n +0000003740 00000 n +0000157099 00000 n +0000003993 00000 n +0000147827 00000 n +0000014700 00000 n +0000099888 00000 n +0000099699 00000 n +0000004109 00000 n +0000105350 00000 n +0000105160 00000 n +0000005055 00000 n +0000110852 00000 n +0000110663 00000 n +0000005991 00000 n +0000006967 00000 n +0000113509 00000 n +0000113315 00000 n +0000007921 00000 n +0000008867 00000 n +0000116111 00000 n +0000115916 00000 n +0000010483 00000 n +0000118082 00000 n +0000117896 00000 n +0000011434 00000 n +0000121108 00000 n +0000120917 00000 n +0000012398 00000 n +0000013393 00000 n +0000014589 00000 n +0000147932 00000 n +0000015756 00000 n +0000014762 00000 n +0000015656 00000 n +0000148037 00000 n +0000021476 00000 n +0000123055 00000 n +0000122861 00000 n +0000015818 00000 n +0000016789 00000 n +0000126610 00000 n +0000126415 00000 n +0000017696 00000 n +0000018678 00000 n +0000129267 00000 n +0000129081 00000 n +0000019655 00000 n +0000020400 00000 n +0000021352 00000 n +0000148236 00000 n +0000021895 00000 n +0000021538 00000 n +0000021850 00000 n +0000148341 00000 n +0000022910 00000 n +0000021957 00000 n +0000022786 00000 n +0000148446 00000 n +0000024211 00000 n +0000022972 00000 n +0000024087 00000 n +0000148551 00000 n +0000024676 00000 n +0000024273 00000 n +0000024631 00000 n +0000148751 00000 n +0000025911 00000 n +0000024738 00000 n +0000025775 00000 n +0000148856 00000 n +0000028034 00000 n +0000140436 00000 n +0000140242 00000 n +0000025973 00000 n +0000026983 00000 n +0000027898 00000 n +0000148961 00000 n +0000028790 00000 n +0000028096 00000 n +0000028745 00000 n +0000149066 00000 n +0000029509 00000 n +0000028852 00000 n +0000029463 00000 n +0000149267 00000 n +0000029967 00000 n +0000029572 00000 n +0000029921 00000 n +0000149375 00000 n +0000031054 00000 n +0000030031 00000 n +0000030929 00000 n +0000149483 00000 n +0000032397 00000 n +0000031118 00000 n +0000032260 00000 n +0000149591 00000 n +0000033147 00000 n +0000032461 00000 n +0000033101 00000 n +0000149896 00000 n +0000033906 00000 n +0000033211 00000 n +0000033860 00000 n +0000150004 00000 n +0000034516 00000 n +0000033970 00000 n +0000034470 00000 n +0000150112 00000 n +0000035766 00000 n +0000034580 00000 n +0000035641 00000 n +0000150220 00000 n +0000036226 00000 n +0000035830 00000 n +0000036180 00000 n +0000150427 00000 n +0000037365 00000 n +0000036290 00000 n +0000037228 00000 n +0000150535 00000 n +0000038833 00000 n +0000037429 00000 n +0000038696 00000 n +0000150643 00000 n +0000039296 00000 n +0000038897 00000 n +0000039250 00000 n +0000150751 00000 n +0000040590 00000 n +0000039360 00000 n +0000040453 00000 n +0000150958 00000 n +0000041793 00000 n +0000040654 00000 n +0000041656 00000 n +0000151066 00000 n +0000042543 00000 n +0000041857 00000 n +0000042497 00000 n +0000151174 00000 n +0000043276 00000 n +0000042607 00000 n +0000043230 00000 n +0000151282 00000 n +0000043724 00000 n +0000043340 00000 n +0000043678 00000 n +0000151489 00000 n +0000044996 00000 n +0000043788 00000 n +0000044871 00000 n +0000151597 00000 n +0000045351 00000 n +0000045060 00000 n +0000045305 00000 n +0000151705 00000 n +0000046669 00000 n +0000045415 00000 n +0000046532 00000 n +0000151813 00000 n +0000047447 00000 n +0000046733 00000 n +0000047401 00000 n +0000151921 00000 n +0000048208 00000 n +0000047511 00000 n +0000048162 00000 n +0000152309 00000 n +0000048787 00000 n +0000048272 00000 n +0000048741 00000 n +0000152417 00000 n +0000049906 00000 n +0000048851 00000 n +0000049758 00000 n +0000152525 00000 n +0000051004 00000 n +0000049970 00000 n +0000050856 00000 n +0000152633 00000 n +0000052331 00000 n +0000051068 00000 n +0000052183 00000 n +0000152840 00000 n +0000052713 00000 n +0000052395 00000 n +0000052667 00000 n +0000152948 00000 n +0000053925 00000 n +0000052777 00000 n +0000053777 00000 n +0000153056 00000 n +0000055275 00000 n +0000053989 00000 n +0000055115 00000 n +0000153164 00000 n +0000056033 00000 n +0000055339 00000 n +0000055987 00000 n +0000153371 00000 n +0000056752 00000 n +0000056097 00000 n +0000056706 00000 n +0000153479 00000 n +0000057332 00000 n +0000056816 00000 n +0000057286 00000 n +0000153587 00000 n +0000058599 00000 n +0000057396 00000 n +0000058451 00000 n +0000153695 00000 n +0000060117 00000 n +0000058663 00000 n +0000059957 00000 n +0000153902 00000 n +0000060863 00000 n +0000060181 00000 n +0000060817 00000 n +0000154010 00000 n +0000061616 00000 n +0000060927 00000 n +0000061570 00000 n +0000154118 00000 n +0000062229 00000 n +0000061680 00000 n +0000062183 00000 n +0000154226 00000 n +0000063701 00000 n +0000062293 00000 n +0000063553 00000 n +0000154531 00000 n +0000064212 00000 n +0000063765 00000 n +0000064166 00000 n +0000154639 00000 n +0000065420 00000 n +0000064276 00000 n +0000065272 00000 n +0000154747 00000 n +0000067035 00000 n +0000065484 00000 n +0000066887 00000 n +0000154855 00000 n +0000067596 00000 n +0000067099 00000 n +0000067550 00000 n +0000155062 00000 n +0000068912 00000 n +0000067660 00000 n +0000068764 00000 n +0000155170 00000 n +0000069314 00000 n +0000068976 00000 n +0000069268 00000 n +0000155278 00000 n +0000070732 00000 n +0000069378 00000 n +0000070572 00000 n +0000155386 00000 n +0000071535 00000 n +0000070796 00000 n +0000071489 00000 n +0000155593 00000 n +0000072303 00000 n +0000071599 00000 n +0000072257 00000 n +0000155701 00000 n +0000072899 00000 n +0000072367 00000 n +0000072853 00000 n +0000155809 00000 n +0000074395 00000 n +0000072963 00000 n +0000074247 00000 n +0000155917 00000 n +0000074873 00000 n +0000074459 00000 n +0000074827 00000 n +0000156124 00000 n +0000076361 00000 n +0000074937 00000 n +0000076201 00000 n +0000156232 00000 n +0000077131 00000 n +0000076425 00000 n +0000077085 00000 n +0000156340 00000 n +0000077878 00000 n +0000077195 00000 n +0000077832 00000 n +0000156448 00000 n +0000078483 00000 n +0000077942 00000 n +0000078437 00000 n +0000156556 00000 n +0000079868 00000 n +0000141853 00000 n +0000141658 00000 n +0000078547 00000 n +0000079470 00000 n +0000079810 00000 n +0000149798 00000 n +0000148142 00000 n +0000148656 00000 n +0000149172 00000 n +0000149699 00000 n +0000152211 00000 n +0000150328 00000 n +0000150859 00000 n +0000151390 00000 n +0000152112 00000 n +0000152029 00000 n +0000154433 00000 n +0000152741 00000 n +0000153272 00000 n +0000153803 00000 n +0000154334 00000 n +0000156846 00000 n +0000154963 00000 n +0000155494 00000 n +0000156025 00000 n +0000156747 00000 n +0000156664 00000 n +0000157231 00000 n +0000157254 00000 n +0000157276 00000 n +trailer +<< +/Size 346 +/Root 2 0 R +/Info 1 0 R +>> +startxref +157397 +%%EOF diff --git a/src/axiom-website/CATS/schaum11.input.pamphlet b/src/axiom-website/CATS/schaum11.input.pamphlet new file mode 100644 index 0000000..fc3117e --- /dev/null +++ b/src/axiom-website/CATS/schaum11.input.pamphlet @@ -0,0 +1,2522 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/input schaum11.input} +\author{Timothy Daly} +\maketitle +\eject +\tableofcontents +\eject +\section{\cite{1}:14.237~~~~~$\displaystyle\int{\frac{dx}{\sqrt{a^2-x^2}}}$} +$$\int{\frac{1}{\sqrt{a^2-x^2}}}=\ln\left(x+\sqrt{a^2-x^2}\right)$$ +<<*>>= +)spool schaum11.output +)set message test on +)set message auto off +)clear all + +--S 1 +aa:=integrate(1/(sqrt(a^2-x^2)),x) +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R (1) - 2atan(----------------) +--R x +--R Type: Union(Expression Integer,...) +--E + +--S 2 +bb:=asin(x/a) +--R +--R x +--R (2) asin(-) +--R a +--R Type: Expression Integer +--E + +--S 3 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a x +--R (3) - 2atan(----------------) - asin(-) +--R x a +--R Type: Expression Integer +--E + +--S 4 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 5 +dd:=atanrule cc +--R +--R +---------+ +--R | 2 2 +--R - \|- x + a + %i x + a x +--R (5) %i log(-------------------------) - asin(-) +--R +---------+ a +--R | 2 2 +--R \|- x + a + %i x - a +--R Type: Expression Complex Integer +--E + +--S 6 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (6) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 7 +ee:=asinrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R \| a - \|- x + a + %i x + a +--R (7) - %i log(--------------------) + %i log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R Type: Expression Complex Integer +--E + +--S 8 +ff:=rootSimp ee +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R %i\|x - a - %i x - \|x - a + x - %i a +--R (8) - %i log(-------------------) + %i log(-----------------------) +--R a +-------+ +--R | 2 2 +--R \|x - a + x + %i a +--R Type: Expression Complex Integer +--E + +--S 9 14:238 Schaums and Axiom agree +gg:=complexNormalize ff +--R +--R (9) 0 +--R Type: Expression Complex Integer +--E + +@ + +\section{\cite{1}:14.238~~~~~$\displaystyle\int{\frac{x~dx}{\sqrt{a^2-x^2}}}$} +$$\int{\frac{x}{\sqrt{a^2-x^2}}}=\sqrt{a^2-x^2}$$ +<<*>>= +)clear all + +--S 10 +aa:=integrate(x/(sqrt(a^2-x^2)),x) +--R +--R +--R 2 +--R x +--R (1) ---------------- +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R Type: Union(Expression Integer,...) +--E + +--S 11 +bb:=-sqrt(a^2-x^2) +--R +--R +---------+ +--R | 2 2 +--R (2) - \|- x + a +--R Type: Expression Integer +--E + +--S 12 14:238 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R (3) - a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.239~~~~~$\displaystyle +\int{\frac{x^2~dx}{\sqrt{a^2-x^2}}}$} +$$\int{\frac{x^2}{\sqrt{a^2-x^2}}}= +\frac{x\sqrt{a^2-x^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 13 +aa:=integrate(x^2/sqrt(a^2-x^2),x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 3 | 2 2 2 2 4 \|- x + a - a +--R (- 4a \|- x + a - 2a x + 4a )atan(----------------) +--R x +--R + +--R +---------+ +--R 3 2 | 2 2 3 3 +--R (- x + 2a x)\|- x + a + 2a x - 2a x +--R / +--R +---------+ +--R | 2 2 2 2 +--R 4a\|- x + a + 2x - 4a +--R Type: Union(Expression Integer,...) +--E + +--S 14 +bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) +--R +--R +---------+ +--R | 2 2 2 x +--R - x\|- x + a + a asin(-) +--R a +--R (2) --------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 15 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 2 \|- x + a - a 2 x +--R - 2a atan(----------------) - a asin(-) +--R x a +--R (3) --------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 16 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 17 +dd:=atanrule cc +--R +--R +---------+ +--R | 2 2 +--R 2 - \|- x + a + %i x + a 2 x +--R %i a log(-------------------------) - a asin(-) +--R +---------+ a +--R | 2 2 +--R \|- x + a + %i x - a +--R (5) ----------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 18 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (6) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 19 +ee:=asinrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 2 \| a 2 - \|- x + a + %i x + a +--R - %i a log(--------------------) + %i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R (7) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 20 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 2 |- x + a 2 | 2 2 +--R - %i a log(a |--------- - %i x) - %i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 2 | 2 2 2 2 +--R %i a log(\|- x + a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 21 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 +--R - %i a log(%i\|x - a + %i x - a) - %i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 2 | 2 2 2 2 +--R %i a log(%i\|x - a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 22 14:239 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E + +@ + +\section{\cite{1}:14.240~~~~~$\displaystyle +\int{\frac{x^3~dx}{\sqrt{a^2-x^2}}}$} +$$\int{\frac{x^3}{\sqrt{a^2-x^2}}}= +\frac{(a^2-x^2)^{3/2}}{3}+a^2\sqrt{a^2-x^2} +$$ +<<*>>= +)clear all + +--S 23 +aa:=integrate(x^3/sqrt(a^2-x^2),x) +--R +--R +--R +---------+ +--R 4 | 2 2 6 2 4 +--R 3a x \|- x + a + x - 3a x +--R (1) --------------------------------------- +--R +---------+ +--R 2 2 | 2 2 2 3 +--R (3x - 12a )\|- x + a - 9a x + 12a +--R Type: Union(Expression Integer,...) +--E + +--S 24 +bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2) +--R +--R +---------+ +--R 2 2 | 2 2 +--R (- x - 2a )\|- x + a +--R (2) ------------------------ +--R 3 +--R Type: Expression Integer +--E + +--S 25 14:240 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 3 +--R 2a +--R (3) - --- +--R 3 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.241~~~~~$\displaystyle\int{\frac{dx}{x\sqrt{a^2-x^2}}}$} +$$\int{\frac{1}{x\sqrt{a^2-x^2}}}= +\frac{1}{a}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 26 +aa:=integrate(1/(x*sqrt(a^2-x^2)),x) +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R log(----------------) +--R x +--R (1) --------------------- +--R a +--R Type: Union(Expression Integer,...) +--E + +--S 27 +bb:=-1/a*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +--R \|- x + a + a +--R log(----------------) +--R x +--R (2) - --------------------- +--R a +--R Type: Expression Integer +--E + +--S 28 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R log(----------------) + log(----------------) +--R x x +--R (3) --------------------------------------------- +--R a +--R Type: Expression Integer +--E + +--S 29 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R log(\|- x + a + a) + log(\|- x + a - a) - 2log(x) +--R (4) ------------------------------------------------------- +--R a +--R Type: Expression Integer +--E + +--S 30 +ee:=complexNormalize dd +--R +--R x +--R 2log(-------) +--R +----+ +--R | 2 +--R \|- x +--R (5) - ------------- +--R a +--R Type: Expression Integer +--E + +--S 31 14:241 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R 2log(\|- 1 ) +--R (6) ------------ +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.242~~~~~$\displaystyle +\int{\frac{dx}{x^2\sqrt{a^2-x^2}}}$} +$$\int{\frac{1}{x^2\sqrt{a^2-x^2}}}= +\frac{\sqrt{a^2-x^2}}{a^2x} +$$ +<<*>>= +)clear all + +--S 32 +aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x) +--R +--R +--R +---------+ +--R | 2 2 2 2 +--R a\|- x + a + x - a +--R (1) ----------------------- +--R +---------+ +--R 2 | 2 2 3 +--R a x\|- x + a - a x +--R Type: Union(Expression Integer,...) +--E + +--S 33 +bb:=-sqrt(a^2-x^2)/(a^2*x) +--R +--R +---------+ +--R | 2 2 +--R \|- x + a +--R (2) - ------------ +--R 2 +--R a x +--R Type: Expression Integer +--E + +--S 34 14:242 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.243~~~~~$\displaystyle\int{\frac{dx}{x^3\sqrt{a^2-x^2}}}$} +$$\int{\frac{1}{x^3\sqrt{a^2-x^2}}}= +-\frac{\sqrt{a^2-x^2}}{2a^2x^2}+\frac{1}{2a^3} +\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 35 +aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 2 | 2 2 4 2 2 \|- x + a - a +--R (2a x \|- x + a + x - 2a x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 3 | 2 2 2 2 4 +--R (- a x + 2a )\|- x + a + 2a x - 2a +--R / +--R +---------+ +--R 4 2 | 2 2 3 4 5 2 +--R 4a x \|- x + a + 2a x - 4a x +--R Type: Union(Expression Integer,...) +--E + +--S 36 +bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +---------+ +--R 2 \|- x + a + a | 2 2 +--R - x log(----------------) - a\|- x + a +--R x +--R (2) ----------------------------------------- +--R 3 2 +--R 2a x +--R Type: Expression Integer +--E + +--S 37 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R log(----------------) + log(----------------) +--R x x +--R (3) --------------------------------------------- +--R 3 +--R 2a +--R Type: Expression Integer +--E + +--S 38 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R log(\|- x + a + a) + log(\|- x + a - a) - 2log(x) +--R (4) ------------------------------------------------------- +--R 3 +--R 2a +--R Type: Expression Integer +--E + +--S 39 +ee:=complexNormalize dd +--R +--R x +--R log(-------) +--R +----+ +--R | 2 +--R \|- x +--R (5) - ------------ +--R 3 +--R a +--R Type: Expression Integer +--E + +--S 40 14:243 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R log(\|- 1 ) +--R (6) ----------- +--R 3 +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.244~~~~~$\displaystyle\int{\sqrt{a^2-x^2}}~dx$} +$$\int{\sqrt{a^2-x^2}}= +\frac{x\sqrt{a^2-x^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 41 +aa:=integrate(sqrt(a^2-x^2),x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 3 | 2 2 2 2 4 \|- x + a - a +--R (- 4a \|- x + a - 2a x + 4a )atan(----------------) +--R x +--R + +--R +---------+ +--R 3 2 | 2 2 3 3 +--R (x - 2a x)\|- x + a - 2a x + 2a x +--R / +--R +---------+ +--R | 2 2 2 2 +--R 4a\|- x + a + 2x - 4a +--R Type: Union(Expression Integer,...) +--E + +--S 42 +bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) +--R +--R +---------+ +--R | 2 2 2 x +--R x\|- x + a + a asin(-) +--R a +--R (2) ------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 43 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 2 \|- x + a - a 2 x +--R - 2a atan(----------------) - a asin(-) +--R x a +--R (3) --------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 44 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (4) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 45 +dd:=asinrule cc +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 2 \| a 2 \|- x + a - a +--R - %i a log(--------------------) - 2a atan(----------------) +--R a x +--R (5) ------------------------------------------------------------ +--R 2 +--R Type: Expression Complex Integer +--E + +--S 46 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 47 +ee:=atanrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 2 \| a 2 - \|- x + a + %i x + a +--R - %i a log(--------------------) + %i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R (7) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 48 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 2 |- x + a 2 | 2 2 +--R - %i a log(a |--------- - %i x) - %i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 2 | 2 2 2 2 +--R %i a log(\|- x + a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 49 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 +--R - %i a log(%i\|x - a + %i x - a) - %i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 2 | 2 2 2 2 +--R %i a log(%i\|x - a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 50 14:244 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.245~~~~~$\displaystyle\int{x\sqrt{a^2-x^2}}~dx$} +$$\int{x\sqrt{a^2-x^2}}= +\frac{(a^2-x^2)^{3/2}}{3} +$$ +<<*>>= +)clear all + +--S 51 +aa:=integrate(x*sqrt(a^2-x^2),x) +--R +--R +--R +---------+ +--R 4 3 2 | 2 2 6 2 4 4 2 +--R (- 3a x + 6a x )\|- x + a - x + 6a x - 6a x +--R (1) -------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 2 3 +--R (3x - 12a )\|- x + a - 9a x + 12a +--R Type: Union(Expression Integer,...) +--E + +--S 52 +bb:=-(a^2-x^2)^(3/2)/3 +--R +--R +---------+ +--R 2 2 | 2 2 +--R (x - a )\|- x + a +--R (2) --------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 53 14:245 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 3 +--R a +--R (3) - -- +--R 3 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.246~~~~~$\displaystyle +\int{x^2\sqrt{a^2-x^2}}~dx$} +$$\int{x^2\sqrt{a^2-x^2}}= +\frac{x(a^2-x^2)^{3/2}}{4}+\frac{a^2x\sqrt{a^2-x^2}}{8}- +\frac{a^4}{8}\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 54 +aa:=integrate(x^2*sqrt(a^2-x^2),x) +--R +--R +--R (1) +--R +---------+ +--R 5 2 7 | 2 2 4 4 6 2 8 +--R ((- 8a x + 16a )\|- x + a - 2a x + 16a x - 16a ) +--R * +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R atan(----------------) +--R x +--R + +--R +---------+ +--R 7 2 5 4 3 6 | 2 2 7 3 5 5 3 7 +--R (2x - 17a x + 24a x - 8a x)\|- x + a - 8a x + 28a x - 28a x + 8a x +--R / +--R +---------+ +--R 2 3 | 2 2 4 2 2 4 +--R (32a x - 64a )\|- x + a + 8x - 64a x + 64a +--R Type: Union(Expression Integer,...) +--E + +--S 55 +bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a) +--R +--R +---------+ +--R 3 2 | 2 2 4 x +--R (2x - a x)\|- x + a + a asin(-) +--R a +--R (2) ----------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 56 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 4 \|- x + a - a 4 x +--R - 2a atan(----------------) - a asin(-) +--R x a +--R (3) --------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 57 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 58 +dd:=atanrule cc +--R +--R +---------+ +--R | 2 2 +--R 4 - \|- x + a + %i x + a 4 x +--R %i a log(-------------------------) - a asin(-) +--R +---------+ a +--R | 2 2 +--R \|- x + a + %i x - a +--R (5) ----------------------------------------------- +--R 8 +--R Type: Expression Complex Integer +--E + +--S 59 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (6) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 60 +ee:=asinrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 4 \| a 4 - \|- x + a + %i x + a +--R - %i a log(--------------------) + %i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R (7) ---------------------------------------------------------------------- +--R 8 +--R Type: Expression Complex Integer +--E + +--S 61 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 4 |- x + a 4 | 2 2 +--R - %i a log(a |--------- - %i x) - %i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 4 | 2 2 4 4 +--R %i a log(\|- x + a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 8 +--R Type: Expression Complex Integer +--E + +--S 62 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 4 | 2 2 4 | 2 2 +--R - %i a log(%i\|x - a + %i x - a) - %i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 4 | 2 2 4 4 +--R %i a log(%i\|x - a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 8 +--R Type: Expression Complex Integer +--E + +--S 63 14:246 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.247~~~~~$\displaystyle +\int{x^3\sqrt{a^2-x^2}}~dx$} +$$\int{x^3\sqrt{a^2-x^2}}= +\frac{(a^2-x^2)^{5/2}}{5}+\frac{a^2(a^2-x^2)^{3/2}}{3} +$$ +<<*>>= +)clear all + +--S 64 +aa:=integrate(x^3*sqrt(a^2-x^2),x) +--R +--R +--R (1) +--R +---------+ +--R 8 3 6 5 4 | 2 2 10 2 8 4 6 6 4 +--R (- 15a x + 65a x - 60a x )\|- x + a - 3x + 40a x - 95a x + 60a x +--R -------------------------------------------------------------------------- +--R +---------+ +--R 4 2 2 4 | 2 2 4 3 2 5 +--R (15x - 180a x + 240a )\|- x + a - 75a x + 300a x - 240a +--R Type: Union(Expression Integer,...) +--E + +--S 65 +bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3 +--R +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (3x - a x - 2a )\|- x + a +--R (2) ------------------------------ +--R 15 +--R Type: Expression Integer +--E + +--S 66 14:247 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 5 +--R 2a +--R (3) - --- +--R 15 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.248~~~~~$\displaystyle +\int{\frac{\sqrt{a^2-x^2}}{x}}~dx$} +$$\int{\frac{\sqrt{a^2-x^2}}{x}}= +\sqrt{a^2-x^2}-a\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 67 +aa:=integrate(sqrt(a^2-x^2)/x,x) +--R +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 \|- x + a - a 2 +--R (a\|- x + a - a )log(----------------) - x +--R x +--R (1) ---------------------------------------------- +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R Type: Union(Expression Integer,...) +--E + +--S 68 +bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +---------+ +--R \|- x + a + a | 2 2 +--R (2) - a log(----------------) + \|- x + a +--R x +--R Type: Expression Integer +--E + +--S 69 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R (3) a log(----------------) + a log(----------------) + a +--R x x +--R Type: Expression Integer +--E + +--S 70 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R (4) a log(\|- x + a + a) + a log(\|- x + a - a) - 2a log(x) + a +--R Type: Expression Integer +--E + +--S 71 +ee:=complexNormalize dd +--R +--R x +--R (5) - 2a log(-------) + a +--R +----+ +--R | 2 +--R \|- x +--R Type: Expression Integer +--E + +--S 72 14:248 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R (6) 2a log(\|- 1 ) + a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.249~~~~~$\displaystyle +\int{\frac{\sqrt{a^2-x^2}}{x^2}}~dx$} +$$\int{\frac{\sqrt{a^2-x^2}}{x^2}}= +-\frac{\sqrt{a^2-x^2}}{x}+\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 73 +aa:=integrate(sqrt(a^2-x^2)/x^2,x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +---------+ +--R | 2 2 \|- x + a - a | 2 2 2 2 +--R (2x\|- x + a - 2a x)atan(----------------) + a\|- x + a + x - a +--R x +--R ----------------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R x\|- x + a - a x +--R Type: Union(Expression Integer,...) +--E + +--S 74 +bb:=-sqrt(a^2-x^2)/x-asin(x/a) +--R +--R +---------+ +--R | 2 2 x +--R - \|- x + a - x asin(-) +--R a +--R (2) -------------------------- +--R x +--R Type: Expression Integer +--E + +--S 75 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a x +--R (3) 2atan(----------------) + asin(-) +--R x a +--R Type: Expression Integer +--E + +--S 76 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (4) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 77 +dd:=asinrule cc +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R \| a \|- x + a - a +--R (5) %i log(--------------------) + 2atan(----------------) +--R a x +--R Type: Expression Complex Integer +--E + +--S 78 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 79 +ee:=atanrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R \| a - \|- x + a + %i x + a +--R (7) %i log(--------------------) - %i log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R Type: Expression Complex Integer +--E + +--S 80 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R |- x + a | 2 2 +--R %i log(a |--------- - %i x) + %i log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R | 2 2 +--R - %i log(\|- x + a - %i x - a) - %i log(a) - %i log(- 1) +--R Type: Expression Complex Integer +--E + +--S 81 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R %i log(%i\|x - a + %i x - a) + %i log(%i\|x - a - %i x) +--R + +--R +-------+ +--R | 2 2 +--R - %i log(%i\|x - a - %i x - a) - %i log(a) - %i log(- 1) +--R Type: Expression Complex Integer +--E + +--S 82 14:249 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.250~~~~~$\displaystyle +\int{\frac{\sqrt{a^2-x^2}}{x^3}}~dx$} +$$\int{\frac{\sqrt{a^2-x^2}}{x^3}}= +-\frac{\sqrt{a^2-x^2}}{2x^2}+\frac{1}{2a} +\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 83 +aa:=integrate(sqrt(a^2-x^2)/x^3,x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 2 | 2 2 4 2 2 \|- x + a - a +--R (- 2a x \|- x + a - x + 2a x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 3 | 2 2 2 2 4 +--R (- a x + 2a )\|- x + a + 2a x - 2a +--R / +--R +---------+ +--R 2 2 | 2 2 4 3 2 +--R 4a x \|- x + a + 2a x - 4a x +--R Type: Union(Expression Integer,...) +--E + +--S 84 +bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +---------+ +--R 2 \|- x + a + a | 2 2 +--R x log(----------------) - a\|- x + a +--R x +--R (2) --------------------------------------- +--R 2 +--R 2a x +--R Type: Expression Integer +--E + +--S 85 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R - log(----------------) - log(----------------) +--R x x +--R (3) ----------------------------------------------- +--R 2a +--R Type: Expression Integer +--E + +--S 86 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R - log(\|- x + a + a) - log(\|- x + a - a) + 2log(x) +--R (4) --------------------------------------------------------- +--R 2a +--R Type: Expression Integer +--E + +--S 87 +ee:=complexNormalize dd +--R +--R x +--R log(-------) +--R +----+ +--R | 2 +--R \|- x +--R (5) ------------ +--R a +--R Type: Expression Integer +--E + +--S 88 14:250 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R log(\|- 1 ) +--R (6) - ----------- +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.251~~~~~$\displaystyle\int{\frac{dx}{(a^2-x^2)^{3/2}}}$} +$$\int{\frac{1}{(a^2-x^2)^{3/2}}}= +-\frac{x}{a^2\sqrt{a^2-x^2}} +$$ +<<*>>= +)clear all + +--S 89 +aa:=integrate(1/(a^2-x^2)^(3/2),x) +--R +--R +--R +---------+ +--R | 2 2 +--R - x\|- x + a + a x +--R (1) -------------------------- +--R +---------+ +--R 3 | 2 2 2 2 4 +--R a \|- x + a + a x - a +--R Type: Union(Expression Integer,...) +--E + +--S 90 +bb:=x/(a^2*sqrt(a^2-x^2)) +--R +--R x +--R (2) -------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- x + a +--R Type: Expression Integer +--E + +--S 91 14:251 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.252~~~~~$\displaystyle +\int{\frac{x~dx}{(a^2-x^2)^{3/2}}}$} +$$\int{\frac{x}{(a^2-x^2)^{3/2}}}= +\frac{-1}{\sqrt{a^2-x^2}} +$$ +<<*>>= +)clear all + +--S 92 +aa:=integrate(x/(a^2-x^2)^(3/2),x) +--R +--R +--R 2 +--R x +--R (1) -------------------------- +--R +---------+ +--R 2 | 2 2 2 3 +--R a \|- x + a + a x - a +--R Type: Union(Expression Integer,...) +--E + +--S 93 +bb:=1/sqrt(a^2-x^2) +--R +--R 1 +--R (2) ------------ +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression Integer +--E + +--S 94 14:252 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 1 +--R (3) - +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.253~~~~~$\displaystyle +\int{\frac{x^2dx}{(a^2-x^2)^{3/2}}}$} +$$\int{\frac{x^2}{(a^2-x^2)^{3/2}}}= +\frac{-x}{\sqrt{a^2-x^2}}+\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 95 +aa:=integrate(x^2/(a^2-x^2)^(3/2),x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +---------+ +--R | 2 2 2 2 \|- x + a - a | 2 2 +--R (2a\|- x + a + 2x - 2a )atan(----------------) - x\|- x + a + a x +--R x +--R ------------------------------------------------------------------------ +--R +---------+ +--R | 2 2 2 2 +--R a\|- x + a + x - a +--R Type: Union(Expression Integer,...) +--E + +--S 96 +bb:=x/sqrt(a^2-x^2)-asin(x/a) +--R +--R +---------+ +--R x | 2 2 +--R - asin(-)\|- x + a + x +--R a +--R (2) ------------------------- +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression Integer +--E + +--S 97 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a x +--R (3) 2atan(----------------) + asin(-) +--R x a +--R Type: Expression Integer +--E + +--S 98 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 99 +dd:=atanrule cc +--R +--R +---------+ +--R | 2 2 +--R - \|- x + a + %i x + a x +--R (5) - %i log(-------------------------) + asin(-) +--R +---------+ a +--R | 2 2 +--R \|- x + a + %i x - a +--R Type: Expression Complex Integer +--E + +--S 100 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (6) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 101 +ee:=asinrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R \| a - \|- x + a + %i x + a +--R (7) %i log(--------------------) - %i log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R Type: Expression Complex Integer +--E + +--S 102 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R |- x + a | 2 2 +--R %i log(a |--------- - %i x) + %i log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R | 2 2 +--R - %i log(\|- x + a - %i x - a) - %i log(a) - %i log(- 1) +--R Type: Expression Complex Integer +--E + +--S 103 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R %i log(%i\|x - a + %i x - a) + %i log(%i\|x - a - %i x) +--R + +--R +-------+ +--R | 2 2 +--R - %i log(%i\|x - a - %i x - a) - %i log(a) - %i log(- 1) +--R Type: Expression Complex Integer +--E + +--S 104 14:253 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.254~~~~~$\displaystyle +\int{\frac{x^3dx}{(a^2-x^2)^{3/2}}}$} +$$\int{\frac{x^3}{(a^2-x^2)^{3/2}}}= +\sqrt{a^2-x^2}-\frac{a^2}{\sqrt{a^2-x^2}} +$$ +<<*>>= +)clear all + +--S 105 +aa:=integrate(x^3/(a^2-x^2)^(3/2),x) +--R +--R +--R 4 +--R x +--R (1) - ------------------------------------ +--R +---------+ +--R 2 2 | 2 2 2 3 +--R (x - 2a )\|- x + a - 2a x + 2a +--R Type: Union(Expression Integer,...) +--E + +--S 106 +bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2) +--R +--R 2 2 +--R - x + 2a +--R (2) ------------ +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression Integer +--E + +--S 107 14:254 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R (3) 2a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.255~~~~~$\displaystyle +\int{\frac{dx}{x(a^2-x^2)^{3/2}}}$} +$$\int{\frac{1}{x(a^2-x^2)^{3/2}}}= +\frac{-1}{a^2\sqrt{a^2-x^2}}- +\frac{1}{a^3}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 108 +aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x) +--R +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 2 \|- x + a - a 2 +--R (a\|- x + a + x - a )log(----------------) + x +--R x +--R (1) --------------------------------------------------- +--R +---------+ +--R 4 | 2 2 3 2 5 +--R a \|- x + a + a x - a +--R Type: Union(Expression Integer,...) +--E + +--S 109 +bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- x + a + a +--R - \|- x + a log(----------------) + a +--R x +--R (2) --------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R a \|- x + a +--R Type: Expression Integer +--E + +--S 110 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R log(----------------) + log(----------------) + 1 +--R x x +--R (3) ------------------------------------------------- +--R 3 +--R a +--R Type: Expression Integer +--E + +--S 111 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R log(\|- x + a + a) + log(\|- x + a - a) - 2log(x) + 1 +--R (4) ----------------------------------------------------------- +--R 3 +--R a +--R Type: Expression Integer +--E + +--S 112 +ee:=complexNormalize dd +--R +--R x +--R - 2log(-------) + 1 +--R +----+ +--R | 2 +--R \|- x +--R (5) ------------------- +--R 3 +--R a +--R Type: Expression Integer +--E + +--S 113 14:255 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R 2log(\|- 1 ) + 1 +--R (6) ---------------- +--R 3 +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.256~~~~~$\displaystyle +\int{\frac{dx}{x^2(a^2-x^2)^{3/2}}}$} +$$\int{\frac{1}{x^2(a^2-x^2)^{3/2}}}= +-\frac{\sqrt{a^2-x^2}}{a^4x}-\frac{x}{a^4\sqrt{a^2-x^2}} +$$ +<<*>>= +)clear all + +--S 114 +aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x) +--R +--R +--R +---------+ +--R 2 3 | 2 2 4 2 2 4 +--R (4a x - 2a )\|- x + a + 2x - 5a x + 2a +--R (1) --------------------------------------------- +--R +---------+ +--R 4 3 6 | 2 2 5 3 7 +--R (a x - 2a x)\|- x + a - 2a x + 2a x +--R Type: Union(Expression Integer,...) +--E + +--S 115 +bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2)) +--R +--R 2 2 +--R 2x - a +--R (2) --------------- +--R +---------+ +--R 4 | 2 2 +--R a x\|- x + a +--R Type: Expression Integer +--E + +--S 116 14:256 Schaums and Axiom agree +cc:=aa-bb +--R +--R (3) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.257~~~~~$\displaystyle +\int{\frac{dx}{x^3(a^2-x^2)^{3/2}}}$} +$$\int{\frac{1}{x^3(a^2-x^2)^{3/2}}}= +\frac{1}{2a^2x^2\sqrt{a^2-x^2}}- +\frac{3}{2a^4\sqrt{a^2-x^2}}- +\frac{3}{2a^5}\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 117 +aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x) +--R +--R +--R (1) +--R +---------+ +--R 4 3 2 | 2 2 6 2 4 4 2 +--R ((9a x - 12a x )\|- x + a + 3x - 15a x + 12a x ) +--R * +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R log(----------------) +--R x +--R + +--R +---------+ +--R 4 3 2 5 | 2 2 6 2 4 4 2 6 +--R (3a x + 5a x - 4a )\|- x + a + 2x - a x - 7a x + 4a +--R / +--R +---------+ +--R 6 4 8 2 | 2 2 5 6 7 4 9 2 +--R (6a x - 8a x )\|- x + a + 2a x - 10a x + 8a x +--R Type: Union(Expression Integer,...) +--E + +--S 118 +bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 | 2 2 \|- x + a + a 2 3 +--R - 3x \|- x + a log(----------------) + 3a x - a +--R x +--R (2) --------------------------------------------------- +--R +---------+ +--R 5 2 | 2 2 +--R 2a x \|- x + a +--R Type: Expression Integer +--E + +--S 119 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R 3log(----------------) + 3log(----------------) + 2 +--R x x +--R (3) --------------------------------------------------- +--R 5 +--R 2a +--R Type: Expression Integer +--E + +--S 120 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R 3log(\|- x + a + a) + 3log(\|- x + a - a) - 6log(x) + 2 +--R (4) ------------------------------------------------------------- +--R 5 +--R 2a +--R Type: Expression Integer +--E + +--S 121 +ee:=complexNormalize dd +--R +--R x +--R - 3log(-------) + 1 +--R +----+ +--R | 2 +--R \|- x +--R (5) ------------------- +--R 5 +--R a +--R Type: Expression Integer +--E + +--S 122 14:257 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R 3log(\|- 1 ) + 1 +--R (6) ---------------- +--R 5 +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.258~~~~~$\displaystyle\int{(a^2-x^2)^{3/2}}~dx$} +$$\int{(a^2-x^2)^{3/2}}= +\frac{x(a^2-x^2)^{3/2}}{4}-\frac{3a^2x\sqrt{a^2-x^2}}{8}+ +\frac{3}{8}a^4\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 123 +aa:=integrate((a^2-x^2)^(3/2),x) +--R +--R +--R (1) +--R +---------+ +--R 5 2 7 | 2 2 4 4 6 2 8 +--R ((- 24a x + 48a )\|- x + a - 6a x + 48a x - 48a ) +--R * +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R atan(----------------) +--R x +--R + +--R +---------+ +--R 7 2 5 4 3 6 | 2 2 7 3 5 5 3 +--R (- 2x + 21a x - 56a x + 40a x)\|- x + a + 8a x - 44a x + 76a x +--R + +--R 7 +--R - 40a x +--R / +--R +---------+ +--R 2 3 | 2 2 4 2 2 4 +--R (32a x - 64a )\|- x + a + 8x - 64a x + 64a +--R Type: Union(Expression Integer,...) +--E + +--S 124 +bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a) +--R +--R +---------+ +--R 3 2 | 2 2 4 x +--R (- 2x + 5a x)\|- x + a + 3a asin(-) +--R a +--R (2) --------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 125 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 4 \|- x + a - a 4 x +--R - 6a atan(----------------) - 3a asin(-) +--R x a +--R (3) ---------------------------------------- +--R 8 +--R Type: Expression Integer +--E + +--S 126 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (4) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 127 +ee:=asinrule cc +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 4 \| a 4 \|- x + a - a +--R - 3%i a log(--------------------) - 6a atan(----------------) +--R a x +--R (5) ------------------------------------------------------------- +--R 8 +--R Type: Expression Complex Integer +--E + +--S 128 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 129 +ff:=atanrule ee +--R +--R (7) +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 4 \| a 4 - \|- x + a + %i x + a +--R - 3%i a log(--------------------) + 3%i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R ------------------------------------------------------------------------ +--R 8 +--R Type: Expression Complex Integer +--E + +--S 130 +gg:=expandLog ff +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 4 |- x + a 4 | 2 2 +--R - 3%i a log(a |--------- - %i x) - 3%i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 4 | 2 2 4 4 +--R 3%i a log(\|- x + a - %i x - a) + 3%i a log(a) + 3%i a log(- 1) +--R / +--R 8 +--R Type: Expression Complex Integer +--E + +--S 131 +hh:=rootSimp gg +--R +--R (9) +--R +-------+ +-------+ +--R 4 | 2 2 4 | 2 2 +--R - 3%i a log(%i\|x - a + %i x - a) - 3%i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 4 | 2 2 4 4 +--R 3%i a log(%i\|x - a - %i x - a) + 3%i a log(a) + 3%i a log(- 1) +--R / +--R 8 +--R Type: Expression Complex Integer +--E + +--S 132 14:258 Schaums and Axiom agree +ii:=complexNormalize hh +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.259~~~~~$\displaystyle\int{x(a^2-x^2)^{3/2}}~dx$} +$$\int{x(a^2-x^2)^{3/2}}=\frac{(a^2-x^2)^{5/2}}{5}$$ +<<*>>= +)clear all + +--S 133 +aa:=integrate(x*(a^2-x^2)^(3/2),x) +--R +--R +--R (1) +--R +---------+ +--R 8 3 6 5 4 7 2 | 2 2 10 2 8 4 6 +--R (5a x - 30a x + 60a x - 40a x )\|- x + a + x - 15a x + 55a x +--R + +--R 6 4 8 2 +--R - 80a x + 40a x +--R / +--R +---------+ +--R 4 2 2 4 | 2 2 4 3 2 5 +--R (5x - 60a x + 80a )\|- x + a - 25a x + 100a x - 80a +--R Type: Union(Expression Integer,...) +--E + +--S 134 +bb:=-(a^2-x^2)^(5/2)/5 +--R +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (- x + 2a x - a )\|- x + a +--R (2) ------------------------------- +--R 5 +--R Type: Expression Integer +--E + +--S 135 14:259 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 5 +--R a +--R (3) - -- +--R 5 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.260~~~~~$\displaystyle\int{x^2(a^2-x^2)^{3/2}}~dx$} +$$\int{x^2(a^2-x^2)^{3/2}}= +\frac{x(a^2-x^2)^{5/2}}{6}+\frac{a^2x(a^2-x^2)^{3/2}}{24}- +\frac{a^4x\sqrt{a^2-x^2}}{16}+ +\frac{a^6}{16}\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 136 +aa:=integrate(x^2*(a^2-x^2)^(3/2),x) +--R +--R +--R (1) +--R +---------+ +--R 7 4 9 2 11 | 2 2 6 6 8 4 +--R (- 36a x + 192a x - 192a )\|- x + a - 6a x + 108a x +--R + +--R 10 2 12 +--R - 288a x + 192a +--R * +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R atan(----------------) +--R x +--R + +--R +---------+ +--R 11 2 9 4 7 6 5 8 3 10 | 2 2 +--R (- 8x + 158a x - 639a x + 982a x - 592a x + 96a x)\|- x + a +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R 48a x - 388a x + 1062a x - 1266a x + 640a x - 96a x +--R / +--R +---------+ +--R 4 3 2 5 | 2 2 6 2 4 4 2 +--R (288a x - 1536a x + 1536a )\|- x + a + 48x - 864a x + 2304a x +--R + +--R 6 +--R - 1536a +--R Type: Union(Expression Integer,...) +--E + +--S 137 +bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a) +--R +--R +---------+ +--R 5 2 3 4 | 2 2 6 x +--R (- 8x + 14a x - 3a x)\|- x + a + 3a asin(-) +--R a +--R (2) ------------------------------------------------ +--R 48 +--R Type: Expression Integer +--E + +--S 138 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 6 \|- x + a - a 6 x +--R - 2a atan(----------------) - a asin(-) +--R x a +--R (3) --------------------------------------- +--R 16 +--R Type: Expression Integer +--E + +--S 139 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (4) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 140 +dd:=atanrule cc +--R +--R +---------+ +--R | 2 2 +--R 6 - \|- x + a + %i x + a 6 x +--R %i a log(-------------------------) - a asin(-) +--R +---------+ a +--R | 2 2 +--R \|- x + a + %i x - a +--R (5) ----------------------------------------------- +--R 16 +--R Type: Expression Complex Integer +--E + +--S 141 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (6) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 142 +ee:=asinrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 6 \| a 6 - \|- x + a + %i x + a +--R - %i a log(--------------------) + %i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R (7) ---------------------------------------------------------------------- +--R 16 +--R Type: Expression Complex Integer +--E + +--S 143 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 6 |- x + a 6 | 2 2 +--R - %i a log(a |--------- - %i x) - %i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 6 | 2 2 6 6 +--R %i a log(\|- x + a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 16 +--R Type: Expression Complex Integer +--E + +--S 144 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 6 | 2 2 6 | 2 2 +--R - %i a log(%i\|x - a + %i x - a) - %i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 6 | 2 2 6 6 +--R %i a log(%i\|x - a - %i x - a) + %i a log(a) + %i a log(- 1) +--R / +--R 16 +--R Type: Expression Complex Integer +--E + +--S 145 14:260 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.261~~~~~$\displaystyle\int{x^3(a^2-x^2)^{3/2}}~dx$} +$$\int{x^3(a^2-x^2)^{3/2}}= +\frac{(a^2-x^2)^{7/2}}{7}+\frac{a^2(a^2-x^2)^{5/2}}{5} +$$ +<<*>>= +)clear all + +--S 146 +aa:=integrate(x^3*(a^2-x^2)^(3/2),x) +--R +--R +--R (1) +--R +---------+ +--R 12 3 10 5 8 7 6 9 4 | 2 2 14 +--R (35a x - 336a x + 1015a x - 1260a x + 560a x )\|- x + a + 5x +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 133a x + 721a x - 1575a x + 1540a x - 560a x +--R / +--R +---------+ +--R 6 2 4 4 2 6 | 2 2 6 3 4 +--R (35x - 840a x + 2800a x - 2240a )\|- x + a - 245a x + 1960a x +--R + +--R 5 2 7 +--R - 3920a x + 2240a +--R Type: Union(Expression Integer,...) +--E + +--S 147 +bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5 +--R +--R +---------+ +--R 6 2 4 4 2 6 | 2 2 +--R (- 5x + 8a x - a x - 2a )\|- x + a +--R (2) ---------------------------------------- +--R 35 +--R Type: Expression Integer +--E + +--S 148 14:261 Schaums and Axiom differ by a constant +cc:=aa-bb +--R +--R 7 +--R 2a +--R (3) - --- +--R 35 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.262~~~~~$\displaystyle +\int{\frac{(a^2-x^2)^{3/2}}{x}}~dx$} +$$\int{\frac{(a^2-x^2)^{3/2}}{x}}= +\frac{(a^2-x^2)^{3/2}}{3}-a^2\sqrt{a^2-x^2}+ +a^3\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 149 +aa:=integrate((a^2-x^2)^(3/2)/x,x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 3 2 5 | 2 2 4 2 6 \|- x + a - a +--R ((3a x - 12a )\|- x + a - 9a x + 12a )log(----------------) +--R x +--R + +--R +---------+ +--R 4 3 2 | 2 2 6 2 4 4 2 +--R (3a x - 12a x )\|- x + a + x - 9a x + 12a x +--R / +--R +---------+ +--R 2 2 | 2 2 2 3 +--R (3x - 12a )\|- x + a - 9a x + 12a +--R Type: Union(Expression Integer,...) +--E + +--S 150 +bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +---------+ +--R 3 \|- x + a + a 2 2 | 2 2 +--R - 3a log(----------------) + (- x + 4a )\|- x + a +--R x +--R (2) ----------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 151 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R 3 \|- x + a + a 3 \|- x + a - a 3 +--R 3a log(----------------) + 3a log(----------------) + 4a +--R x x +--R (3) --------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 152 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R 3 | 2 2 3 | 2 2 3 3 +--R 3a log(\|- x + a + a) + 3a log(\|- x + a - a) - 6a log(x) + 4a +--R (4) --------------------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 153 +ee:=complexNormalize dd +--R +--R 3 x 3 +--R - 6a log(-------) + 4a +--R +----+ +--R | 2 +--R \|- x +--R (5) ----------------------- +--R 3 +--R Type: Expression Integer +--E + +--S 154 14:262 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R 3 +---+ 3 +--R 6a log(\|- 1 ) + 4a +--R (6) -------------------- +--R 3 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.263~~~~~$\displaystyle +\int{\frac{(a^2-x^2)^{3/2}}{x^2}}~dx$} +$$\int{\frac{(a^2-x^2)^{3/2}}{x^2}}= +-\frac{(a^2-x^2)^{3/2}}{x}+\frac{3x\sqrt{a^2-x^2}}{2}- +\frac{3}{2}a^2\ln\left(x+\sqrt{a^2-x^2}\right) +$$ +<<*>>= +)clear all + +--S 155 +aa:=integrate((a^2-x^2)^{3/2}/x^2,x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 2 3 4 | 2 2 3 3 5 \|- x + a - a +--R ((6a x - 24a x)\|- x + a - 18a x + 24a x)atan(----------------) +--R x +--R + +--R +---------+ +--R 4 3 2 5 | 2 2 6 2 4 4 2 6 +--R (3a x + 2a x - 8a )\|- x + a + x - 3a x - 6a x + 8a +--R / +--R +---------+ +--R 3 2 | 2 2 3 3 +--R (2x - 8a x)\|- x + a - 6a x + 8a x +--R Type: Union(Expression Integer,...) +--E + +--S 156 +bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a) +--R +--R +---------+ +--R 2 2 | 2 2 2 x +--R (- x - 2a )\|- x + a - 3a x asin(-) +--R a +--R (2) --------------------------------------- +--R 2x +--R Type: Expression Integer +--E + +--S 157 +cc:=aa-bb +--R +--R +---------+ +--R | 2 2 +--R 2 \|- x + a - a 2 x +--R 6a atan(----------------) + 3a asin(-) +--R x a +--R (3) -------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 158 +asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) +--R +--R +--------+ +--R | 2 +--R (4) asin(x) == %i log(\|- x + 1 - %i x) +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 159 +dd:=asinrule cc +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 2 \| a 2 \|- x + a - a +--R 3%i a log(--------------------) + 6a atan(----------------) +--R a x +--R (5) ----------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 160 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (6) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 161 +ee:=atanrule dd +--R +--R +---------+ +--R | 2 2 +--R |- x + a +--R a |--------- - %i x +---------+ +--R | 2 | 2 2 +--R 2 \| a 2 - \|- x + a + %i x + a +--R 3%i a log(--------------------) - 3%i a log(-------------------------) +--R a +---------+ +--R | 2 2 +--R \|- x + a + %i x - a +--R (7) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E + +--S 162 +ff:=expandLog ee +--R +--R (8) +--R +---------+ +--R | 2 2 +---------+ +--R 2 |- x + a 2 | 2 2 +--R 3%i a log(a |--------- - %i x) + 3%i a log(\|- x + a + %i x - a) +--R | 2 +--R \| a +--R + +--R +---------+ +--R 2 | 2 2 2 2 +--R - 3%i a log(\|- x + a - %i x - a) - 3%i a log(a) - 3%i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 163 +gg:=rootSimp ff +--R +--R (9) +--R +-------+ +-------+ +--R 2 | 2 2 2 | 2 2 +--R 3%i a log(%i\|x - a + %i x - a) + 3%i a log(%i\|x - a - %i x) +--R + +--R +-------+ +--R 2 | 2 2 2 2 +--R - 3%i a log(%i\|x - a - %i x - a) - 3%i a log(a) - 3%i a log(- 1) +--R / +--R 2 +--R Type: Expression Complex Integer +--E + +--S 164 14:263 Schaums and Axiom agree +hh:=complexNormalize gg +--R +--R (10) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.264~~~~~$\displaystyle +\int{\frac{(a^2-x^2)^{3/2}}{x^3}}~dx$} +$$\int{\frac{(a^2-x^2)^{3/2}}{x^3}}= +-\frac{(a^2-x^2)^{3/2}}{2x^2}+\frac{3}{2}\sqrt{a^2-x^2}- +\frac{3}{2}a\sec^{-1}\left|\frac{x}{a}\right| +$$ +<<*>>= +)clear all + +--S 165 +aa:=integrate((a^2-x^2)^(3/2)/x^3,x) +--R +--R +--R (1) +--R +---------+ +--R +---------+ | 2 2 +--R 4 3 2 | 2 2 2 4 4 2 \|- x + a - a +--R ((- 3a x + 12a x )\|- x + a + 9a x - 12a x )log(----------------) +--R x +--R + +--R +---------+ +--R 4 3 2 5 | 2 2 6 2 4 4 2 6 +--R (4a x + 3a x - 4a )\|- x + a + 2x - 3a x - 5a x + 4a +--R / +--R +---------+ +--R 4 2 2 | 2 2 4 3 2 +--R (2x - 8a x )\|- x + a - 6a x + 8a x +--R Type: Union(Expression Integer,...) +--E + +--S 166 +bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x) +--R +--R +---------+ +--R | 2 2 +---------+ +--R 2 \|- x + a + a 2 2 | 2 2 +--R 3a x log(----------------) + (- 2x - a )\|- x + a +--R x +--R (2) ----------------------------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E + +--S 167 +cc:=aa-bb +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R \|- x + a + a \|- x + a - a +--R - 3a log(----------------) - 3a log(----------------) - 2a +--R x x +--R (3) ---------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 168 +dd:=expandLog cc +--R +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R - 3a log(\|- x + a + a) - 3a log(\|- x + a - a) + 6a log(x) - 2a +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E + +--S 169 +ee:=complexNormalize dd +--R +--R x +--R (5) 3a log(-------) - a +--R +----+ +--R | 2 +--R \|- x +--R Type: Expression Integer +--E + +--S 170 14:264 Schaums and Axiom differ by a constant +ff:=rootSimp ee +--R +--R +---+ +--R (6) - 3a log(\|- 1 ) - a +--R Type: Expression Integer +--E + +)spool +)lisp (bye) +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} Spiegel, Murray R. +{\sl Mathematical Handbook of Formulas and Tables}\\ +Schaum's Outline Series McGraw-Hill 1968 pp68-69 +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/schaum11.input.pdf b/src/axiom-website/CATS/schaum11.input.pdf new file mode 100644 index 0000000..cb7ac08 --- /dev/null +++ b/src/axiom-website/CATS/schaum11.input.pdf @@ -0,0 +1,3980 @@ +%PDF-1.2 +7 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +10 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F1 +/FontDescriptor 9 0 R +/BaseFont/XGVGVP+CMR17 +/FirstChar 33 +/LastChar 196 +/Widths[249.6 458.6 772.1 458.6 772.1 719.8 249.6 354.1 354.1 458.6 719.8 249.6 301.9 +249.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 249.6 249.6 +249.6 719.8 432.5 432.5 719.8 693.3 654.3 667.6 706.6 628.2 602.1 726.3 693.3 327.6 +471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 +693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 +458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 +510.9 484.7 667.6 484.7 484.7 406.4 458.6 917.2 458.6 458.6 458.6 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 576 772.1 719.8 641.1 615.3 693.3 +667.6 719.8 667.6 719.8 0 0 667.6 525.4 499.3 499.3 748.9 748.9 249.6 275.8 458.6 +458.6 458.6 458.6 458.6 693.3 406.4 458.6 667.6 719.8 458.6 837.2 941.7 719.8 249.6 +458.6] +>> +endobj +13 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F2 +/FontDescriptor 12 0 R +/BaseFont/EEFPIB+CMR12 +/FirstChar 33 +/LastChar 196 +/Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 +462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 +734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 +272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 +544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 +489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 +761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 +299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 +761.6 272 489.6] +>> +endobj +16 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F3 +/FontDescriptor 15 0 R +/BaseFont/TAMYWG+CMR10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +18 0 obj +<< +/Filter[/FlateDecode] +/Length 180 +>> +stream +x%=0w m"G-5 ݌1*$&>r^ !Ȣ$O QiHh,ʶ3˼3%\m-y%!ξXTơ0)N'Qri%/`o! +zˉaTF +YĈicѪQh6A +endstream +endobj +20 0 obj +<< +/F1 10 0 R +/F2 13 0 R +/F3 16 0 R +>> +endobj +6 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 20 0 R +>> +endobj +25 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F4 +/FontDescriptor 24 0 R +/BaseFont/IJTCAF+CMBX12 +/FirstChar 33 +/LastChar 196 +/Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 +562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 +875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 +675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 +687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 +343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 +593.7 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 +656.2 625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 +812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] +>> +endobj +28 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F5 +/FontDescriptor 27 0 R +/BaseFont/EBENTK+CMBX10 +/FirstChar 33 +/LastChar 196 +/Widths[350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 +575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 +869.4 818.1 830.6 881.9 755.6 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 +863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 +319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 +319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 +511.1 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 691.7 958.3 894.4 805.6 766.7 900 830.6 894.4 830.6 894.4 0 0 830.6 670.8 +638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 +575 1041.7 1169.4 894.4 319.4 575] +>> +endobj +31 0 obj +<< +/Type/Font +/Subtype/Type1 +/Name/F6 +/FontDescriptor 30 0 R +/BaseFont/CSSXYP+CMEX10 +/FirstChar 33 +/LastChar 196 +/Widths[791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 +1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 +888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 +1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 +833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 +1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 +1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 458.3 458.3 416.7 416.7 +472.2 472.2 472.2 472.2 583.3 583.3 0 0 472.2 472.2 333.3 555.6 577.8 577.8 597.2 +597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 +791.7 777.8] +>> +endobj +32 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/omega/epsilon/theta1/pi1/rho1/sigma1/phi1/arrowlefttophalf/arrowleftbothalf/arrowrighttophalf/arrowrightbothalf/arrowhookleft/arrowhookright/triangleright/triangleleft/zerooldstyle/oneoldstyle/twooldstyle/threeoldstyle/fouroldstyle/fiveoldstyle/sixoldstyle/sevenoldstyle/eightoldstyle/nineoldstyle/period/comma/less/slash/greater/star/partialdiff/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/flat/natural/sharp/slurbelow/slurabove/lscript/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/dotlessi/dotlessj/weierstrass/vector/tie/psi +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/tie] +>> +endobj +35 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F7 +/FontDescriptor 34 0 R +/BaseFont/PFTUWD+CMMI10 +/FirstChar 33 +/LastChar 196 +/Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 +750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 +762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 +388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 +298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 +465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 +639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 +570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] +>> +endobj +36 0 obj +<< +/Type/Encoding +/Differences[0/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/arrowright/arrowup/arrowdown/arrowboth/arrownortheast/arrowsoutheast/similarequal/arrowdblleft/arrowdblright/arrowdblup/arrowdbldown/arrowdblboth/arrownorthwest/arrowsouthwest/proportional/prime/infinity/element/owner/triangle/triangleinv/negationslash/mapsto/universal/existential/logicalnot/emptyset/Rfractur/Ifractur/latticetop/perpendicular/aleph/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/union/intersection/unionmulti/logicaland/logicalor/turnstileleft/turnstileright/floorleft/floorright/ceilingleft/ceilingright/braceleft/braceright/angbracketleft/angbracketright/bar/bardbl/arrowbothv/arrowdblbothv/backslash/wreathproduct/radical/coproduct/nabla/integral/unionsq/intersectionsq/subsetsqequal/supersetsqequal/section/dagger/daggerdbl/paragraph/club/diamond/heart/spade/arrowleft +161/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus +173/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/spade] +>> +endobj +39 0 obj +<< +/Encoding 36 0 R +/Type/Font +/Subtype/Type1 +/Name/F8 +/FontDescriptor 38 0 R +/BaseFont/XQGLQC+CMSY10 +/FirstChar 33 +/LastChar 196 +/Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 +275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 +611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 +820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 +666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 +500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 +444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 +777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 +777.8 777.8 1000 1000 777.8 777.8 1000 777.8] +>> +endobj +42 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F9 +/FontDescriptor 41 0 R +/BaseFont/TAMMEO+CMR7 +/FirstChar 33 +/LastChar 196 +/Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 +323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 +323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 +874 706.4 1027.8 843.3 877 767.9 877 829.4 631 815.5 843.3 843.3 1150.8 843.3 843.3 +692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 +323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 +600.2 600.2 507.9 569.4 1138.9 569.4 569.4 569.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 +877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 +843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] +>> +endobj +45 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F10 +/FontDescriptor 44 0 R +/BaseFont/RJRYYM+CMMI7 +/FirstChar 33 +/LastChar 196 +/Widths[719.7 539.7 689.9 950 592.7 439.2 751.4 1138.9 1138.9 1138.9 1138.9 339.3 +339.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 339.3 +339.3 892.9 585.3 892.9 585.3 610.1 859.1 863.2 819.4 934.1 838.7 724.5 889.4 935.6 +506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 +1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 +594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 +530.4 539.2 431.6 675.4 571.4 826.4 647.8 579.4 545.8 398.6 442 730.1 585.3 339.3 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 693.8 954.4 868.9 +797.6 844.5 935.6 886.3 677.6 769.8 716.9 0 0 880 742.7 647.8 600.1 519.2 476.1 519.8 +588.6 544.1 422.8 668.8 677.6 694.6 572.8 519.8 668 592.7 662 526.8 632.9 686.9 713.8 +756 339.3] +>> +endobj +46 0 obj +<< +/Filter[/FlateDecode] +/Length 1104 +>> +stream +x՘I7 :>FEQK^@I\@ ?4hFciNcSEEm it^yЁ|?|^J:y``0$K/sh1m֎*@M>w( 4xmVx{ uDG5DcP$ MP ų~Ц gcУNC`?i,ߔ9$u +Beuٖ%:(ͧuVgD)IEtĠcĩ\b/*TÀ(3kt=hY}l` p 7/6RuManU֮Nj6nMPQ[i5AtIP z-hK&h .cHfYG"[8g6DjuI8L%wO˥;bk@~LY]婍S8+ysjbCYU moڛ3WA$/)YBAfN;SnBN0zg/Cf+358%d=Qeϥ:E@Fc^̑qqE!W+1i9L dwU&+9 g3 F΂8~qkqJ=C!qx[Ro9D^IMY.ܲGj{+YY[c/wdf8?M{j,WV'+UE]r. bZE=.:hЅq4B7 +WDc<Р#a:e.]FSݸ P m9(߶1>69>z>JBYA̬$+e @¸FX6}!![OvIr'{9$ .pӣI ˸t3-qJK\c6 +ɲNEnI)w(;C^ﭐ#^l隋 y+*= ꑍXzX +։hevώY0U;߷}6Ӥ7Fj.HkHąX  +endstream +endobj +47 0 obj +<< +/F4 25 0 R +/F5 28 0 R +/F6 31 0 R +/F7 35 0 R +/F8 39 0 R +/F9 42 0 R +/F3 16 0 R +/F10 45 0 R +>> +endobj +22 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 47 0 R +>> +endobj +50 0 obj +<< +/Filter[/FlateDecode] +/Length 818 +>> +stream +x=0{~ʤȞvW0pВ+jчm8 X+}?Dz|wZxF `J 펵<[T@Owf2hF|ЁX|<:<bGqVoZq @RS|IKm2<㦝9![yah@F8ݶ\Dr>Ia==ew;r^֮@>9QVSk*% ]0&c&$YwKt T;1TAaE}*^4/0Kc`F1! +2] fTYaƭa0fqWc&%fc7賙a+f&E7g,zf]-!! OR`(WBNQ@O~% +Υ%-[s"*Lxl0$dkLrCJg>|Ҙ&ÄL+1>0)=))}|zo}~<5; _M|+10yj 2$F?1wS(o^L[kA5Nj^jkŴ]ě&׍xu&ߖ\Rwkk՗b\IS뼽8/N}z:єG<*S/Ws> +endobj +49 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 51 0 R +>> +endobj +56 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F11 +/FontDescriptor 55 0 R +/BaseFont/IAEDAF+CMMI12 +/FirstChar 33 +/LastChar 196 +/Widths[609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 +761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.9 772.4 811.3 431.9 541.2 833 666.2 +947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 +380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 +334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 +699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 +652.8 598 0 0 757.6 622.8 552.8 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 +589.1 483.8 427.7 555.4 505 556.5 425.2 527.8 579.5 613.4 636.6 272] +>> +endobj +57 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +60 0 obj +<< +/Encoding 57 0 R +/Type/Font +/Subtype/Type1 +/Name/F12 +/FontDescriptor 59 0 R +/BaseFont/SPMOLI+CMTI10 +/FirstChar 33 +/LastChar 196 +/Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 +306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 +306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 +525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 +743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 +460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 +460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 +766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 +511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] +>> +endobj +61 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/dieresis/visiblespace +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/dieresis] +>> +endobj +64 0 obj +<< +/Encoding 61 0 R +/Type/Font +/Subtype/Type1 +/Name/F13 +/FontDescriptor 63 0 R +/BaseFont/RKAXVR+CMTT10 +/FirstChar 33 +/LastChar 196 +/Widths[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 525 525 525 525 525 525 525 525 525 0 0 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525] +>> +endobj +65 0 obj +<< +/Filter[/FlateDecode] +/Length 849 +>> +stream +xVߏ8~/nmo$^VwWҦ8 mЂD7|3!qNHwyC^ƯIEff5dBQ kC<&aD!DO+%s*#s fY(1g#y o4]ϗ`JtQ[!23aIqV/2ibBuf惴3&%(1"#x7kM,d)ߟ2HcRFL`U^Rﻻ{TȈ؄{9gPjOL F3sRg +ӵjot#ٍ0: J0OG-n +`q7) #OСQǜHi^讞YwNwr{LWLni| + +TF= `Φ hl>AQ[˧j1_ۻ/]5]?xD댮}ꡎަǫ{UfϹ-jEF #V1tlMe!ewӔE h Q9zٖ'C<&pM)7{btlzց:T, +r&wzT̮٥ʢBtC~ wLd"uհPf'[6W5^pX=a{__!o==LE.!Jޕ7 +endstream +endobj +66 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +53 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 66 0 R +>> +endobj +69 0 obj +<< +/Filter[/FlateDecode] +/Length 580 +>> +stream +xV0+|Y J8R.mU{L64BJ*ll,aU`ޘ{o AkO}|@|ԗR7=”]ĔJ9ł 4gCa:u3# pnAnubtw /S`grFg32Sl{%1[gŻMVY\";֬yY4,Uĉ!Vټ" i0'T,ycS-s1#`k2gHV֛|iqcmiO'eCF4RUF9d7EE6"7od߲5 Bv;Ŕ/Z>d8P BO~ġ|d[q1TV"f km4ahlwfU֗yPiusd m46ꪞs*Ԟc"`NbX/hkWWBӦe|r;ЍTêgL{S;v:xyv<pX#&_Y +[# P L B૶ +!THW"~ ^GB +endstream +endobj +70 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +68 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 70 0 R +>> +endobj +73 0 obj +<< +/Filter[/FlateDecode] +/Length 381 +>> +stream +xڽTn0^"?HHv萰Qj(R54Є*]rϹ?F4܄a@")@ ݳ†r˷_G$Iq0)|H:eA8?B9Ɩp4@0u;@G&~fEjC#!pit`m_j(}e*Z:?Y;:Ǥ *5iZY~dt<,x:j~=\Fo%=07BNmm%G\feBw~*0iUjMoXfU5=!?҆~Plz[g۶ͫ> +endobj +72 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 74 0 R +>> +endobj +77 0 obj +<< +/Filter[/FlateDecode] +/Length 757 +>> +stream +xVMo0 Wh+ Æv\pҴ ]a.?ʒ#'N,K#H! #wy|"Fp $[9E }DN9*WDW/8pڻpn@By T :QMlHp' N[<!-(I&pa~J `mA r+a BAŦd!5NZF@)$k,ыl/BҜjt*n `H!RsP20lץmRz ܁pJB6"26t(Ώr](v[B7ؓ)Jˮ]=V~Ly؛{ɁJCa"]½Z +!TǙilWɮ%ic&_1/*|Z-sު1 3/ (KE0rڼwxj0-ӻeY}ZfuUׂע]]}OJvÄV2tc4+4$p`?i %_Du,X/4(ZnjN޹.=?Mm1{\YVǟ}_wgGzǃ![76+RsCG4a]QZ}/h/&χULhqCXno?o?&պZyL&aUZ_WW +{ޣL. )# +endstream +endobj +78 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +76 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 78 0 R +>> +endobj +81 0 obj +<< +/Filter[/FlateDecode] +/Length 1032 +>> +stream +xڥVKoFW쑴}?R)c\&ueUξՒFܙofofHD 3 +[$BH3bFh1c\5 Xqڏ۟o5ri˜!Rx˯X,’hr&b1Y| +(l[@w[(CsySYXߣwN[eA #2)90%dϐ'E&+u) nUYg%Z{A%"g#baY9в 60M,/c83@ 1 +)$@@frx014!rNғ'Ak<\%J12FXs*FоJvpWhtRh2e)SM ݔi$_D[Ց Lϓ\1ek9O%\xpEFKQą6s[%9V/}^AB8`^I&~$%,7u|̍ D0]i-N1iʦZoU2U^Lܿڵ]hwv(T HmC&ǧC'~5'kS x2A`ο4`g'f`@liqCܐ!j}HO88·:pdע~ji Ы2mǥS_jIL`\]2H`ES֕2̪>ԝ> +\y;>v//?>/ !d, 9ubX<75_ݚ/qݟvNj5r5B\IX2# riSY9gD pXj{|5d YlU +endstream +endobj +82 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +80 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 82 0 R +>> +endobj +85 0 obj +<< +/Filter[/FlateDecode] +/Length 583 +>> +stream +xڽVM0W 51q\fr+64BJ*_'`XD ~<3!jަ'r ad$LbA!Ib$>$s1~M? !Y +b$0ZyM5J孊ojGqJDqS%?db| +Sùb>WNE+Jvy||ecV9ē$ PT,*xbWT}!Bn}YuHVr%3l@ZHg<쏻LY Bb +T~7〓2V'r02 +SX̻h#ɡʱ 3 Pi bzSKQdE}&qHf]I\ ( \q +&{nazm=nu1hH쎲DޣFoIY %iQ,[^:16^m Ze<*#iB"6l}cXt$7HXpI-iguY#]d):ӤZ9 rZso)~'W̻}چdʨS +> +endobj +84 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 86 0 R +>> +endobj +89 0 obj +<< +/Filter[/FlateDecode] +/Length 590 +>> +stream +xڵVn0WR8R/MWӖ[Ckl`r1aͼgJ PwpW,q +D"(jq1$cş'@b|DF1kw7ӈ, ABk  7EQ?f$.SBׄٞBL8$NLg+9+)Eʈ(ey4>L!7L~VK}//'#{A PmSFrQPWJT!&L4?6$O3W2;1~ g=Qr&gΡ"i?߮Zׇn_n۝~ھtϕ)j-z$i"|nM=zu[Wh'E1wORMDQ2Y,'/=0ЬW %}8-TzB {633}8˞Gr/UKC"rPn7,μGj9@pSKcyUco[KukƕdCӬnm}U]S*pC2]lӜorcJJp.OL1LUlyj4!Y Ï> +endobj +88 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 90 0 R +>> +endobj +93 0 obj +<< +/Filter[/FlateDecode] +/Length 241 +>> +stream +xڵQ=O07:u$ڦ2D8%E +zPD%t~g);L0FLK'BcDKNER(!+(޹,0 C6oں;1zߤHf"1(9;̮aS%7G%9h6GңxsM44]14S' +endstream +endobj +94 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +92 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 94 0 R +>> +endobj +97 0 obj +<< +/Filter[/FlateDecode] +/Length 972 +>> +stream +xVn7+E!E^hѢN.keL d9`ˮ +cvцCsI8'Hl~#,gIEwf5V1!P!@9FⓏ?f ̛"eJc_)X#T1BN)D6 yG48+/gZGFr23-=u^ E!cAg kȳ"sSY])-An ;r̘@S(A.b +XTp`FbB`G.b 59aކ͌'ѪՑBK.P28%Ӿhh d@&R(FyF[C- ܹ5b6*c$ V&f"1 +<{J $s6/7\LH1)2]I?] y_*]sWiDtZQ`~܋x e~a!96;dlS)Y$}i&^-8ghN!07ӵ۾:y~ הk@[Oǭp9z1)IuYOU5_lwͧ}uܔFeQ=@9y{JOÿnocÎzg}uYj5_t|~ϰIcoz'<"pr'I|jFfgmRv{w7KcЬwc;^^UEW8"*= Njӑi=L^nt_2Mx˰<_ j +endstream +endobj +98 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +96 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 98 0 R +>> +endobj +103 0 obj +<< +/Encoding 36 0 R +/Type/Font +/Subtype/Type1 +/Name/F14 +/FontDescriptor 102 0 R +/BaseFont/CQTQCY+CMSY7 +/FirstChar 33 +/LastChar 196 +/Widths[1138.9 585.3 585.3 1138.9 1138.9 1138.9 892.9 1138.9 1138.9 708.3 708.3 1138.9 +1138.9 1138.9 892.9 329.4 1138.9 769.8 769.8 1015.9 1015.9 0 0 646.8 646.8 769.8 +585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.6 +646.5 782.1 871.7 791.7 1342.7 935.6 905.8 809.2 935.9 981 702.2 647.8 717.8 719.9 +1135.1 818.9 764.4 823.1 769.8 769.8 769.8 769.8 769.8 708.3 708.3 523.8 523.8 523.8 +523.8 585.3 585.3 462.3 462.3 339.3 585.3 585.3 708.3 585.3 339.3 938.5 859.1 954.4 +493.6 769.8 769.8 892.9 892.9 523.8 523.8 523.8 708.3 892.9 892.9 892.9 892.9 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 892.9 339.3 892.9 585.3 +892.9 585.3 892.9 892.9 892.9 892.9 0 0 892.9 892.9 892.9 1138.9 585.3 585.3 892.9 +892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 1138.9 892.9 +892.9 1138.9 892.9] +>> +endobj +104 0 obj +<< +/Filter[/FlateDecode] +/Length 884 +>> +stream +xڵVKo@+7ɾrA.[ T +mI*xƻv#|3|;6a!=y)HE߈`5Vdb3ʹУ ~9E+xv893ă7 ,Cr-8Oa U]iC LC_{Vj8C~ (_37rav% W F[\1X.8qq3=hA \cɅ{|a'aͲwRunj~}5bſӀP,z]bSk{m4X,]+8#V}P">! GcyDc;tc!* +A |D[PUBALtоg W0Ljkrw{滇jqCk7e[:]IqxBq;"> +endobj +100 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 105 0 R +>> +endobj +108 0 obj +<< +/Filter[/FlateDecode] +/Length 453 +>> +stream +xڵUAO0+zb[ +4N17LA64xt눚 }~+#f@nev~I +03 `D|Ɂхń:{S$t}e-Z߶+> 9@do$hIexmy/fl:^miY6\XB<> +endobj +107 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 109 0 R +>> +endobj +112 0 obj +<< +/Filter[/FlateDecode] +/Length 831 +>> +stream +xڵV]o0}߯c(v$6Ǖi@YDiƤ]NH"m$:k€1rO'ab0$Mx&B##3zAgdSL \F +E'mJs G ~Ql"" )=ɂN v؟ DlP̐*P ֓;ݱ9&ՠyQ)cLTXԚ&hi n S mC$\~i"mD1FT }VةX|}|M+ylugH9snmeWd'e1ujIbΔ}b)F :Jy |Λв8Gs=nf/o%t5?ᜊx3>k {ۼub\78b,ec)Wkޛ.fŪGbQːA +/=(TT^|2_/<<܊K*MkGS覮7iwzW)w ʧ~Ͳ,{@"_'DzAm;i'\[F"T?ݣ4](op$͒;~[Οyry^k|۟V=%ͩBpDwFpP6T&[[m:pw8B c4ƚ}4Vf4hv/ˡXn^M_ο̟j6kN) J4opTG_ +endstream +endobj +113 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +111 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 113 0 R +>> +endobj +116 0 obj +<< +/Filter[/FlateDecode] +/Length 1099 +>> +stream +xڵWKo7W+9|-R)c\Ǖ T;|i}Ȋ&o8&qNIxL~ܬ+"l$F0 &>UB>k%ϛ_W q"eJ&=*δ$T1]8xrACfPӰƐ/y#ѩ 9ēe!  jL5dl? E &L@"#ӺrDC$Aj1Ђca*ȲC} +FÚXG j`+725ECxRC3#Y9bW _0iKDqc1∨##!" &8V'׎-h%^h|5<[FEʜwW38pI^q=f( CdT ̚BeQPIÖ7̖m!2;;`OzI1%8lvA扸 +8`!ؐ`y)כ[y2ΠGKJa3D/W_` c*:AZ7w#1м>Z@t$Skrfw_ۊ~lf\'t`Q) }I7>|H:O)23( nbgN>4;JԱ9nd4NiMcDf\jv?>>|}l~_1Ʀy}fq1XjVTlE!M`™WYj^Jan\:cZ&I0wϴ.~R +endstream +endobj +117 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +115 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 117 0 R +>> +endobj +120 0 obj +<< +/Filter[/FlateDecode] +/Length 524 +>> +stream +xVK0+|L9Wb;R 88%RP[,kBdyHbd^ʹ=0*@F )F$!H^ @9(a$H|a#͌ +␇YA2Oc> uNy> 2,=複fz𗕮go槰R 2%ę> +S^r﬩)dJ!%SAUkt*oګޛ@6_kյYols~Kׁ9欋R W^&ƻ3ZϨL2!tM cEG$J]S}hUv(+k7 Í$*\ #GZW0n:W㿜 Np]tH0 V};UE^veS(Es󗇧2æO>R4mYV'ql\ =G:W~(\ !1&&y78 +endstream +endobj +121 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +119 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 121 0 R +>> +endobj +124 0 obj +<< +/Filter[/FlateDecode] +/Length 133 +>> +stream +xE0 Dwc2؍FD`DceG!ӝӁ#砃%+MkH(2`e1g^ߘ֢x19NuQ:k9dglK"Bbz~% +endstream +endobj +125 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +123 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 125 0 R +>> +endobj +128 0 obj +<< +/Filter[/FlateDecode] +/Length 969 +>> +stream +xڭVMo6W(yC.9^NͥV65u@~|Zi% E̛J3go_7Ť"ۿjBe +׿^WB @!yL@ FG? DV`BDC@--L9B5re~'ch|d-@UB +KifA9f,G@J$Oz=x7pb͙3#vS񨐜L|jXSɬJP1$Cf( c6i f%":ü `Ξ3f|`Tcv49bRV c!H\ +80BsIà_Υ^1Rِ+Jb2yh&=0$}2 Rw c^wB/ " 3kF!gB2f8 9 !tC:'b4<0K#Z̺&2Ɋ_HD{"lS'J=l?/Q"P4 +bvynZjjgOrtLroPSv㘀jf0 m}>Ozzxj4뮩6&_RJRX[Ug'0pPշJp'j257ebn( m&H^צFN<đ<_..M TB:S{쓫,u([W j=rE gqP,^TIׅu)SAl4ݦNwZվfD)&!?}FG|N1SW: Il.Ӧװ.;[^NS[(F߭sέEnOy"G>AQK0 +/m͏|@|*|yp' +endstream +endobj +129 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +127 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 129 0 R +>> +endobj +132 0 obj +<< +/Filter[/FlateDecode] +/Length 602 +>> +stream +xVˮ0+4vl#i˭%7K(@TGޱ, 93G"@/d# BA811ǯk!p¼4B2+}C^`8*WAeJezz. +q8-ooI<%O԰*OE~>s|ۼ_Iًt)~RZe riַwV(7epU\R;I}1UzPL]+4-řYu5};7;_|h ͛@3(DL0;gR9gĥ +pjG}yUkvk:=mӞO׈jj٣j +A=E">)x0bܢОjG$sFJ LdR.'*MLMiO lۀZ$^@y961V=0<E8k/tUA7< +endstream +endobj +133 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +131 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 133 0 R +>> +endobj +136 0 obj +<< +/Filter[/FlateDecode] +/Length 590 +>> +stream +xڵVMo02?p^v-H (!+ǯ! 6Vb03̛y j._DrW@D`9Iߋ?O8Mb8\n`Y@T. SAm {$1.SBof{ +*Gܒ8*qLWrV"RWQ؛oFl) [Ѻ.xRGIP&@=7uAU,FC_G_ pؐ,ETwbj".f>rMΡ"i7߶\ׇv_nyڼe_؏[Y{[ID~lQUnvOژ=I/{B(n'ʎ~)Vɤao(S.o"5pjf̰,{ɽT5/{ pDg9;pd +9mWQ=%Zd_Wf\I:v4oۗXU=EbH7$?bcܜ挌eDϿGxUcv=P +PspubB ef{S;nb(~4?4cƓL(Z$t)]qx +endstream +endobj +137 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +135 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 137 0 R +>> +endobj +140 0 obj +<< +/Filter[/FlateDecode] +/Length 239 +>> +stream +xڵQ;O07:G@``(CT\'RPR׃ *Fwdnʥ2 3T f'BcB+NYPh+i!{}PXLDZڈ?)?,*I13e[̅#(ۗ謧kf. UU>. My?|,aQEv.>(|f+TC{S +endstream +endobj +141 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +139 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 141 0 R +>> +endobj +144 0 obj +<< +/Filter[/FlateDecode] +/Length 892 +>> +stream +xڝVn8Wp)7  dѢ`f9q7@v@⤶|Yl9o(uι2aA'89W jBO*7 ]}h%}}xXFт., 1lg6ugbNǼހ\NNmDp1'Dh 2oUR6攻-HKx,JXBwPJTeϰ͠6Em^XG` Mɯ-#] ڔutA4H-w88S+"]p6&}jsFHc=Zdݗ;p$1MbV۳A8 Nٝ N?zGeQ?T;Xq+(}Z췅P0+&>wEWAv'lbĊA6?S!Wh]i*~j,cTRxp,˳yQ_{wa ^CNЎ/Ǫ̛jnkiZhFQS^(W;ՕQaZ4pV՛hU>@2)!F+urŭ^5=jنtUzq`Gl*$W"+L>G"k@POBfCJ)=h_H.\>qO~?rlj^s|=%-z.z>,no#m\o氎l|Ѷt:=p@]kh韑BvR?-CȵBj5/L?g\^ +endstream +endobj +145 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F8 39 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +143 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 145 0 R +>> +endobj +148 0 obj +<< +/Filter[/FlateDecode] +/Length 1169 +>> +stream +xڭWKo6W𸏐K|)q.b@IumU)iIQ gof(8'_H\~$_*"\N`Vj,SF-xjχxMA)^AV6t<9;(^͔%^ЖCCP'Sy)vD1*!9f 'X\J kΜ+»>3oA"LO=Ƈ@DHDQǖ+^p4xDLq?bE3 .9y<`0gЏ.L tK\J8@gV.W7X2rrq)kGIUYr(Vq9dV1>f E`rl#й8*Pw؏Փ[ޅYER1Xq}X&vOWuL.uhF uIrt[;d*@^ֆvkrm%L≱!cQ=a̕J,R>NM"doSxQ <0!rLzH2 |''a`e3jLjd6LLQ)lקSxscUO% Ȥՠ0 TT-y HKMcڻGphFJBFYnۋl=lko~^vfpY +m5Xb*WPª͞}E:t|`hhq}p\jؚ[N* !fC{}k7ܶ Ͷi^N;0H!hMg7T@y;ؗ!Є`EYVD!.~í{G0豖p3PcIEPai%x +6"^tEJ6r˅j|Nu{nZ[*Bf=Ω[mme9=!Y&ANk:^e@rF#$53+1A>/za ]uǧ'?) ܸ +Qzn%b 7f{Pxenި۵OiwhkR + )JAP +V5whĢϝVg8{~"c8j-^CiV^z2G&|Q/#D +endstream +endobj +149 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +147 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 149 0 R +>> +endobj +152 0 obj +<< +/Filter[/FlateDecode] +/Length 590 +>> +stream +xڽVˎ0+Ø)]J+1!I*Gl RU"ŀ9$-P6?p3|# #~gY, >?_OkKy:/o(Յ8#q!A* 4}. ])9~̪ljG_+YH*%ۧ]gu?5 +&Q.kTԚ٢d=ԡ˖:eD(s x|L$y^FI$Ovb) +ٲr s;lSfŃ[ogT}~&DLf 3 +SFS7+60a"ժ[(u^O%_+2*~wy SP)1HEL%ŵMwFSkACSV jƘnb"jqnn/6^c QxU#Ca4)W9p;@UxI"ͳF&zogl'k0Hk> +endobj +151 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 153 0 R +>> +endobj +156 0 obj +<< +/Filter[/FlateDecode] +/Length 599 +>> +stream +xڽVM0WRrH\ڲU-= aH,Aď$y3y3lDbBP79<XK++}}0~aD$w)?3-vgc,jGa˽l|qwDFz6#,AqʣHk&K@m꡸Lp$n&o&*ZDũ/8&>@7ˣ]@n9#w 4Dm|aǵu\5;z. LBH4z0LbrQry*ƘP/;Za%Cw9njGͫȮu7ٱ;6R:`N%2N\iZ̳Od{I +endstream +endobj +157 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +155 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 157 0 R +>> +endobj +160 0 obj +<< +/Filter[/FlateDecode] +/Length 330 +>> +stream +xڭRN0 +/H*;u%-FbHIS ԏlj]HE{}وJQzG7Ii%JސaɈ({0^Xk% vg$" @$%L, ((׺)xIzeke֗K#h ,ߛGYHJCwO9|Ӂw 2iaPEϝ"vטξ]i\wfd1޷r*&ιjݾu[ԕe1+jzzj]_ l|3+^/ vG_W-~<I +aļg1+7c +endstream +endobj +161 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +159 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 161 0 R +>> +endobj +164 0 obj +<< +/Filter[/FlateDecode] +/Length 1013 +>> +stream +xWr6+ś":vY %ˉflٕ2Ń"DfQoH9e3 "Td~O 0 5)\PinBɧ )Yi| Z)!D6-&1ms>IJJ2]A3ea&ڟ\q +m_D` X#1 s5yK YKCѡ +z&W~r>2tI4gNg5]SŜ#Tp&Mm ɴ)FtM࣏킯{@pl&bdu}MMy?:I:7JxisV̲_qC &nA8 sq)yYI7>t~B[,XmV۠OGRcCY7hUm'D + s2lN{ %eǫyͺ?Wx0y\zsbe(01KjWqqn]wq8vb үPZa +endstream +endobj +165 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +163 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 165 0 R +>> +endobj +168 0 obj +<< +/Filter[/FlateDecode] +/Length 942 +>> +stream +xWKo7WBR)c^MTǕ D;CaKD9oR[o SFhöS[ƽƲ/ +A50aaǢlP*,pϬ:J k'R`W[z VX'lh{.eT簱p%U۬ОL$ gU(ӏȤqFa!e&)y&03 +V@2Qq ?GZ$0%L7rU^ +\%͹wj}%1=17.pF+wG{82E|+' + @(02:/'3T<80yHABiM1y{̥ڳqwSi`.?'@ԸN(M I3K?WaU toۖjiHq,)!L}fUӌY(.P_5*i@Wʲqzv뱝M!뼜cޒˎ(W7]uXq/jo\fIwYeP=SYT?B8>]~%W^)ּvo NCzM ̳)sp`)pWxe y{s5b*3ѣ\ܖ}$n]c\peYʄY ++}yY^)<[fnr_WLJbWLMp} +^z$9:kx`O<!! +uLgs!ImTDe%#N\V>>ޜ6 eqjg!qаLݒ vQeLknM8a20 +endstream +endobj +169 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +167 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 169 0 R +>> +endobj +172 0 obj +<< +/Filter[/FlateDecode] +/Length 414 +>> +stream +xڽTO0W!e-k)q3qI% fdb"{ !V<;ws` 03 #:ZԠ +C6ma,xY,b 1 i'dzȑgh$Z*40B=ނ> +endobj +171 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 173 0 R +>> +endobj +176 0 obj +<< +/Filter[/FlateDecode] +/Length 963 +>> +stream +xWMo0+|LXz_J +#,Ҳ@m%ďgl'l>] $xf޼yI!%{:{h4[}b3;#ag.Ps˼6]a KE0YQhp Ŋr0`(fܨ+Cc)Ytքt*UPi:n(BXΠD ɦ'hQ#b!y$ĄGG@`ThRAa[ BC.EtmWl-,9kA=S +,mE=ޭxBI 4tAmPקI +)S1G'M`JIFH=EIƎ:7Ik/9qǎ'A64&8hȩ1܎& 62:La0&xT[8jzgKx誏HsԷ:z#B**"X}iv0ðL <OH{7Czs.B՛(hf]msn=Xm66IHр7iөv0Tۇm.ۇ2> ?`'uϙr0des8X}o1N5)Kf)#_M$HrDWӁq2\>+_<ծDA[*A˃jʼznˌ~Th?xuD4No_8/n\HhOF3E*lnLoooWv}OˠbZ}M@z|jyGR EϪ}ل|hmyliDD(.$5H?p +3L^W:UW̳jf'ģ"ev qn-h3R+Tw3 G~<(h>=y +endstream +endobj +177 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +175 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 177 0 R +>> +endobj +180 0 obj +<< +/Filter[/FlateDecode] +/Length 563 +>> +stream +xV߯0}I[’F'oVr˒M6#&-mQޫ1vJ}p`Ng$Ip~i H~_TR%,gR 3ܾ6"uQYB/Tzկ\~ÁNG"""#;Ѱ`A:UmJUx fxuR^Y67KbT lQ> +endobj +179 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 181 0 R +>> +endobj +184 0 obj +<< +/Filter[/FlateDecode] +/Length 543 +>> +stream +xڽVM0W2klcZU{h=] H! h_;0!rg33 2_@80;Ȉ) 9rjEfr(nZ2I[ .#Nw1XN0G@(̉\`1YQ6J[:ݭTbL@.NۼܨeQ9ɒ4ӱE:B-i0O*<(3e$9¹o$hLH=IT33I|'3Λ1V1}Y6-#ۺ0Cfm*rSf+7À߼L*kЂ:YF75J'H,e̋JYp#F0+^p٦[y>Uo7l;@sToHS%r "d5jy_isi>Ѩ`/ PU +7OjBeЇm +*.u7QYv3F_ۻ2Lsp5rq~7 +endstream +endobj +185 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +183 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 185 0 R +>> +endobj +188 0 obj +<< +/Filter[/FlateDecode] +/Length 1052 +>> +stream +xWKoFW쑴k[/E=6a ЮP6Pȏ.)KR{.|30V=؇X}5T.lRRu RG3Lj:O5h|yM= gRSz*")뾧<H +̽dTz ~?TqIbBC +s/iAh ,!ɠkZwYaW#Cp03Յ"n'{OT%^G, ېEtcX^n\7AK/<,4r7A1%Bj>l[:Q FTzKeJ:)% qeOIΘ!A:b4 bFᱪŢ9!2a8=+QqӺ'RT/V 1@jI}8&TXZ u%6.vY,wґtFpΉ.mBB.rrW3z`QI)ewb89)tGLGCN&?hk;ͩ.dDɺ;n?Ԛѫ&wM^=<}]Z F;i\gK8ņwʹuUxN_$zB #3:Bǫܠ}<9XFyw󩕍^Мb7ϬySdeН~KVzD4ZU[*W9zYdN^ 8 +ဖuɪdZp0 <5|ww᷷۫oid'B?:Hy +endstream +endobj +189 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F8 39 0 R +/F11 56 0 R +/F3 16 0 R +/F7 35 0 R +/F9 42 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +187 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 189 0 R +>> +endobj +192 0 obj +<< +/Filter[/FlateDecode] +/Length 500 +>> +stream +xڽVn0+|E6 尫MWnel0YQhՏIi*gތX}_ 218ۓ#@3Bsjal|Y_mډ Fٹ .EVBRBZ5itW?<\ʨulχ謋1U5=uNB'[n~neD=JJ'!7zDhj[Vv,܋#qƥHp.*){6np^&4{*cgkn?֗2𥳐}|%j#-M"w~ZWv4;~Wbl9;mE#,ts5)b̝Lq.vԹ,Z,SO3C}RydY8J_Ee|.vbBfjHit[7Lsp_;T +endstream +endobj +193 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +191 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 193 0 R +>> +endobj +196 0 obj +<< +/Filter[/FlateDecode] +/Length 818 +>> +stream +xڵV[o0~W1S/bC &]*uh(~q>s/j6$rD[N l@p9OMcє9tQE:3ɀ'ak=> y$fqN(7iE53zU({;fn^.'lOɚ(FӮGu%<u%O|0[΋Kwe ƗAjl-E1/Vu<3:̳ 7yƇn=ۆqi[bM)TMu^$QB>;|Jp(n/3'TgPTup%/xs(=&jB,xH_0f2,X=M: Ud#f_OQPZ<|o6=lT`7gS~iI`:'焝mola"jHC+RR1Z݆CwUfqQ#70@z\S~]Uu H +endstream +endobj +197 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +195 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 197 0 R +>> +endobj +200 0 obj +<< +/Filter[/FlateDecode] +/Length 829 +>> +stream +xVMo1W4HZ5cC/&BHDH +T%R~|kڻ Q/⏙y7QB)C} %b&H3b†e3UvɮF\M5jV!?cV#,.Fe7;&F߈SJEX$qCmKtQ9B.~vEF2*$aW8[cs# +.Y?p^2<0TfӘ֓ [ADDT-4a<-rEpgԐ% Q^rE6?[o$y"M5ΡU)E7=&A| 7ƖL1Vڑ)&ΉN}Cddi8YMP+`/S<1Sjƌ4P#8ܸNu}>Ӫ}gjq]inq/1 '2䌱q\\r^X{].4N*/r4^unXd5ǻk^ L avsfͶ\mfr +endstream +endobj +201 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +199 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 201 0 R +>> +endobj +204 0 obj +<< +/Filter[/FlateDecode] +/Length 979 +>> +stream +xVKo6W(uC.9| R)c4$֎6-!)J]@BR3O;EbRgbPdc%lM]}6Z֟3LFGߓ:J4*1އe!Aԁf!4+P/30mδ$w{> lȜQ[5G&,-ATq36Ă;H/ $0dP{yG*O/Ʀ tS88ؒDX 54G s6ef̈!@ @^#!t?YĚ9e>`gdfS ".q姪%R{yGg<C)CC8¢#NmE@aM8,\ +0򉝯; L7!P~{$sUMOX|w f2:dtЙ;N,Wcqu6sK.CTPpcC~c +{o!9 )Gb TxIAyqZ΃w;f[튑8|!́|q7?T% +(}NgY6}9][`V +(U[5oXʶs+6V,N EV4?iQOtTQ笪w!HpVmGs)t\`^mӄ-8:;SgbֶOAܣ<;_GU>+ ;wR1[7Iogw?`Os$ߐai0\s/FoכS1?bڿjީS6vf\(WQa'/gab&I 8|eC6/#-!f|:68E{;jPvjps^_ϧr)SZYh$ 4y7ݏ&` +endstream +endobj +205 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +203 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 205 0 R +>> +endobj +208 0 obj +<< +/Filter[/FlateDecode] +/Length 579 +>> +stream +xV0+|A +u;eִZR TM>ۄ8`gRp3D"BzOhd$C)Rp¢TSb D-mLJ"SI-Ы,2XzP,rjΛ}]nkuYMGn>2]Wm?7t>li5 BQu \bsx MG̴X2X5#*o}Eq.^ޮj 3!ԋW]˅lz_r2y]ZMgO Ub$D 0(KZ@fܒ8T81"\isoXh g6,܂r8-?_tgߜG_Z) +>jNK/Y:i͕t[e6k-(%%l`kHG'.>J7n;H4K) 17fl0lS> +endobj +207 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 209 0 R +>> +endobj +212 0 obj +<< +/Filter[/FlateDecode] +/Length 552 +>> +stream +xڽVˎ0+ 6)>2Uj "SV64Cck{= Cx{>a +\l@Nl&(BFMHp;M rMViWC%^; sz1~_c?9 72C̢2uϏS &/1R}8̉$Д :8C?m* pTur8^,j;쟒,\ı}9QT*ix.IԊ)UqEZ-ŴhiZzTc1>yun3t5:m_>ʬU=Fȩ/K-5j.J3+˂U]O,MsZW7ҩpZ fܸt^p7y͹˖]: wsVoYG> +endobj +211 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 213 0 R +>> +endobj +216 0 obj +<< +/Filter[/FlateDecode] +/Length 905 +>> +stream +xVKo;+ω.K &i +ڴ$A7Hx3ɤ y}p9D򖼚M("njBbBp#*8E3jqnƐi_4)DGKbe4GbXV:<r7\ΰ E'9%͙n\6 :8VT'ƒ>.XZSRA Q:_Lh1@qό#2BI &ck>Tgp-9]ls%0yo%14SɌJ1BpOF7 +ų+7yjs0N.zXP(x>k) >KJpL_C ;_x.cJz~5;xx1cvxS.$9! Z %!=}pdoEÔEC{k!;s^KG*<$ 1X`Qy 8C @̤µp0??.O_9~փL _|UA8eQd}w؁WQ)n=Qu=XwOzTE} t *x%RIIB*)BvA*uJT`x5/ho(`vFr `ߛcW* f}:ը7d $y+UVP4fhzf>TXn^0N#~y_|zenғ6RҰzRC2H4BYNzt [*x'Q}XmSPSWmS&n^Wq{]6["_^+Y,uM_CL9-]  |O +endstream +endobj +217 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +215 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 217 0 R +>> +endobj +220 0 obj +<< +/Filter[/FlateDecode] +/Length 1059 +>> +stream +xڽVn#7+x춆Y$njrh;c@8(||d/MK>ŮI8<|]WD(&A`Vj)M?|,/@{C<&ؠ$ߒ[oRtP3 +1g_c޶=yvJ"A2ª桙2NRm2ib"eIz[nj [h*Pb yvyLnٹcJސikp2m 0HKi/dˈ힚y4/a 33mD3ɴCCCfA#' +"g%nMuwߴ`6<1UaycɄfq6Fkm9:ZO?h}'YK$E%i*f=Z`9F +Man ^MVq2{մ]0)Xꗒj'}=')VmRBpU--TmU5! ԡ=\ +/V}VzF4J 8O\ ͧ 5GgTZpT햍|P$<.VCi>r*Gqg;[PAR˟y +Bc\vRd/mXeUPO>6IקOUqsx~ٽ@; t뺦wwtq0V2>pOTBF + Upxj| +wyK +endstream +endobj +221 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F2 13 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +219 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 221 0 R +>> +endobj +224 0 obj +<< +/Filter[/FlateDecode] +/Length 506 +>> +stream +xڵo0+|$Loêզi[ف!JRN`!!rAVkm|s ΁@@r GHqxzL&aMMs@|[L՝7&xduro( zdh )?X:6~nTd69on2/Nƕ|jėֶGeLMZe[.uýo1,2b%zH [AtI,% 4VJKHjS]]< cE2i`:HJ}zIIf? ;|^RlYZM?ʸg[{t>E]Z> +endobj +223 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 225 0 R +>> +endobj +228 0 obj +<< +/Filter[/FlateDecode] +/Length 982 +>> +stream +xڽWKo6W(ū1Ç Т٢=6 dl$:);),o Eot-k?BVJ@Ͷ?~$ !>rVBi| YA&ҢXPOa[o&9[8p=0pNN,4MIP,!=C:#:T*[s=O,b(6i~oWl{3aihbS A:Zrp69'[1XRO<5԰DN%hdJؚI,A2B;-'3;-,C O&i|GO =Ģ7?TT:&e)]̶r@_4=n9}eԢ66jБ%8qr5|p>nh|e;y+!J2bqH,)NH nt +h{7B<*K*va^>8{셤;HBssVy:ݰM5[M㬿ȻA5Q]1ݥ\7zՆ { F!3p^o_veWeb]e͕,ln{Xe~Lag?;8džK#7dψW YB*}4V8(n7f> +endobj +227 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 229 0 R +>> +endobj +232 0 obj +<< +/Filter[/FlateDecode] +/Length 1209 +>> +stream +xWKo6W(KR4[Ǯ{jhn ͦI@~|$Rd;)Bo8CW2VTav}/+.JsjTE Pwk+9#tl{]9괗A*U^"DΓZiE_ڡƨqіZ]QށnW}@?& \PsVhED2$?ֻ14Ud v^"&YKՃS;'8T/3`R4A1.@0g*tNS 1v&@ʙ! +dU:CծjmjD0zu 5cs`^TSmsЙ~ex<_2r23c@9T +_<"zTDi#@c UZ5F51at7y`tm;klL6Μ_n\@?.(ʡP@h +|7j$˂2{byiIGHriq⋑u~r=CoV_(|Www}|蹋!R1}=5ɷ}756Zrfubkzws^qH2 +|Jg YoHm +R /iP%ؑ~16ݭ{iK[Mx̐.j^Șu!%ۊ@nФYWC8륌 q>`{MשwTIכ&ŷ(,Uo+@-X(,XتiB]19֢PᎈbPU(V7{! Lۣ$ɳswH="[X(o8X~oJ; y"2|'}R:qQN ;X|X|X?Mf]Nifɛ u&zw(`;$rFTv5ˋciN[]j=%.Me'1FoI٠1҂\9c\aPڿ`{[?ڄh +endstream +endobj +233 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +231 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 233 0 R +>> +endobj +236 0 obj +<< +/Filter[/FlateDecode] +/Length 523 +>> +stream +xڵVˮ0+EEV.v &E +%ĭm=Üx@B` x<=cHGr@`G`9qo_mHGTʷ!#ZVvYYcWkcGvE$#[Ҡ0}D('~2&(\3|!fYD#t'8 ac|YN&6oޔݔЂW# MxWnm"aR0qhaӥdc_д-r%asUWQ|.&.y=B*>ZT 4=*C6o0#jړTR{wMy\F_mm_ʄ'M qTd=8TJGEgS'<O\ۑe¦2Cs cUDW~Xuѻ狩O0e#T$fʼ-~zfz9¦5n>4۲/2Jjw> +endobj +235 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 237 0 R +>> +endobj +240 0 obj +<< +/Filter[/FlateDecode] +/Length 196 +>> +stream +xuP= @ \/׻K(VQnҊ:(퇢H呼B@I0тbHeI2:-قo&@!"ίAG`R">e.Zm=YnµrRM^bh;BrҘI%5'8~뱮~U݊ yg0Z|GɄ;p ^`RY +endstream +endobj +241 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +239 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 241 0 R +>> +endobj +244 0 obj +<< +/Filter[/FlateDecode] +/Length 1180 +>> +stream +xڥWKo6W踏K2KQhsiJM k +wH"E뭳'fmeǏׇ +\hNj6T-xjχii Jr.& +r&n3pa^܏R10TThaidk :|aXFh"̲3ym+Lr1$4d6Ve` TC^s'"\P5/AJQPkhM[34y +M5mC&y?yw4/8mi3{2yk'[IY~N +YLɈuR)þmkm$h|Im`7W8dҽi?`rw;?2>QR92Z8 l,W+ fmQ +j۵*-Mq% 2;WKǸs0@1w(b5ցa**귒Z{RJMW5{v6Yiij;MMWA]T0G)`@Ǟʀ5&^4(dI3Arw_pģ0A/C'+W5 eHwp _'zI*|3/ͼzd w:? [\-K;>XO?$!n?nΗ!v8g!F!ɼ/.o_cPdn{moqG;tV$\U un$=+ۨ@)bL!G( K=#ҀKې/eppڰm+YCfAsOx)ZE +* X2^m aEY`sWx1.~5Ra4zyZ0)*GPn +TJ+̓y5WԪ}D_g~"Ae\ֈXiBWd]' IjCt 9s@N3ThiOsQ+Us13~FNj_ؒW -q||C)]CWD>}6nJvL v/r?bá +9lvlw_9Xi ^O?ө" ԧ&O_ΈlyUq݌T2Ux'n"ƿ҆k +endstream +endobj +245 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F2 13 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +243 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 245 0 R +>> +endobj +248 0 obj +<< +/Filter[/FlateDecode] +/Length 616 +>> +stream +xڕVM0WR)ivl'FҖ#ͭi,J +TM%~|vB 'x潙06^>y3=Ie?D Q½7e=a8fHz( +2Bh})n/ C\ט]D84@K X Wds汨]c[Q^GERs <0qvX05tCtU蕗T&ԱK ˹)bYO=ܔ'{ȰEt+ ׀U Yn@nt}4n' k04kaea7fURwAvZOKP4=}8:ʪӐSIH%p۰lk{9 WU cgcZ6C< `k;e֘)RHgqOGt I9)6jaܴfik d: +y ?,il.h,6gOE=tsFJM`p_xjFjt_C0Qjg&ue?sH +endstream +endobj +249 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +247 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 249 0 R +>> +endobj +252 0 obj +<< +/Filter[/FlateDecode] +/Length 595 +>> +stream +xڵVM0WR(8٪UOYnH5ll@TMl\77&A +P/_tq ́@@ 8 a df7d07,8wY$v zf?oHxŘsJ1ARKtGSYuT:|T>V;ufsui[~HGs$m[Ce$ϗ⠣0QP+рXjg&0ނ?< 1!gWܾn<6"Ɯ/K}ͺacRNCꬳ:J Fr;iުKSGԮ,fBL7@?Btk|-p{Y62EFgHkص(eNf{YX\98Cb_h5Linhd@+HoIu5}lpj7kHV0lM\oWFnGK LRW⼆IbrtP:N~CLǾ29_uMɡ,Š|!ƣXd5ɴJ~= +endstream +endobj +253 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +251 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 253 0 R +>> +endobj +256 0 obj +<< +/Filter[/FlateDecode] +/Length 391 +>> +stream +xڭO0+b!--t،>xY x  &r{wJPmE4RQE($KF{S'vT캏-)%@×Jui7Y4; &b&U`=~:X~ܚUiǻҨ)?=mJk 3~wDWxO}'s(;Mpj~u\;{ᗲmtq8qiFo=E&m26+Lv~щ. +MZ'D5Y7oc&B-lL~2ͳƗZ,㳅m./*}6ar)T7P!h4Q!I #"3'_U +endstream +endobj +257 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +255 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 257 0 R +>> +endobj +260 0 obj +<< +/Filter[/FlateDecode] +/Length 932 +>> +stream +xڥW[O0~߯cήv*i0m{)-UiKb'M:}qsAP_>ىDL! +iFBX"ab8csP㪜/N4*I Hr.&߃c-Dۤ :<RZD*=("uA* J2bl-V (]4.#Nv&0; +\i27d| mJB_}H0D蜡19h +0GO2Ě.9%Ҥ4rӘj-­MU0 '~!.-[$(#l7O&7(mLRI8a7X?D2?b|@&Mnڷ3n ĵ1EvMTͺ~`㷾P +!&mOi]UQ_p* wec߯F1SFA3Ls*btDO J ;) +wїU(5a!:ퟘ_W퀡Qƹl֎:bΧ֗ٹ[IU.$P4I6*35XQ]xmﰉ'&eGȪi<JfXdLINi5o!9k74XW蚩C BS#ҭZ+G:8tmVaw{O;rdQnԋfG$=TTapƩ 4ƀ?YrUɹ~?oc~ uApu}|OVKG@> +endobj +259 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 261 0 R +>> +endobj +264 0 obj +<< +/Filter[/FlateDecode] +/Length 1286 +>> +stream +xڵXKo6W >_:E{lK1Ԁ뺶n(R(Qv=ͺ\s.7^4WA4 -݇[ |<'5b[l<ِ`s0uNX]cX ׶aa3?$ nw㈹{a!p#^OؖHGA;i& a ~= 2); +O +2'q<1PL( roS(ttHd O '( +r|9@=\W|[ڇyD&vhS*;b ɪ y­R-T䯂^=z_{ +U+#as+LϷͻ0+0b+ =ݷJrK~Jdzl zck,Pn_8u9h}FvT>XjF`z *2ݴn~N1S9JXpV.Qz$^?_5'3RND䯭w +gΔtvj$&<MCf+l".mU +@9ur{lGs3(0$}:6kyvشגa{}ب=]ߜl1zi>\0u)H0Rov,*zS6O~(zG)W/\ٹ"(2@1m1IflZ +E,,7eZ'6ChKU@h Ȋv;#KI, `}VZG+tc6Su O!#- nl;/ TJKN- B )*P²GNuh4ֻֻ uy)RArU{Wi{J,pYO儿*jUW-INqQR9W}MyZ }޽~Ѱ #Zj; ꐎEv򢓗ڔR`|ԤصKs> +endobj +263 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 265 0 R +>> +endobj +268 0 obj +<< +/Filter[/FlateDecode] +/Length 597 +>> +stream +xڭV0+|AJuۉeeSRi?ہv mAqf2~y"!h FO4F*ReQB",Y}`< LDc*HB,`Ib*%RDpe_AHrs<&kz4†fNya.709"=ǐbWyy)1W^A-ǗWL˲UTߛrlv1=lnWWfy/֕}dqgKo^GIQw->rk[(,crM|g3ŧ^ymRl*ްSNtY^H]dn.-IJ:Fa^ގ :YS/a}.}ea;%.վi1Џ?6p+\ (&:z52}:t4zf;WWjR?N]SFSx73 ߩI=-*d&p^T$fX) +endstream +endobj +269 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +267 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 269 0 R +>> +endobj +272 0 obj +<< +/Filter[/FlateDecode] +/Length 619 +>> +stream +xڵVQϚ0}߯˒:Vl m/-ߓml ՘8u2Wڢ ˆ@9=0]:~" ]ABAq(@+D1 [` %3Oz{Qi Lzf[e"8<2HPfמy iAoag}7Y0̗`۳D-\TrT6b1L"a}RsCIݏFQ ΊA֎wU4 +%(ŭd!1pWR6-t1=KHgmGJ"Sצ;!Zg_ H/M4+k2X'݀[}[/h<]@=x@^yqTM<V:\aV4b9l*= 9D:33AꀄGe1ּectQ[ګ/*v[YR1iH5xH_\P4!D'/"DjZᆺTՄ=SݩN[^ZsWnfx zG: 7<޳K{-^o{q4W%a> +endobj +271 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 273 0 R +>> +endobj +276 0 obj +<< +/Filter[/FlateDecode] +/Length 407 +>> +stream +xڥTn0+|B&#Fʡj=4J(uI%Zk0QIQ\gYl|Mh }A(/@t@8w!#/@bKjN<ӬS?1̉]02g|l n?meąIYGB}d@B˽LmLlX:6XVV|Kôʆ=t]X(:4ᵗR +kgL6[S[[<^N+l*uMn*_VE4Mk6v)ʾ1L |y|FY; LC‘EUmv7Jti٫U8Yآ2K釲 ZcTOq ^u=;5̸?\lfcvR ( +endstream +endobj +277 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +275 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 277 0 R +>> +endobj +280 0 obj +<< +/Filter[/FlateDecode] +/Length 1061 +>> +stream +xWMoFWHjw|hQhzi,'l9]T;AZJr˙y;*(Xo/;Q0A(wbDˢR\9Yg>,SEMjecJP҅ G>Ѥ6$583f]TCSn\3\Gxfc Q*2UzN+;нYX|84A&mJLZ~`ŔW@ WqƈDP־Uc*uR@Uw +81#Rlׯ UD/+='s8l2WhbP+idck õ6:<4+?JX]\06V@(~\~ +B9dZvn<%q8m߻4Dؓ'#\b2мߴOJ۹wPtUuLvqݽl>>/7M@fvӔ|׷{f򟇀+&~fCā3QE.&(D::x@)ZTKPI˯!-s&zdEh*\ ]z, {,.F25K3kUn'܁Y%BbįkZ7O*8ϓm~&ŀEQw1E;E3Χt+ΐZGo3Ygjٝ?Kۋ2ICi M& 1%Ft7%30U//ϛwk}5<%GձٛZ\v+t4UIm8H*uel^#͛v5i c8ѥZTRA S= &D3L`^?<<vn6aeq^Ym[VxW9n xTg4HT~Q/8> +˵ +endstream +endobj +281 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 56 0 R +/F3 16 0 R +/F2 13 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +279 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 281 0 R +>> +endobj +284 0 obj +<< +/Filter[/FlateDecode] +/Length 141 +>> +stream +xm0Cwt5z #"E0l1T]J2aɲ, =&9ZHB!ЭEaHۓXia:D~Z+6*=~UOs^:~~>q^@sSؗeL'ǹ+ +endstream +endobj +285 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +283 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 285 0 R +>> +endobj +288 0 obj +<< +/Filter[/FlateDecode] +/Length 1116 +>> +stream +xڵWKo7WB_:E{lK1v׀츲@~|]r_"{J>)D DL! ҌQic3U}Z|iF8cJ*xFe($.zUta,("5Df0Dp1h9mn5l D!>f 0<ޚE*=xzY´fH7 FEOJ\{>r8X׈"ee|rB0Ĉ>QK,CXϒDAs&p kC5PΞcD7#@L;{w9V:c!8ԖZ'Ĵ!Vw-{yLX4K^,T04rs95QG11߁ HpɉrjQ#jԜ4^tR8o~ i1/'$hli`.#呌'2:EAKK)Ls(_IVCnglk˓hEJ +3ВC2/gmor(X\#^(I#y7q}6AZn/9Ksg1jJWcmv>Z`[㌿ДiNQts +n!ݶ/M۵YI}x5mo޶5-u%V^b_k#U? bx6FVK>qZ&(M=s<2$bMW0E+%u˾;\' + 멿h9$e""t*B@>Lc<׋srͤWBPWxcXFq46"We9' kԙ9œ-#> +endobj +287 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 289 0 R +>> +endobj +292 0 obj +<< +/Filter[/FlateDecode] +/Length 534 +>> +stream +xŖK0>!gvġU٪UCɭCC@l?&6΃]yؙo&(DA=}{L + +HJ #F ` Ocl$T$?/q Gs2#EGw GuJ#EAȇe]356x0b*o"Wc1-,i TKUM5P;^dУQT!22iJ=UN"Ag>; v¹5܃FN*?ٟʧ & '\''n-NZy&!ZO"+Vdzނ& +[Lݙ|k)]]@q ĭއHQu 0—3W̘ML[|;]}x_m̥~ZXsՍ$?> +endobj +291 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 293 0 R +>> +endobj +296 0 obj +<< +/Filter[/FlateDecode] +/Length 1196 +>> +stream +xWKo7W(Y! R)c\:USEcܗl=DZ΃373R,=go5-f_ l݇5@I Z}kYF +]XL~ +{%f\5-Id:r9,1a>۩q)N\qGcJe;"FJ)\ &@~g[.1Wg"iܛIjβvig<\RQ9ŀ]UTGm_3áwC" $ZR#;S+,pDsrMThW;_SGyd%nso\) gP^<.tDt)RRTK ?* +mn R( ^M{9LJ)QjP;ű'}2 +cRe& GSCƋ~4K8Bl>͋`MJt\G`U2#j%UD`\Dv̈*@9+aV6UCA mB*E~{7>ғj'fpiT̺DeJtS()_j-Okh@lӹ#aK=ޟ+BJuoe4ܱz6Mt]3#fl]Pޖih.vOa ĝ$hr&e! yCt\!opGm-}YW,r0ΐ{Xrŕ N6lfGhђ alk@*qY)bh_0rmCOz*^n~gIK$BDûׅMCݭ/ |3V|yj+>bYt9#BKm%,[%+YA˫9³ܖg^iNDuM%$kK  \RC(Ba8ijuh$ܯpW2ey>ĈyV|we{px|y8o}pyj)ԖۖVY{S%' r8bl0ܐ{YSwaEqtnaTW|~1 DlX(aO e%|5> +endobj +295 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 297 0 R +>> +endobj +300 0 obj +<< +/Filter[/FlateDecode] +/Length 593 +>> +stream +xV0+|͚)٪=fVB4&)IU*;! {l"`xfޛy +"!h O4D2?PL",Xs~aq".><1-”2m$).Xoy8׼ __Cɫ_mº-$yc0%cYN޼ޟMQM{2^'(t߻bTYV`\ᡚ~̣2_} q k5F%߬go҆ۮS-P"j])bYzpyU>CFø2,o=^^ˆec|/W&LbAtg]1$#Ű36LW$VQٳ(ܖ@{49JzHN'+:?(A D[ S*}4C +endstream +endobj +301 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +299 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 301 0 R +>> +endobj +304 0 obj +<< +/Filter[/FlateDecode] +/Length 594 +>> +stream +xڭVM0W2q\fV=u-= ŠHـJ56ě./7fͼ!J.t) -r үρRe~w?[5`N Ƒ4(oBBA'ĝL ARu MFG5>H霐G=lG&Ip׉X\TzͲ41Fv«:eA1_]h[YGlf6.cuÛ2(n2'~NXzLDټ>8M_! Ӈq/c~/Ss{hW]H`>AS+r_UKm`EqkINY +&unfypagV~Wk˂ӣqZ1tN:bƣDQyZSX +endstream +endobj +305 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +303 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 305 0 R +>> +endobj +308 0 obj +<< +/Filter[/FlateDecode] +/Length 296 +>> +stream +xڵRN0Lޖ!q1pt'.XW@4~ -1;WsJQ&sBJ^Q$%#@\.L8|S'5lI53q8f`LJI1QHx2ԛdrԲ cq}_4y_7U[j;]3-gqwq鏕RIn>O߫ގ[r(bYZy]MWMWe ˖\Yႉpi)kI'AHr sI?]:a +endstream +endobj +309 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +307 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 309 0 R +>> +endobj +312 0 obj +<< +/Filter[/FlateDecode] +/Length 1208 +>> +stream +xWKO$7Wڸʯ6(l,RC& X+e"OnwX=zʆI!%a3q{^3BiY0˶?}:f}gVo>o=}o +\XM~O +8x%f\ 4vGI`1B[&MRr)$mFXxP}}SQhMSгX%:8Oז,n.Df0R8OL0 g+3D4ޘ$]Y:д3R.*qypZ `܆%J4n̳gVxDG +DgS+,=bn{ɅvMm#@YȽ=j!<  q*_T9*@ZCECT*B w@0;kLƳ?i)u&w:s@ +`wnlq1KWi9z 4a/KU'xNcE7oz :BM/ՁsxZH&m]awR۹p<_@g;R ۷OnFTC5YDi۳ۇ~GGD{pHpζw,r0Jx=Isw"X#mIfߺMq42אpKI"|GRäto޻7V.$?#R6bz8nݧ/j:rCQT*tES`".YFNQOj@NطJF35tM !f;YiIԔugSG |zĢ<{kR5Okj.! yx">ϒLJ/~_ ?B7`s>7 BRuBxBzql\LUin_^^,V.P `^e9Wk>x^ +VZyQO@_ +(![%獊G܂ԩbE,\ګ]^_-\ˍ *N17^v.?? +endstream +endobj +313 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F2 13 0 R +/F11 56 0 R +/F3 16 0 R +/F8 39 0 R +/F7 35 0 R +/F9 42 0 R +/F10 45 0 R +/F14 103 0 R +/F12 60 0 R +/F13 64 0 R +>> +endobj +311 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 313 0 R +>> +endobj +316 0 obj +<< +/Filter[/FlateDecode] +/Length 512 +>> +stream +xVK0W 1RZU=4J4 0 +Vdل(j}0 !|G + pr #. zmW{ 1vE/§ht` q&1|v . f39FHq'F9 ly1d)W;':NK,-.^; ,8cR{LgNhѭ)|"_'255zeh Z^6M*r'c듐xpc0 &id['UYv;=@ I<]lm‰?@I甽vs;P?0(&R*B_ԾLiPlvtwIԤu_i WŋgQ] t*Uj/o\L,RCU!L,\:l򲶺R,glɕ,vZbXHyӵ'ֽ:=]`܀ r1f7< +endstream +endobj +317 0 obj +<< +/F13 64 0 R +/F3 16 0 R +>> +endobj +315 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 317 0 R +>> +endobj +322 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F15 +/FontDescriptor 321 0 R +/BaseFont/EVJXTH+CMSL10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 808.6 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +323 0 obj +<< +/Filter[/FlateDecode] +/Length 266 +>> +stream +xePn +V +ccVU*žE9'V ,3; Vsb11HN</gtmW _]&@S-}kLqyLP>f'L踌Q? ē?%8 +*s4ݶfKӄ>8ޝ +Wcaz1F +ǮD%Tj S}dޗ;r;vrf[km"R{K + $Hkd/ +endstream +endobj +324 0 obj +<< +/F4 25 0 R +/F3 16 0 R +/F15 322 0 R +>> +endobj +319 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 324 0 R +>> +endobj +9 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-33 -250 945 749] +/FontName/XGVGVP+CMR17 +/ItalicAngle 0 +/StemV 53 +/FontFile 8 0 R +/Flags 4 +>> +endobj +8 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 3815 +/Length3 533 +/Length 4365 +>> +stream +xgXۚ6`@PJ*"$@$$!$Tқ )DtKQ@Dzrp9gg5|Ϻ׻22J@-#sPFR ,C@H ZG(ee H(#VP@- tqkvAExWy Z``HW@#<8/\‘0< D~3飝1@_2g <^?S1h/pHcWCP(cs6K#p@# CjGCQHJ%!=u>)s:CQ?uw ekkm*ב4"xK_be>#-)--sn<ena8Cp(/ߡ451>`0P$' TBd + rE?UCނvFOA|b;QALMr8;ң%G3==~Y-2Hi^/OsO/J_%k(Z~ Tߣfނ͛_;ŘdJћކŲ*.v\ PpնUpۂuk aְ#gɿFW"{teЖ .g\jKẝghɢWl)+N˥DqR MA]fYI{"Ô^EU 5o1 [O2=8 KŤBs+Bh,bA¼ Bb!2w]/k QJp>_~J?jOU,鞚x@uWU[UFNO9SѮNIjnp`Vqoi$:YYb/$iT:#ǐJ!#a ⎟ا$Yu4tk+6amginEZaP@=qkW,Ɍ7\-qwn+=%i,S,~M-e˥ޢ|4O D˟;gqHB6};q'X_7_+pA?C?Q͍oz>H~nux;MD];K1ĖoO5~!Yt\ 8 L,Et +JZօo,RogOw#R[R@V5A ~!+ 0qGS){f{~C#Zex!,V=g"o]T%^p5x$#Q@˙\uqRi;PvFjWӴAGm~ԼTN%< ;2mۨ!?Om~RYܝ$R^6Vt9;HwY%(!w[ ,n͟1hz%u'ߛkpMҖ_) YH_^ wu!E@/)PcqBE +zeĹV܍#SjWb %j?ܵ=5fs!#˱mrЃۂMN]$ nsPtEWJ&snåi\&ᢦ{ӱvrwOwh= 7 , Qf|5cc ̟1tM(W6oVfK_c3J,TPrpGFyUnX_ram,߃"LB$_;+iot,u=H>8)&*mle^H&Hm)S=s/XIǤxKGeO=$* ^ 2mlj]~hVaG: TD;\e򖣭4 =0rWKC$?Y!cOT3, r +_4' UqE¬d=Y򄞮~qNLxW + 2ʍ_KJ'neEEQ&6V&~EOYoRRJ>Gu '[*[T.w֪WRt&,BEVɆ v$G m1NC:0Ff|BA/cBys+7,O$BY~G_LP.[Rȧ -CBMLOt8 L]`c/{<+09}M@9f3%"\*\vY!eFttYb^;|- +ϔkXtX|2iokj$,=#vd7f!dph^"Nt#VWP\ۦ>1zʴq1Ҿ}%;] IP&P<`d>m<*%\J%3"S`/#u?C(_VW1wi8nFzQܲn3·::Bc*K iw9/_#rA}eH GIu~XV`GtB? %m(uf@eJI,y5 ۚl :JЭWQ7x^8hz3-3S˩ɯ>uC.MFV!kv>.kx]ë1LO{3)BƒVh Q hW'ϢFĤ>[aqKoT}3c^1ON:F,M1zqcXOz=mZ;McƹX2SYK8#!Un[f:X=6i{RiNP+.@7o>W e7լp$U mQM>);]#Y\xWm#xxd̘ lu5}ͿoGR݆H@ ?J&^ f}a/lQ;̥,Y@6F0`[3_~2'k9Ljm (*&ȣ+GW=aJ vM}M(-eyfL{ ³ӎͶ(>nMHU +y82ɇEKe]HZ\hMR!KliBHyJ3Ÿ,j_f%Ȭs:ys{YwUbV-}),*V?D w( `@ +endstream +endobj +12 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-34 -251 988 750] +/FontName/EEFPIB+CMR12 +/ItalicAngle 0 +/StemV 65 +/FontFile 11 0 R +/Flags 4 +>> +endobj +11 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 4273 +/Length3 533 +/Length 4821 +>> +stream +xgXۚ*EZ6%ҋ@ M4 %$B )R7E H w*HwADzU:s\k5g>[F*p7; +# +ȁt ! O bnP BT@`9%%HF:8b@jBA*4EtGdC"0X1HdO!~QRB 8!(J?Qn d?[Oh_\ _B_p7 GS: P=\EGs6h߭ftp߻ rpAIHO 7APOğ:;į *'E0Xgk }$e%Ta^h4/u_A 0T<6w nI}ʖ$#}T.bSNa4[Q\JU1?X`<`wWcDmw6"R>֤7փ[lu3R /kMr g:"i6?*PJ F?נ;&Gʢ&/>h9ͭx%7s]Kn~JRZ5&6'Մ⢜we/Q ufC2+_]U<-\D0P`@>,Ѿ1*O9?,sLge;!8MQvuImT]:3-'=~0S:/zB(SdfVoQٙ]ux\dzLa`.W-m!rl:]$iGk:֙>i!s(kG.n)EzVbnyW5|=ks@01 оSbމ_6aɹ[ؒ0oUiQp}Aa +T`\7''Xk9hKlh< R2y$gMMlX[7+s:|fl2⛎{ ժS"@DcKχY*foTs()|wޙ73R_.'(#|`˿h6`@MP:w߲֊ngyl*IW8,?_r5pL_UN)--M1(ERN^vn +F"o`FvϘgGىWNiZr-藿q6瘞RX F͜2  +$`|j!BU˯}BTX}u/K: QW"gׁ;>qÎ] UV]*9W8 hĝZl"|Tpڤ:z8{qn(qBu7fsƆiKCBvT2#w2A]`e-lEurgWH쮪 EonqNPO-I§-?)p>$Ϛ<hc{p@ٖ&5/x5 1[wI)8~^W sAmCR,+ +Т;$qr H_yMɒ%, 7Ѐ[NRM~1B]s cY6~v ʘß*Y]7NKhC/TS~"D=|[= +F{NUI}"@ӽ /a{V6\פ0jFzWGaZBqm) G˨۩e≮I{:lq?}$2:ĕL}v|7T4"RN/w;)37߱/n7# r}|7ёZ"nЈ^tc0a>tT<x#|o7ԲW,b zdɚvmᥐK&.uzΙ#zN.lzHKFUၰnL<.v!7;(ӑݜxa=̔ +D3O=AAf,N.VX;٬ka w'=lOT7](fpVW4V  jWnu/>'K(Yt+x\kdÇ}͡b8JVɪ x˥S +-: B6pڱbc3FyP 2WR00|`(f~|0D͐{9uv)h`qx 2K<}A\DtSkKfm0ؑy&NgnH~Tp*ѯػn+lkyܕGt$jKQUB3&e+Gz]_h]Zj ob4SMdύ:;Fw1/H7{^> x^EE~,ήWh{W úwk]'E~ghD+#7|"oq,3s>$oGi>_ 8zKP)\TiGW)smaEu6o. БyT0d;0aqh\WLzskE/4i#'N(BlͬS9+|-+8U=/q3@B+gTH]_|%V"3FUJ@7 sDQ XAd}+Q(0+E2CgZX4"dL8ekƫk§; &@}F LFUnQ]iH13kY?[:gyA Ǽ^̨u+aV'4!E&']!:N2\m|TL.$*/=co~$oW0#'+*ZzmRiLZ;49TabW~d̮tdGfʏeaor3r-Pފbuke-䙓`ey(TϮ<7ǻ]ZC?PpfH/hԠ =0`k ۥ#DӫNTa)|]Y~|EPBMQ;Mg&079 j[OO4gzR—Ҫ q!z ,SK%.i(1'aI L89j%Z0u3Q-;ø_5p2~nzQk_p$9lL:44Oezmw'G_ɬ:"fi@ SW|@D<xh!NU:wea)M^|6YVqS]!G[b[4Aw.ZB3{~bcu֑:Q9u4ACQÄSl_ e0ǿ\m!]B6&r)i[.V1k}KZɮ4$מ<}d=ZJacP +sNryNsJ^A9ƍ G1(rF +/?sA@7W(ڙ +endstream +endobj +15 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-251 -250 1009 969] +/FontName/TAMYWG+CMR10 +/ItalicAngle 0 +/StemV 69 +/FontFile 14 0 R +/Flags 4 +>> +endobj +14 0 obj +<< +/Filter[/FlateDecode] +/Length1 720 +/Length2 8955 +/Length3 533 +/Length 9509 +>> +stream +xeT\݂44 8k&hڸww<[p'rf}e|5:_*zj5Mv))D-QpspqI8B@Ζv g[X 1;d=-X8dHB-@P2b dд38{pR66Ѐ8A]!`44nn` +b E 4?KG\2r60Sz4`7sQoeڻ8Cv`#ߥ:)C.^UpXIA@\JY:YCjfsy;ONG뿊j K3lg?qt|_¿?g,l tA G%;;qq W%(Ϭ#ϛw[1CTWf:aZ&"2.c` +}. +|yהUx3(RoȄWo|x]:(63-v>y.rWubmlHqQQa +mT#T[l.4SO n`2Dd}'$Ab,c=cy·m,jvMr)nCBфdu;5ƒ +A |=~_C%3eI߶=vX4pCW$~zTGЖlNxxlM{Y~TY_A }mtWRiRVꇌ<%a{[c=]͒G0C=؆ k叙Rj3&憶B]TzkJ3ˑIԀ}-|4敐=TL +\S^$Å|?y%˫ fFě >v/EI5׸N_(9>pUz*cy%7eVʒEo.Ia/߶W+ |b,'$g%#_)UASO%i6.U+M5R>5ˮhP\8a(C$_[9qȳzpoX)n S~t\Fx8%\/q͐oE HtdEV=g32[dͫ63<2r' + T2 6H)"YnyyU,"\;_1t;B*aBUq" +o^/wrG; MED^zޑY;F\㈱+}/æ 7v:#D`)cc1Mԥ5~tWr :DtzP)7+ݐқ64٢^ͅEX.og%Ƹ5S\gaD[v䄷E%WQA~-#~:s$LLiczgZv^߾R+sI)>WJ줛2289̭>| {N^LmE8PSdd,.19 ;jgm&ʞZsr9-vzu20d@AІZ-#p=`=$7(t‰3Y$<}Qh7 +B9wF.c:Ϣdjs?6m% cly4u |`__UNiT? rhxz}h'&},2zc`. I`b nk9!5Cpߞ@٪9/IMYڎsh,ߖ1b}q?v?qTe)òa_~>ܶ\LDoucD;)iwȚoP1B˥#Y{-4Wu17y̖+xC!|vGD5Q&];b\hC^ic[ƿYӂcV\ 嶃xQNRl^,5+H)nFs,|C"G&nnJϵml˫#UyYI zqfňMA/]}O$d6b6Տr0~F=nˈ8.QY-U>BUi.6oqJ|Ol(07]oLf~9oH@BPeMR^6L4j.7ׄy_{>X`B/;y5^9dCֹ6j}8o)QeWBYCRte턣%0dic)U!s㴡 'M$EvוhRObf?P9ӊ3Q8TjQύxꓝcPha( Y#*?Rg]X`VZx5v]ý%6_NAتi2i-G"/zG1sЏS~!@l룰~pswY鯕z۟^ ;=,3f+e"^&\GK|dYhG|"3y)zʪ`K +f%Ԩ4IX?%[n\b;/6NPg63>Ŋu&钗<++K]L3bFq0+՚~ +ɏ4z{W^J .6߈xQZ[~=y$i2@2UZEetRE;8etAlKmig}j7 8CDNςFI +cJ0&FUszF1p/>ӎs!^ ާ(l4a*v~M5Fpw~?Ix+3獃W/*ߜ\;ϝo b 7كXHљr]^黫Nl6ʞYc$s +]YsdR\ i6Y%. +]Dhӊ^&$Gt-Uf߼efzGu8'BC^0l%BmY)*R)Y]QaG5Az@G޼^r0?eZجsܩCM'5R. RC!7ÁRiD¥v=(97<8X9_0n'U5=H9=yd_ m/M]>:qi_ng^ +-2E Omq F7Yc ْ=[I1rjt$8LO +E򦼐i[\aTw3+ CK[f-{qy9qVyӵm'UZrP82+ kq}$@mҁB "{(y}W\Ԧ=qa1pGqiWͥ b1"Жmj8Ӎq瓙) 7C$GM, $ =[d-: )7 uGNK&cqp> ӎ%xx>M~ıM!/үrˇAH)wr'AV enRAb3>G7|&Y-z[7&BY|{h"E#g쵋!YEwݙiz^)gr0$M]&2#_>~VkFo6;.#o]RΣh zCw5R;W E5HH׭4: ,ԕ̄8P~K09yjW7v6D u@XEOXKZyN"Zd'Ǹ)|$Shf.Es69Em1f^P;w$1! +_;hZ{Gygn#2 +w$Q!0÷pXiK;鐠0Fqsu2}|:Jؐ[v|ȭg<20DI/J + ݀]xgkm񘥒RRQ+ɁǬxto 3O2k8͠heF™Ȕv^~K FzZoXM;O9#ulRYT1``mEE ck.| +!ZAz +3 nG ~GDc`κʡޜ)ل_qo&#Ti11Yծ'e Une1V<\od# L]HRi0#RX\!Ԇ?^lZdfgF۾o(3{m|/YWc0q -ࡨ{Yy߰[I4Vݗvxg{wrE" <W SҼ'%̶@~}'GaY!GN*v2=Ҽ O tPyOR̼kbj*#iW4d +M1BU= JyQϦV;yoY23F"(7t޴>(%[CRS)\Ge9ŚO6avniji驏"qa+Djt7ٯ<~%MR'%f|jQ]uɌF&}XLT6\~WP`kN؊.=wL۸NφMSuo%">'yzkS'r֢Q$fbC:1z\g 'gfp|{uDJNJZluOo)K#Gui +h~!\@vXo9_RgÊ\)~1n94φS1*Ncab"k `:.6F[WԞ#@XotUpӬ҂D#KTr]'Z_I +[oi.6^ NS~QA\p4Ky'Nj~zd _"vk\ڲG:xm4+"`nZ6VK +ѧpSOs t #zVmЕa NIyxi[tTÿonm9E>G_J9*dwP ((ǰ޲~Җn7R"HKLl&2 j4'G^vl)~6b>I[='*L̴CKɎYtlk%Pr!'4ZLy "=Oڔ_"ktEXvIzRd^]wkT!SQK + $+ J_t GJ@[GFzTݞE'V=]# 7\, p|ZW7l+}?"~4{8T}OXttdK+y3ꅆ}lyIIAQS!dqx^XBʅ_':/47RKQզ*^$Q`mhu0~Gڌ\n13W|δ]^2d0o`nҵжQޚc=}En鳮D*d=ߩ/Բ;hgF eޮaUI Z=SRE%wgZ^ ND3F֍ܚ:Wܳ>O$NA&{= +lɜcv G7TDM]"6Yi|Y҉6EԻ9L!|> V>)w\-̱iգl~0TJxw_j6}u9th1-Vvͻ +mfY-ߠ81g5c1šW.9kw&ŸŌ`> +endobj +23 0 obj +<< +/Filter[/FlateDecode] +/Length1 716 +/Length2 4421 +/Length3 533 +/Length 4967 +>> +stream +xgXSA$ Rz %THh-HA^ D.H9;Ϝ;_o_zoy9LEHmW V* +i[@APQW Ǣ\1p,RԼ@TZ^BR^Jif}2^B$at`&?{d}|(6TC%6@!\9 zX*nCdX2u8Oϖju8djFTZ;OխF;Lj'"Ōh hqi\B$®̏TẼum$PwV~KM6NRo'~Ͱ k2|̜֐s8;;3sW(Ϥ9Pl^, &94kCubH]\}CUw1G}<{D VJέ.q=z_Q6S\]YQނ&8\w|ig<ŝsR7 "T"pc'7HloR9=(*fsC,<H֫Y%BG"(FζHs}"HwsvăXuM}}QttԙZgJ`.8Xc 6Wu[%w.({[ 4hH,zA%&/su#K+(QⵜKS512J~W-w,'| mrbMҒ,h^ zFLw[URVu 5R:Q/ tG61,X[w4@Oy#EFJ5+0= ++t˧v8A*J4"_I%11n ׎Uy R=)UR28Ls^3(1Mt#}a~ +}ٱ58y5>.Q{/_}a)rTk +QfR5MqbP +ű响ew]9g5`ј]o$~4q􍹋q0Ӝ"ylXqQW}N*Ya> +z7@md f;=ޞeI~sO>5xeKU~z#$s}-*{ KWK?rhLKl@k_9ic[AVlUKۖV7?kޛ+Yƨ#eu>_{g@]lrPOsIf4TsEWg.{d8paZolY4'y<#8H͹|=~Ow*h༝6 HU*DTj:ߑ?eoHpfbk_ CBvO6({sہ&ݞnp-tƗX +q6u+@$J=HK~r`)_ðnj"'Q_IvD]hIWۡ8Y'B%,Gr@+G0=Yر69“TPDZ;Z1|4r ArXwdoV&W0jXǴH! S2{hjQ > =ݍ~8=ؐP.wOdjI>ì4Јb w VCIJ4&'ȿfF69O{tid/.y{p *R3nN:7>T[&~~{+hY2k wPU9l˳R<&'%/OΓ5tyl4c;D_u2z4[Ze+yT3<WU3\q (M="{Zÿ<+AuklHT)sw\ңn||avqh$f=iBqX˒sx8#6l:/@w@;Ҙ[똕z5PGk#)S#[e!g*{Wܑ)rܘjUnXyh1+7}0״HZvn:f jkD{ػ WSĺ߫6:شH5sNo)nG#i 7\$;԰)„Ksmɛi: 8110|h)͋=W*瑈lbhcJ٬L;ήRh=$(c9 M7W="ӷJa>~,Sݩgq £8Aֹ[PYa\s>`d[FXh(+tu6hC=Zvj\]Il\ CZeFZK.:Q˲k5h4 wE*|L聴K6/ޠ6)>~7حV# "uL/)ɠ}M[S M+]5$gsO1M wa%6Lb7 .єٕ \'֡#z]L<bq,0UDi|w'u0}Ot&\W! ,@Ҩ~U¶]j`~mHn2x+n|IqB)sk^66KNLC}9:VZ>(=*%䖩ǣy tk8CL1q6rو‹>4U~mڪbkusWų yzx"V𤆢bk0ifA{7oC }ҼTE j"Y 'H\˃8':&)cfxr#fUYnj%{ +ӜZ,E7\p~',K-TkkWV?iY1z *Gryw=eһ#{pܾ®fcD]O +/Nڕ^J|L,h|]Bvu%u!똆l$YZM;p |]q0u:`[j~|Gcw6;BԖjKps#T]^qK/cmyeĴYQ }G4#YvʼnJy uSC;T{sQOt\6+wwPqŽ'f|#مA,hiU WII^)/0 sMNro`{h7$M\^^za|8%R%[ڠ8)3(t,ECpG4wTYDɒ!Ч(SUVJQm> +endobj +26 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 4447 +/Length3 533 +/Length 5001 +>> +stream +xg8\mEFmh0%:Qcme!j!E-JH-"DH Z"Ǔ}s=_u?k^[RBuAb18 iIi%4(- i}0 ! Prxd@PtEET)5+ 4< W +huE"p@& +_㏀K@8tA#1? 0nX_i?K .oRQ'A7-E? +u C#QP`^~8 G`."¢BjbQ W!q@7;p1R:Z:[U׿|32xt1_ ϕߺ`\p$ha0N _I]3iyY DVU 7r HA^w  y1 " +47!2 +bu.1~Zr[RN^~\+|Ы> :cltZݫ:9 +5TJn0z kj[G {dOo9ZF_Y3RT:h7E4FD5Œ8xRX98<^)4-L/(t MΠ6Dt B +ͮ 0WE Yuz)EV'&yݻ'KiC1\Zi-@as}|׬ q{90K{:OG+% n*zwG9.+m|1{ +Q|'+Wc1 +, "- _'L9\3|׫W} @FSxZ=8>=z^|FD N)֤0=:& \%2[y[ebhsrwEQ&$ȓta4c&/sC%xJ$Ð@O + ~3*TRe@cM+"O0"Öc[vfoj; $)Cߡbaχ\]f&l#Fvn%T*ffyz $ +w7$ Tڮh[}:6+GFwDoI Xlqv֒`ޢ[ +-6u?2_?>]˰k+ݚgN]jTҁ$t=.m +."p8a7/Rqo}i7KfgM}9qvQ2$("OFvMg:pǪ3{, "E%gQ1iSIM؃ C*2(r^ ]0ݪq^8nޫ@p2'`Kv2]5yKD/ gBbmh{.;sr>}!S;?J.ιj?āڸyR/clIlV"xKՠ>xHZ֟?y0c!ƯSMOi  + j]?֕ l~0*H[6($^p#)`+;dJQʟiMJ|F3#ˆBQ%a}8-LBѯM݁C[ +.gk!"!qrgDM˦b'Tp\%KCԛ7䠾2 י)Z:"l h%㤝޼,$deo~vT뮒Q Zc7`q_jR29o{ϢrΊ稑WZOWq6GHs|O.{탖$ae士 ]?ځ>oGjEb1K屻÷yCÑ-dǖ#ट2mէdiib߷nWE|cD(]=b=1(eR%^`KmjI1td22.:o.y= Y*ȩ)[#EcȈ<[Tj +#͹Fguq(ߒqT93H8QJpQ!J:Q6>?aQ9.7Rp,;Ɍdt`e{SwO(uH[jٍl;i 'T5Mk}OjF (K>e=*0|I S)P0^{iG얡P kf lX6pP/_FZhTyOhN꣛b/k% w}kef5`Y}weql}| +DrI*h%ki[LOYe5Pv@UxB|!]bR,~#PZN`;1dr:+MfOzKFЫd"J#^#r3ePP=ޝZ+-)&p[)=;TqDR-{5g 8!zU=)8k|SZߏ"pڦP8&*#3|P2HFi=y+u_SK,cD +fDa*fnr+D>yuz}kT>r9u&a\4)ҫ+yRj#/(J?Y:wc}+BJge VwjxLjz^?LRACrwhk͎FCEo;>^;+{h=U^pvBGˁ~Jӗ2h46)N15I>1ϩbmP'۷z$bh"NfFOP8Ҽ|4;'f҉RGvnFNHf NڡHgmoD D;}m/{)PA OUIJr5gƏ ^N9ngrȱ|dD)UC41Vc@ϙ}Os\Ws2nǨtgqP+&Sd_};{&:QbG<> U SIpAw"Bh֐dd%7IiE4LLaD**+(IrL/Zn3olIsTpkKwO]!U1WG*M) ;u`2$/ݖW&;XeGsWH;k3#g$*N$+;udTaxf_׀Nz%-fN eM!LLBQ@m1$ccˠLc (6pZ[d|lZf3ovlE7xq2y֓aFvԃyc{C_Usnp TR|߬b٠l=#0ub=sz *9'Bcg3^(*x@<7Kn x!]/ft;QW 6^Cץzg僢ݣoH U&I|*L8`Oq֛K)nJ::VJ|P_w _fKغlڼdzK8t͠+B~-Y?6MDAXYlKnc: +Oxؒ 6?8==޸!,iA.D0 eT,u%e7mTv:3ޘR ۥfno5PAvKS)*mYZl-hKyj7|L25;QQZpa2Q,mo\uwQ2^GW%Beg?w ԞȒa 7f{&N#EKUFe,CDWNE-G!9Rqꖍɒ mf"%MIjgwWWKDSRfdK4 O0  +endstream +endobj +30 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-24 -2960 1454 772] +/FontName/CSSXYP+CMEX10 +/ItalicAngle 0 +/StemV 47 +/FontFile 29 0 R +/Flags 4 +>> +endobj +29 0 obj +<< +/Filter[/FlateDecode] +/Length1 886 +/Length2 1710 +/Length3 534 +/Length 2349 +>> +stream +xRy<?edk,%o5dXkeRY;,̌p&J +1i%IRIȒJd~s?|>秵 @b, ` h iG l X#b-`0- +!Z0!.p!2 CԄLn,2rӁ]K%`@! @ĄT93,%M .@gI. Ia1|Ra("Kt(7~lNIV'1 :+ lEq.  +g:sItg 8B\r0@%9rdR~!rnYu_PWCwc"A ƈdb)@bI|" +@L +@H2ʐJ+bÖV98"+dBIlI\[1CE7ϐ $:Ie,b(KkZWlmY($@bME8VL&:&h43^Β"M*[LDS $bm{ϡrrN㟐J^YjGRkcPU=n[%LqO)>F=A\]t99h#ss&輒81Zރmէf4T ѫI#̩u҇[/9؇k1%R1l˩e +iۙj+ȿe& %^]wSvr }Kkiٱ[>(%L \R2z~EA 4uM?GP}i<~:ixb=~㧚0B:u*b `JӋ (rJرCf +N0 S)T}͟&;Xqx%2 5 +ߨ܇^6N볦XH_k5{ݷj~x`WZ!/itũ/OӀG VE/n4$_y\ {̬-Q+VP bQcҁīC*3JbE6MͶ??g$8$*$^!IGvtqwJ^6As= +jQYdŠV:Tv +30gNM35s{W[%AWn{Mـi8xV6io%,?+'>aF/J:0];Y{NS7C>(W+zCOyy#ƗI +aw* (ߩ¸/rJIҸ#Dmg]+K +~IL gjҳOO8beZ2>ad3q9ɒᶸ8ae"pS3g왦)=f B[iS5S7>_ +7]*nw9 g3]yccI'?0ZTZ{ 'zUUꎸƜ53<9=~~xmT4(x@"OT{")X`J@ >-ss袢~JsR}B|ze!(tڛmgn}g DKV͈dȲV[k(eTI| Z8βt3a7/4B*pfϐwQDܬmkx\#0 ҚٶN~D~KhV|֜74U`ƺΝ[pβ;'~4ۄ҂ԕtkql2% +Kû== mY{WknqkMe?U%C#~ (4neJm6EL)~q9@$\~y[Ӂ)DX̤'/T.Ӽmٷ&mni3+xG;!P/3r eg90a +d7몊M:7MfaN/,ݻ<#A | ѕ0s]Z ޼'|ԅw =~UFWGSqe,a- +?Z{ nYy%wY Co4 Ab{a +endstream +endobj +34 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-32 -250 1048 750] +/FontName/PFTUWD+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/FontFile 33 0 R +/Flags 68 +>> +endobj +33 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 1752 +/Length3 533 +/Length 2293 +>> +stream +xk8DZF2(#3 `r% K2f^ c13T4Q!B2m-b"*CQRjMZum_}!cU`Cngu`PQ\/Om{=pdoLAU .K,yLR_\],I')PwJj? )>y62sK{T.[SK(_a,笡(ϖiїG,r% +Ćez>zKMn -R~NZ"{c+l|m˥6R7Qir57E> $/vB_*ˇh.i> +P4z~/!NvដBTiٍU{R6egߑ?3x`NSZ)>꼅[QW>ksuy"UCk#UFw?USLl ^jih? r䣈OYND\M"n*&y|L2<͗[r[7S˯ V!$m'̼#GDX2Y^dx!-`j!G`NHE؞ځuT +?)`$uF +[+v{\ww5hgTryrkKV+޹-vmjb-^-Ֆomv3rfG/͒a"gLH>y ѽVL:ht*[8 0':,dt㊴EKrԻ HtyZ5'窿Os{"=GB8ğ8#/6{(=9jN1_Qo3ꨭAY;'XɶƜ+(;U٭VЊ) vL4Wx^Uf쾾[QILܛ*LoLaf,~Rl3!'/h+Ѣ B%g䏁7|!T&>!5+?K{A|@6wZxX6fR!ZW$%~OxᓱfVcLۦP$AꈊQp^WwM*(pbf #EY6tm2'cbP]瓡Z%+1'c9Cɢ!C~ǹN> +endobj +37 0 obj +<< +/Filter[/FlateDecode] +/Length1 724 +/Length2 1132 +/Length3 533 +/Length 1671 +>> +stream +xSU uLOJu+53Rp 44P03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ !S U[PZZZ4<8Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D?"'Yـ̼ʂTr0SQfB!P!Xh%d+$$0]_QkdkiLjf +榵 +C2 KS=]L , L.-*J+'aL`(V&s͞##5ˁJNaz&CIMXǞ;w\[Žg40њ3;nY($ǝg0eXWҞ1Jԗ]aKuz]XU- ݣ%6 t6,`N|+Kgdq;)yAWpq3z]K&j؟u~x?˰ *wO٭\vwv%|3:YY}|v߿Xd?/ya^:-w^fys[Ӟ|g;} +[ף~m7 {?hr=<ɩ qKݮ<:w}Լ8wÛK3?'lqf>H~I9qŧϞM69}o=[,_JqUl9Y&˩H)n;AۍvCNǏy2`R\=#cGeIC6Xp0zm%2pz,+`-4rˇ6I7o|qmG/gl\_}ªzmSV=(|5p9}T= +SvnQ[).46p0, HIM,*M, +endstream +endobj +41 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-27 -250 1122 750] +/FontName/TAMMEO+CMR7 +/ItalicAngle 0 +/StemV 79 +/FontFile 40 0 R +/Flags 4 +>> +endobj +40 0 obj +<< +/Filter[/FlateDecode] +/Length1 712 +/Length2 2182 +/Length3 533 +/Length 2721 +>> +stream +xy<E!-28ˈ4d/3Mfa%6(ٲJXDD, T-C9u;}y>(8`4MЊBiµH`s*(d , Dp8`.rR:w@վSH%dI[!8,PpFS"pKS ^ <G|@?ɖKJ@jT(2A_=ek5p?7T?[X1MŒD?t +) R4R?Z]hhO&ҰDΔG!Ȋ +4 K A2G}C>bF[v5,L;B+[ g5*!i`-ױֲ$(xаd"%Tjw07GIɸ 9XS+ty}Kb~e*%)yA9ǟշmT=A9ߦNX{fA6VXA[k8md>*;f +whrzB`^v~KXu>iB/4_m0TnG  Xeݱ.-YЀ/\󟢒Rݘ_[Mnʽ/Vx+%A#HRgNW!Mw t46M*['1W$S. 6KZ5f{@(>9*FX4\W>z]ϼ5>^۳l[콐LQ+W)Nn; JyՈ+Z +<˹t/^WOY͹GQx겑.l=D'LzҤܔvM^<y1HZP̻2+ZqLI#TFĬƷ]Vt}6h)Z|:1VgPfH9'iC u[H<3hLsé2)\wLk&yog]7\ߦ2x3㓛/}2m'M".?׍-=Qzdʌt;2V]}nrWM*}1q gzwئ*isヤ,-8{:?]m}|4[FsW0 ϟ/(np9pX$hXE34ìL&?VCEw F[vYPV:KzEMuva=ArS* +w#dЂM\L#0 g*ìX4ODAԗsR oCJ "ly쪑1U,zH=]>?h-=Q4<1~ ~4}+DJ@ ]p:+2{5UfṇⴘGVuvbgInFwDbZC:8$xI?q6iCVMQ7>f<80g9ZsiFp?~lX2 iDip*%cw;W×&MmKC!aDb4 + K@D +endstream +endobj +44 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[0 -250 1171 750] +/FontName/RJRYYM+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/FontFile 43 0 R +/Flags 68 +>> +endobj +43 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 1103 +/Length3 533 +/Length 1639 +>> +stream +xSU uLOJu+53Rp4W2 TURK2\KR --Js ̭LKU9(3=DAY\17(391O7$#5hHrbBp~rfjIcNBHKBPjqjQYjBJfrBRjzf>Uyi +TYjQ1] +`j*ݙSƥ/]膻%悌tbnfN%TA~nAiIjo~JjQT|SS2Kse=Ks2sRt M L n)% +i9ũ`Լt H_mHB$3JB* R |CFE +z@@cŢY暗\XtS~EA-мTOS sc #hriQQj^ 8- eC(5"5iMyy= eye~/ț1gFɡ&+Uq)Ңcs}`b <*1 7NĤgw-E-$xUaë,-Yv可UEӽDv4N;vR>ͯkO/LΓq™c}˲Y.'iKh:$EQfqQ %f(qRqR?n q;U^}Q;gw3u*;a@:"-f,O6}vBχyݿ< V#x|+?4U#+߳ ZU;| =ed_ lV3_-t*Ǧ)._=_bg7=])u[nZpmLvӓ^l=]|rA26eU߿D ǀB5j0 9'5$?7( 5uxJ +endstream +endobj +55 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-30 -250 1026 750] +/FontName/IAEDAF+CMMI12 +/ItalicAngle -14.04 +/StemV 65 +/FontFile 54 0 R +/Flags 68 +>> +endobj +54 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 2695 +/Length3 533 +/Length 3246 +>> +stream +xy<[&Kd+Kw3AXFv!˘1̢19I!K%'%d߷$EB#L@H&`@d" LB$P[: 2C`@6|؀ #$P$ L&Ӡ`Ҽ2)V~*{$:@/%}o?p?7\?c)K>JA2A@g#'$?wM +h@ #P,LE?tFdo~?8TM N`OvZ4]? aQ#QMAf.83\4H'iހ-@#А +D05uDiꈋlƀ:yC%2 ;_yoH pTȕB-÷qHi[Tv\GKLg>R|Q寸j7>6hql[GZ`@Hv;f}/ D / K3>Mwz*iS)vE-֒/-%^(gw ƗtNJڊV*6 ۚguY"7MR60qK-Hk;"i 2QX 1!?2T9=S};W(E$5<,2iA!)_xx*2k:/]@7iSK3KIP~!2PuEo)s{Fjx50nNr=M5.ژέ<S0a$?bދ6m4H/\@:%t-Vf*m_߬S'5]QB ڏMSo̮L`q{(h8au&o4puz^2rnؾH 4XRDqzNbZU['= 5r48Qts|11VLj9r]xizAdгOǹ?V'LQ=/$ϙq vlEhU$RS0=WO |}握ZWUxsajѫ$.3w5Ğ8J $do69 +e6=ZڍӍն%cKiFxîb.sNlRh;&эmʍ$>(ss {t71 \^__-~+w8r!ʴǵ]'4L+qx >ZzvʁG~s97.wSh^/ˢNwźB≑NwC  +{mvg_sB^TFXAy#eEXs;Jx~z2%WU턀UuoL|y7W{kݶ1H5 +<sJh`Og#jпrL $/_V2{>JmP;"TN 0+w~QN1zRnwʪRjnJHes3ˮXУGNeseڠ#L.FMfXC,j"} uQ$t|Ϯ|߾ +Uq a꬚Иak>#g"ܧMgj37 l^j X!ͯ"lGuQ}IruZ'd[dK[~E Nآjf^{]#ӎԙwM7خJV#)۴ tYթՠapn|'s8M[]Tk~!|@܈xs +*5 iu.4}搠n>31UȻ>hv|ڢd2x]B:# +7<N=[ڥ92e3q@Or#i!gsgϏ~H|P;qVE/ o +`.7=tQǘx7>yS&-r]y3*49{Ӈ^i;GNX2SO}wUT-A{tj򰄕C(LPY230L^6_ +t ׳jBUP-̘hL1b4Zp\Ez.hw!{BLHVw87V3 aɸ؊G,o_[ă8mߺ_b/ +/]**pq? =VhxIiۂOrZwc"[*K0S>-/fqDLy{Y ڤ9;GB1,^zO> +endobj +58 0 obj +<< +/Filter[/FlateDecode] +/Length1 728 +/Length2 1814 +/Length3 533 +/Length 2357 +>> +stream +x{8T%)tr2"F*RƬ5c1fD3B&r'Q)Юv))&JI{<~hz@F Ġ(%{`1#ttpLȆt"ƀ(^KS3KLqo b$"AMYf$8_wymVF-\/׌Gc+|,',1'Ts=7 {AfrYyً_]5ZQves< X+ _IAxa}ltZm/Ty!Deɶ+VԨE ) dt%&4ⲣ'Y䮉/DR~лm_>.J.y־C6XU Ϯn\Su`]372;4#{ӿk^e<™1[k2.rDr(EEN +n9_^| ?>>g+.]{uў{'?]֟ײwM~8xhsSnhjC=%MȡU Gfnpa2, +_^@BD&A#2Cu +endstream +endobj +63 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-4 -235 731 800] +/FontName/RKAXVR+CMTT10 +/ItalicAngle 0 +/StemV 69 +/FontFile 62 0 R +/Flags 4 +>> +endobj +62 0 obj +<< +/Filter[/FlateDecode] +/Length1 719 +/Length2 10301 +/Length3 533 +/Length 10859 +>> +stream +xUTѶq܃q qwܝl4wwwIpkpws=~o=V=Ԝ}5kꡨɿ2ٛ휘ؘ +jjl6fVV1$jjqN `D DB;C,,tPqDmA+Sc;% @ + Tq#@̘fVN?dJ9;gq')=/; dĢhw>_c ׿K9(ouc[+P:8; {3ߥ)̬m*dlce*jga+e(e2jdj p8ٙ;EE^TKCU[9;?g?+7.yoIڙڛYYŤ!fTbbnL& ;' 9d%<fM!?os@ 7) 2+a9 ]Kq:r^sW5J5 'V1_9o# d{LtLdE#fdFprKڃ7SK-]XҖ*S41q ە%ܕaAn_y`$QȝЎR'e㈩KFz6BgF{ɐ,,xd0# RjL^RytgP?(;l.$sc'BkФǒ_N%¼h!{UoI/u$;f6TW4z|$Ep-[Mp>vmS_5CYՍgv,]aXnM9[C07flTZFSz^j3Ź&jcDQ À'va0|ƚ` 1KRP3- lvO⣊=6lpPY"`ʪu8?S +;;r931 t-) ʛȷBc,1{꩗ A xmוS#(+l:3\ =]@Հ`VܝNdŇm(ܐ{Ŷc8w2uX9WU,~^U![oX{X8) +.X%{E:O s [SHxmԬV~St$շpjOFaya kYt}(¦bM<سLILYE +$dIKt n Sfd6ZcͤۅOiRiF_ܿ㕦bH8! jŭ'``^HRferAe'+ŷ h|'/QUXs V{xQ`lǁXgD2T]F*/Ī=k4P3Ի" +4 +A:*䗦;6?/}oT&`aggT!^T zIqm9OC_{rC*pЎ‚B}(z(>4XkS;sfH Q}p˄*,:+$`̤EEx1KB1ލBαT  4Zbƞp +WD==)4]I}IACCU"EmRES(6H/GU@"Ćƭ̈́V)dm4H\d xi,קPP{y ٘/=$19E~4kXoQŧlΟF,YFI̓wJ@y=p''4FGd4tw_0h^յKyMʞYZee!~tEG{*y@p-*OlK?aPLYܙylP#Br-ƮZh<@LZ6 #:=O I@w TKLMi8[ĆToKd*d%qVNO8U^{>~[܊4^ؘ> [2xaK%ܪKf/4ᛅr(b*llS>K˛0 >$4fh.(ExwhAHGqһ/C7Fᬺ mޠ]8nsH3]4Xi>zi[6vl@#R '@+GbGy@ `WFȼ!/h +k[vV R-BP/!E8ja޽9Vj>X#9$t: r%:y;m-ƞH/pFY:I#Aď,;WWs^*tЊ=&>[޻SQ8=cPҒMA +\Rc,ڳ&p Yc$4G婀i`-H &F=DGA!9:_ K-A]2wo c]rpl'#_1d&|&b:DCnqq~ <ۺZ轱PcD!Q5KlC1Јf]*sĿK@/)"FuZ_ T<HZtXTG">$ZHr+}Fb3N_T`H|0\q;<&hB`f٩C'2Av[T"T6\n TK1fLN399mnnqgCGz*0aע+P)3dtSuy _(' wV<}{K`pÄROXWwV ].6umA +/ 9Ԟώ/+):^MMSBʭw-dZ}1q_L,-U9';5d.`毲ب9'6D& ! h7,ˆE"~WZ-EW3^ik_l1vÉ/M ?,`kArNqFt5 ڢּIf2??:E78$qBb\7[AsYo7 rXmV MoVy'-d3( gg.U;K/V' nzo٘/W7䵗X?HlnYZSŒ2tb?2 Ѩ`< E'GnKn'RjG`Ќ{V+ۺH?|Z%?)~bN;xJZ񲗥|]("1=j4"*jtVlgڪpYU&N"ÉzDe: )=p$ 'n=L+36#RLŵkĶduS?Yۗ 5_uޮ5? *܌Un`{h<G*(uz%'Z'T]  + 0sh=xQpR2CJy$h 㤓K +[?4rJ3І'K<6R'>K)T@umFif)mkxޤ徢etfQZD<>^ԃ#fB&^dCfM%z{mo[mWV"sISp +q%2s(\1EN9ч^hO*'XM6(4VLG>~Wʊ\4o~6,''a?;/RfPHpRuj.5xҤ;-}"3j؊njԞUqW^yLp Ӭ?]Ӝ a8`UXF CT$(=q0t> VQ qX6#4] ˝n_tĞI |%͕뾄 h>=mP2-B*\"90{#ȶV% q{Ah!.16ʞJℽI^wfnX ekv0n]nГ',3a4zgNAdm3fЊo6̡ZRz]9ӳ&~BIg?0 0O{j~AԿ3ރ[y]ф^QsS +ͣ:%_;~C)`ԠFeзm!eVOi3A3z -!sr54]QgMTB5+ VY&y%3GظJYqqȂO?0ͭ'P(kzM3 |Zo BptJO'6d:."`Pr8Z@:3q1ϚfS(^ܯ:@ҘMV:1(Ϙ{n˪|nU9NiKokB-5pY9P4 qlc?eK\:9Y.Xz3¦a˕ "ȹF$7,81ΣtB2VRlDGR.>-=tJ*OuSF*:$*6Rŧ YBUZIlN:v&@sx9G[ b" yna&WPevw՞8Oo!YO :=d'v<2axZ}iן2Rn̹5\nkdӈԯ|[:Li,b RYt)]Q$6Gz$Nsip Of+#k(`.wg |ǩ 2:YJBR%mSуr` RMhfP _}c>TaO]aKSNxNw)"fԽoE<.GB`PQET e 4ػ6PYiA.4~JM`褤hOtw tΜ n?sZ64z?'9HȨnG21!Ҧ-?UOQ D@&JK[tlIL"M3la nF_-[3GRm|r#V@KD`rFV%sMq]5P$XRBquVtE "KIӧ,r \CͶr"8a1RW^3Ud Mpwn/0a)Kdwék9Iy՜D6̘ҟ8e{Q5)(<9J0!?a!kVf$`QRXuǯ1f+d (,[Kۜ~NxOǐ[r0Ek/[^Ų>:氮;K5$n2JRaQ Qp:,#ѥ'kŜ/FbЦv@~Q@@Ft r?jC6C.zZL,z^7QVVhZ}Yԟ"< pqĎ}#|381y -vX{}$Vy-q(3I1OơW.L orD4/)PyjcƱWF EXdf!T ?ù}ޟwzԞ̉\Ú*4;(y J7sN/{ zEC(<`C8M/tdȪ/KEmpPw + 3l@d!]"9{襮ye_Γo[}x pLt |!`A9L|a o nDqH$ܨh?3,6`+R9 IM"6FF6o1D'O'Hcڌ0lI :6}$Hc%9a,i9 6Iݫx)s'qN{c~] lRg 昮 :Vr=_ahB(48*t}:餠} =H'B15,0F,c=+opw~Ɗa+}VpYͬ,NnRRÆucWNv#kd,Wk~s|Qar)^!H THR"uiM +W&P>gyh|AE``l(qmru5cj3i[' |qC7vqSv%{ŜCxy6\ ``,EZ[t:8q'e-8T3*A%9ZcE~ښO59R +g.).k bSn%aģ|&%x"Y%AbQFg:(zS pgH|jw+'ρdA@>k7B++dLheh獆 +<-MѮnzZA嵪kDIxE">fV9l[U(0|.v+m9 s[5 t~w.hrfE>đeE$*5kt ހ& eBc#S$M*%Vry7LL T#4Cgr̯܎ MkFdM+8l T $'mAGH2"(3ЗlW ##Hb_M}FuƄaJ2"H7/t2Z?~h+tVN ,СT4Gy^W1TpL$UvO8>NJܩ}),>iw| XFmxoᏞp؇tgTgq:s^; )97WuB?cW|K@lNpUfqO%0D[H +3=!Ci8"AQÓ, ]Wކ&U7אHnM{BcJCͅ+ +uJaDԊfc˺g|4O +LgY`jSŰf!O*p(>[)[ugr[9֝r yw'Si +O2cD"4M\]qC>]^P톄@E %ph]Zmtۗ+`SkͯmEZ5xPSZt=y!Vi ƎI"><-H$h voo 5"&o+ZܧNW71W=g奞tusϦ^:@PR`DǙ| "ݢlUXÕK^ImɉBl\OQU +ç46B=kE< p ,1Dۦ]v +aF^(Ә8oyK^ ˻}d"FcAaYPxzNԓό=n)?Um oi1[n~w2?T=2j1`iv_޸1 +VsWCK]DUU4Kz>$A/~4GPPPՔCAzvz@Oڀ!Nk$_ +endstream +endobj +102 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-15 -951 1252 782] +/FontName/CQTQCY+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/FontFile 101 0 R +/Flags 68 +>> +endobj +101 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 599 +/Length3 533 +/Length 1109 +>> +stream +xSU uLOJu+53Rp 4W03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ A!S U[PZZZ4<6Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D90$9Rɀ̼ʂTj0RQfB!P!Xh%d+$$0_Q LC +FF +F +C2 KS=]L , ɥEEy%0 ԊdsD3ud&|9pU)|׉s77Rd(wirkSsk|^1=6Zsas_y2-3%^ Jړ}9_+l5_ ?ܛ%a{TĆ6ႮԦ,؉v3k02<[RZlez_ 6n? qܸs)_Ǵ3٩F&dL淖g2)D^c]Q,'$'Z㛾 l>uy;Mwָhl49"K]9h\8?Lj#oY~8qo{ jVf4HOc_s&z򏲫۽;|]}xNezesC&Ꝧ[֭fS!ES:ZK8sJhOOʝv2+ìRZޖ(ynY҇3 +=m^un)[TZbeQ9E%E\\w +endstream +endobj +321 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-62 -250 1123 750] +/FontName/EVJXTH+CMSL10 +/ItalicAngle -9.46 +/StemV 79 +/FontFile 320 0 R +/Flags 68 +>> +endobj +320 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 5038 +/Length3 533 +/Length 5592 +>> +stream +xUT\ۖqw N + +wwww¥@p 4@pNsoK~{s@!vȻ8@@0@FMG0d< V0 " R^v>0/07@jg0˰H9C<6V.5+=9 j@W<O7 ` ` `pb +K{ |0?s).N~0Sy53뿡{VP'8\ݼ`+w/85 j#bpyP_X +Z9yB!.࿃<O N9}eC]EؿVP/5_<. |oɹظ.v ¿SIKps87 _z.Pw/,K@HOs3<?k[ _ lb(;ۥEKaBBLAX4E+9Ee㝻6R$pЉQj#(J 1t6ښr }xE!߸];'|BYEBH}U:p,ϐ:DmVK0d +cz;®!X8ʶq.f3 Ϫ\3H#3 I=+OEFԬ^4\T@vt Iu{}z.ԮlWp"v4`wsجIZet汝Wl$uzIȎt5۞ۨ^G%}Trg_™o 2Dv>}Bu| ѽJ(j2Lҭ1Ѩ8,Wv;w8]1^e|Y?kъ=(`WuI5n\vo%#b]@򵍡SC::99R+k3"$؋/C$1ƯM{ +d +?dnw@2ƪ fŊswY&Iuxe9Hx" P_AC| P_rv;߿i8sCI[&eW7;$ 2hOuƧ%#h r +A_: K0M1M0?6"7_4haݟgT=A[lڈc.ޫMvգ3<=*+t0rdL!.6*Φhك/AΘ6!",xgEztW޸ptӶ?'ffb U`δh0$Z#ۓa^ =09m.r[ʠ@4:FɕmU/6ihҺ&ϓZ~u-O6O*GrKlgVR8ȿh)?L.vp)1FY"Kk{'Dr_= qbi\.PO%r,u8߁mI7u=~2͗n)gP"qiKκ[]uw1{962I HWܛ*z@ih|?,>$@ qΩ24wT$\Sd#$Bȭ7\/u-ƨsO͸j7|:}ڤ [DO EqN|m[X9dxl]45K&$`}!k:mAkŒ Cܺ^`zQs%8T y}0*7EoH؆V5ᅆ cKZ1Pr—:a݅SPK9<.)nۗn+JG}~g=ϼf+{ELAy3qX2·F,pStajߝ3Eɉc9"61AkWėyX{$GG/+>)g}["መu?J)dM^җ6_U$ :\a^6U?IylOtͤ6SI$R&s>-͌c{LITB}NVx}Jh?TvK%c +Qm`!7gjKZW@P B,{A!Չatd9Jo$G>:9S1PgrRiYVJg/BdLfl- d}u+y);JN: :JוG"Bu|=ƩBvxj >0TcokDiۣ>1Vi-_w7L5TB֬Dfp"^e]Wģ~=q?,^i ^a=et+\1Jb7HGpjfUJ|1m6viŐ.iG} +#)ם?cM,9ԣY{u,(Et:ԋւ*&VXE4b4}S] g5(u-~NQ:ap >O7Zq'J,Xׅ-ɟh"kz0p36w}CXAf!parCD7}ůęRIO霬^Q­H㚇NA`og*~Qᒭ3FaT):bԤ<*=R{cF-S8%@3`YgX\㣨`~I>ƃzyTɋDLtFcc O>7 ym*~a@2˽7R@Z嚟8d>X ŏ,o?xum_՛Z2"p{f!5J㖪\#ߋ4Q؎6AGbg4(Bp176vE.>H-0mΔDrJ6κ V27rDd;uó?֛Z!<̠baտ'Oa U]t`QMyOS$;, ָ?7(ZAn<Ǭ{>-&w"ۃAd JOz/],VJM7 +i_)у~t6Ouֆ3l_.ߌwܥ|';SgM6i"-H%(.w'3uhr*F?dVxCЇZH (|6]A۬A;FSj\@Tû +_oeH +ʲсsurZ֮BJ TZ +Es+wqa-nFx|TArMtIQH _φy)7hNo z-tu +aLy:Ä!{,״Z.?0mB<)N?Ҵt O48b,jRݞ+dDJSTYC0tR\ʾMckQB)as".j-8|q3ʭ 4WZGe:;%H+F弼["eOPmfQ'M<Fa)FUfJecɚ~ d]m +AW󠍁W:ǰڗL#jLˆYs| hwKI('=+ :(QyJ#I'8JE't8~QOJ*|)O +-XS<+A@LҜtW?v8涝/qцL|q0FG>bq" mJz=dX%$ZCC`X}L!i>劉ҫeM15M@W +VoQaB F%RloD%SDǾjJ2|fM4i1̠lhVZ4rQQ>emQBԈ_>@A.ā!*5^X oUx^~.6-L;xvJxB~%[LM uX_G@bdG\щyz 9>ث:M;H=J2ub8džC$x_s,^Ĵ=5fztogU(pkqRL#ˢ m-F ~'圕^vDVj4B42O2rFɮt?os:Ǵ6bVZf\6<|냍 jզ0>tG݂о߁Ң鱿[OzM |,aQ|Kqw,xB]PRp֚2kf](Ϣ6GyQe j$?a@T­R0&, $p|FW +?P qhEJ|^>6ؾ2 m;{.bo=\kMh,ص!ǣ< 9s6-nL,]bEii=ٺY/N" 7Ł:_p{ |cY,4?TD3N K>vO|)X呣F yc.=h|B+v8Ҟn6G'[1HMҜ;?F5v}̽]Z.G<%-CSo[/{R:U_Ci,q78p]P8ͲUn@lYL,ʪd ߅yV׾ O +F̈#( "Ň -gb3՞C*.kذsy ?Vw.5l62 2 +3;@N/}wz +2_i@~n/KG rE` +*;GR 9Pu VΈ&aL!Ĕeڑzhsgr~tczEm _`4K5dw@cO`D04o!`Bj7>dņRc.dmn.XEQO>U͑-#@X¬;FYT>hGn?fGgH7\69]_J +ILBB)j P>>,krژ|ڧ54 TnO$/AI;ْ?D_iyjIh͚ǟj1[1hFw@_6ͥeG(^80 >KzVTr//?`:[y8b` +endstream +endobj +1 0 obj +<< +/Creator( TeX output 2008.06.15:1852) +/Producer(dvipdfm 0.13.2c, Copyright \251 1998, by Mark A. Wicks) +/CreationDate(D:20080615185349-05'00') +>> +endobj +5 0 obj +<< +/Type/Page +/Resources 6 0 R +/Contents[17 0 R 4 0 R 18 0 R 19 0 R] +/Parent 326 0 R +>> +endobj +21 0 obj +<< +/Type/Page +/Resources 22 0 R +/Contents[17 0 R 4 0 R 46 0 R 19 0 R] +/Parent 326 0 R +>> +endobj +48 0 obj +<< +/Type/Page +/Resources 49 0 R +/Contents[17 0 R 4 0 R 50 0 R 19 0 R] +/Parent 326 0 R +>> +endobj +52 0 obj +<< +/Type/Page +/Resources 53 0 R +/Contents[17 0 R 4 0 R 65 0 R 19 0 R] +/Parent 326 0 R +>> +endobj +326 0 obj +<< +/Type/Pages +/Count 4 +/Kids[5 0 R 21 0 R 48 0 R 52 0 R] +/Parent 325 0 R +>> +endobj +67 0 obj +<< +/Type/Page +/Resources 68 0 R +/Contents[17 0 R 4 0 R 69 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +71 0 obj +<< +/Type/Page +/Resources 72 0 R +/Contents[17 0 R 4 0 R 73 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +75 0 obj +<< +/Type/Page +/Resources 76 0 R +/Contents[17 0 R 4 0 R 77 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +79 0 obj +<< +/Type/Page +/Resources 80 0 R +/Contents[17 0 R 4 0 R 81 0 R 19 0 R] +/Parent 327 0 R +>> +endobj +327 0 obj +<< +/Type/Pages +/Count 4 +/Kids[67 0 R 71 0 R 75 0 R 79 0 R] +/Parent 325 0 R +>> +endobj +83 0 obj +<< +/Type/Page +/Resources 84 0 R +/Contents[17 0 R 4 0 R 85 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +87 0 obj +<< +/Type/Page +/Resources 88 0 R +/Contents[17 0 R 4 0 R 89 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +91 0 obj +<< +/Type/Page +/Resources 92 0 R +/Contents[17 0 R 4 0 R 93 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +95 0 obj +<< +/Type/Page +/Resources 96 0 R +/Contents[17 0 R 4 0 R 97 0 R 19 0 R] +/Parent 328 0 R +>> +endobj +328 0 obj +<< +/Type/Pages +/Count 4 +/Kids[83 0 R 87 0 R 91 0 R 95 0 R] +/Parent 325 0 R +>> +endobj +99 0 obj +<< +/Type/Page +/Resources 100 0 R +/Contents[17 0 R 4 0 R 104 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +106 0 obj +<< +/Type/Page +/Resources 107 0 R +/Contents[17 0 R 4 0 R 108 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +110 0 obj +<< +/Type/Page +/Resources 111 0 R +/Contents[17 0 R 4 0 R 112 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +114 0 obj +<< +/Type/Page +/Resources 115 0 R +/Contents[17 0 R 4 0 R 116 0 R 19 0 R] +/Parent 329 0 R +>> +endobj +329 0 obj +<< +/Type/Pages +/Count 4 +/Kids[99 0 R 106 0 R 110 0 R 114 0 R] +/Parent 325 0 R +>> +endobj +325 0 obj +<< +/Type/Pages +/Count 16 +/Kids[326 0 R 327 0 R 328 0 R 329 0 R] +/Parent 3 0 R +>> +endobj +118 0 obj +<< +/Type/Page +/Resources 119 0 R +/Contents[17 0 R 4 0 R 120 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +122 0 obj +<< +/Type/Page +/Resources 123 0 R +/Contents[17 0 R 4 0 R 124 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +126 0 obj +<< +/Type/Page +/Resources 127 0 R +/Contents[17 0 R 4 0 R 128 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +130 0 obj +<< +/Type/Page +/Resources 131 0 R +/Contents[17 0 R 4 0 R 132 0 R 19 0 R] +/Parent 331 0 R +>> +endobj +331 0 obj +<< +/Type/Pages +/Count 4 +/Kids[118 0 R 122 0 R 126 0 R 130 0 R] +/Parent 330 0 R +>> +endobj +134 0 obj +<< +/Type/Page +/Resources 135 0 R +/Contents[17 0 R 4 0 R 136 0 R 19 0 R] +/Parent 332 0 R +>> +endobj +138 0 obj +<< +/Type/Page +/Resources 139 0 R +/Contents[17 0 R 4 0 R 140 0 R 19 0 R] +/Parent 332 0 R +>> +endobj +142 0 obj +<< +/Type/Page +/Resources 143 0 R +/Contents[17 0 R 4 0 R 144 0 R 19 0 R] +/Parent 332 0 R +>> +endobj +146 0 obj +<< +/Type/Page +/Resources 147 0 R +/Contents[17 0 R 4 0 R 148 0 R 19 0 R] +/Parent 332 0 R +>> +endobj +332 0 obj +<< +/Type/Pages +/Count 4 +/Kids[134 0 R 138 0 R 142 0 R 146 0 R] +/Parent 330 0 R +>> +endobj +150 0 obj +<< +/Type/Page +/Resources 151 0 R +/Contents[17 0 R 4 0 R 152 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +154 0 obj +<< +/Type/Page +/Resources 155 0 R +/Contents[17 0 R 4 0 R 156 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +158 0 obj +<< +/Type/Page +/Resources 159 0 R +/Contents[17 0 R 4 0 R 160 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +162 0 obj +<< +/Type/Page +/Resources 163 0 R +/Contents[17 0 R 4 0 R 164 0 R 19 0 R] +/Parent 333 0 R +>> +endobj +333 0 obj +<< +/Type/Pages +/Count 4 +/Kids[150 0 R 154 0 R 158 0 R 162 0 R] +/Parent 330 0 R +>> +endobj +166 0 obj +<< +/Type/Page +/Resources 167 0 R +/Contents[17 0 R 4 0 R 168 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +170 0 obj +<< +/Type/Page +/Resources 171 0 R +/Contents[17 0 R 4 0 R 172 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +174 0 obj +<< +/Type/Page +/Resources 175 0 R +/Contents[17 0 R 4 0 R 176 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +178 0 obj +<< +/Type/Page +/Resources 179 0 R +/Contents[17 0 R 4 0 R 180 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +182 0 obj +<< +/Type/Page +/Resources 183 0 R +/Contents[17 0 R 4 0 R 184 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +335 0 obj +<< +/Type/Pages +/Count 2 +/Kids[178 0 R 182 0 R] +/Parent 334 0 R +>> +endobj +334 0 obj +<< +/Type/Pages +/Count 5 +/Kids[166 0 R 170 0 R 174 0 R 335 0 R] +/Parent 330 0 R +>> +endobj +330 0 obj +<< +/Type/Pages +/Count 17 +/Kids[331 0 R 332 0 R 333 0 R 334 0 R] +/Parent 3 0 R +>> +endobj +186 0 obj +<< +/Type/Page +/Resources 187 0 R +/Contents[17 0 R 4 0 R 188 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +190 0 obj +<< +/Type/Page +/Resources 191 0 R +/Contents[17 0 R 4 0 R 192 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +194 0 obj +<< +/Type/Page +/Resources 195 0 R +/Contents[17 0 R 4 0 R 196 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +198 0 obj +<< +/Type/Page +/Resources 199 0 R +/Contents[17 0 R 4 0 R 200 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +337 0 obj +<< +/Type/Pages +/Count 4 +/Kids[186 0 R 190 0 R 194 0 R 198 0 R] +/Parent 336 0 R +>> +endobj +202 0 obj +<< +/Type/Page +/Resources 203 0 R +/Contents[17 0 R 4 0 R 204 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +206 0 obj +<< +/Type/Page +/Resources 207 0 R +/Contents[17 0 R 4 0 R 208 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +210 0 obj +<< +/Type/Page +/Resources 211 0 R +/Contents[17 0 R 4 0 R 212 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +214 0 obj +<< +/Type/Page +/Resources 215 0 R +/Contents[17 0 R 4 0 R 216 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +338 0 obj +<< +/Type/Pages +/Count 4 +/Kids[202 0 R 206 0 R 210 0 R 214 0 R] +/Parent 336 0 R +>> +endobj +218 0 obj +<< +/Type/Page +/Resources 219 0 R +/Contents[17 0 R 4 0 R 220 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +222 0 obj +<< +/Type/Page +/Resources 223 0 R +/Contents[17 0 R 4 0 R 224 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +226 0 obj +<< +/Type/Page +/Resources 227 0 R +/Contents[17 0 R 4 0 R 228 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +230 0 obj +<< +/Type/Page +/Resources 231 0 R +/Contents[17 0 R 4 0 R 232 0 R 19 0 R] +/Parent 339 0 R +>> +endobj +339 0 obj +<< +/Type/Pages +/Count 4 +/Kids[218 0 R 222 0 R 226 0 R 230 0 R] +/Parent 336 0 R +>> +endobj +234 0 obj +<< +/Type/Page +/Resources 235 0 R +/Contents[17 0 R 4 0 R 236 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +238 0 obj +<< +/Type/Page +/Resources 239 0 R +/Contents[17 0 R 4 0 R 240 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +242 0 obj +<< +/Type/Page +/Resources 243 0 R +/Contents[17 0 R 4 0 R 244 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +246 0 obj +<< +/Type/Page +/Resources 247 0 R +/Contents[17 0 R 4 0 R 248 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +250 0 obj +<< +/Type/Page +/Resources 251 0 R +/Contents[17 0 R 4 0 R 252 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +341 0 obj +<< +/Type/Pages +/Count 2 +/Kids[246 0 R 250 0 R] +/Parent 340 0 R +>> +endobj +340 0 obj +<< +/Type/Pages +/Count 5 +/Kids[234 0 R 238 0 R 242 0 R 341 0 R] +/Parent 336 0 R +>> +endobj +336 0 obj +<< +/Type/Pages +/Count 17 +/Kids[337 0 R 338 0 R 339 0 R 340 0 R] +/Parent 3 0 R +>> +endobj +254 0 obj +<< +/Type/Page +/Resources 255 0 R +/Contents[17 0 R 4 0 R 256 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +258 0 obj +<< +/Type/Page +/Resources 259 0 R +/Contents[17 0 R 4 0 R 260 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +262 0 obj +<< +/Type/Page +/Resources 263 0 R +/Contents[17 0 R 4 0 R 264 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +266 0 obj +<< +/Type/Page +/Resources 267 0 R +/Contents[17 0 R 4 0 R 268 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +343 0 obj +<< +/Type/Pages +/Count 4 +/Kids[254 0 R 258 0 R 262 0 R 266 0 R] +/Parent 342 0 R +>> +endobj +270 0 obj +<< +/Type/Page +/Resources 271 0 R +/Contents[17 0 R 4 0 R 272 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +274 0 obj +<< +/Type/Page +/Resources 275 0 R +/Contents[17 0 R 4 0 R 276 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +278 0 obj +<< +/Type/Page +/Resources 279 0 R +/Contents[17 0 R 4 0 R 280 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +282 0 obj +<< +/Type/Page +/Resources 283 0 R +/Contents[17 0 R 4 0 R 284 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +344 0 obj +<< +/Type/Pages +/Count 4 +/Kids[270 0 R 274 0 R 278 0 R 282 0 R] +/Parent 342 0 R +>> +endobj +286 0 obj +<< +/Type/Page +/Resources 287 0 R +/Contents[17 0 R 4 0 R 288 0 R 19 0 R] +/Parent 345 0 R +>> +endobj +290 0 obj +<< +/Type/Page +/Resources 291 0 R +/Contents[17 0 R 4 0 R 292 0 R 19 0 R] +/Parent 345 0 R +>> +endobj +294 0 obj +<< +/Type/Page +/Resources 295 0 R +/Contents[17 0 R 4 0 R 296 0 R 19 0 R] +/Parent 345 0 R +>> +endobj +298 0 obj +<< +/Type/Page +/Resources 299 0 R +/Contents[17 0 R 4 0 R 300 0 R 19 0 R] +/Parent 345 0 R +>> +endobj +345 0 obj +<< +/Type/Pages +/Count 4 +/Kids[286 0 R 290 0 R 294 0 R 298 0 R] +/Parent 342 0 R +>> +endobj +302 0 obj +<< +/Type/Page +/Resources 303 0 R +/Contents[17 0 R 4 0 R 304 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +306 0 obj +<< +/Type/Page +/Resources 307 0 R +/Contents[17 0 R 4 0 R 308 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +310 0 obj +<< +/Type/Page +/Resources 311 0 R +/Contents[17 0 R 4 0 R 312 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +314 0 obj +<< +/Type/Page +/Resources 315 0 R +/Contents[17 0 R 4 0 R 316 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +318 0 obj +<< +/Type/Page +/Resources 319 0 R +/Contents[17 0 R 4 0 R 323 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +347 0 obj +<< +/Type/Pages +/Count 2 +/Kids[314 0 R 318 0 R] +/Parent 346 0 R +>> +endobj +346 0 obj +<< +/Type/Pages +/Count 5 +/Kids[302 0 R 306 0 R 310 0 R 347 0 R] +/Parent 342 0 R +>> +endobj +342 0 obj +<< +/Type/Pages +/Count 17 +/Kids[343 0 R 344 0 R 345 0 R 346 0 R] +/Parent 3 0 R +>> +endobj +3 0 obj +<< +/Type/Pages +/Count 67 +/Kids[325 0 R 330 0 R 336 0 R 342 0 R] +/MediaBox[0 0 595 842] +>> +endobj +17 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +19 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +4 0 obj +<< +/Length 33 +>> +stream +1.00028 0 0 1.00028 72 769.82 cm +endstream +endobj +348 0 obj +<< +>> +endobj +349 0 obj +null +endobj +350 0 obj +<< +>> +endobj +2 0 obj +<< +/Type/Catalog +/Pages 3 0 R +/Outlines 348 0 R +/Threads 349 0 R +/Names 350 0 R +>> +endobj +xref +0 351 +0000000000 65535 f +0000148990 00000 n +0000158917 00000 n +0000158562 00000 n +0000158767 00000 n +0000149154 00000 n +0000004048 00000 n +0000000009 00000 n +0000082105 00000 n +0000081921 00000 n +0000000913 00000 n +0000086769 00000 n +0000086583 00000 n +0000001906 00000 n +0000091892 00000 n +0000091704 00000 n +0000002823 00000 n +0000158667 00000 n +0000003740 00000 n +0000158717 00000 n +0000003993 00000 n +0000149257 00000 n +0000014682 00000 n +0000101704 00000 n +0000101515 00000 n +0000004109 00000 n +0000106975 00000 n +0000106785 00000 n +0000005055 00000 n +0000112279 00000 n +0000112090 00000 n +0000005991 00000 n +0000006967 00000 n +0000114936 00000 n +0000114742 00000 n +0000007921 00000 n +0000008867 00000 n +0000117538 00000 n +0000117343 00000 n +0000010483 00000 n +0000119509 00000 n +0000119323 00000 n +0000011434 00000 n +0000122535 00000 n +0000122344 00000 n +0000012398 00000 n +0000013393 00000 n +0000014571 00000 n +0000149362 00000 n +0000015735 00000 n +0000014744 00000 n +0000015635 00000 n +0000149467 00000 n +0000021425 00000 n +0000124482 00000 n +0000124288 00000 n +0000015797 00000 n +0000016768 00000 n +0000128037 00000 n +0000127842 00000 n +0000017675 00000 n +0000018657 00000 n +0000130694 00000 n +0000130508 00000 n +0000019634 00000 n +0000020379 00000 n +0000021301 00000 n +0000149666 00000 n +0000022185 00000 n +0000021487 00000 n +0000022140 00000 n +0000149771 00000 n +0000022746 00000 n +0000022247 00000 n +0000022701 00000 n +0000149876 00000 n +0000023762 00000 n +0000022808 00000 n +0000023638 00000 n +0000149981 00000 n +0000025054 00000 n +0000023824 00000 n +0000024930 00000 n +0000150181 00000 n +0000025817 00000 n +0000025116 00000 n +0000025772 00000 n +0000150286 00000 n +0000026587 00000 n +0000025879 00000 n +0000026542 00000 n +0000150391 00000 n +0000027008 00000 n +0000026649 00000 n +0000026963 00000 n +0000150496 00000 n +0000028251 00000 n +0000027070 00000 n +0000028115 00000 n +0000150696 00000 n +0000030421 00000 n +0000141865 00000 n +0000141669 00000 n +0000028313 00000 n +0000029325 00000 n +0000030283 00000 n +0000150803 00000 n +0000031058 00000 n +0000030485 00000 n +0000031012 00000 n +0000150911 00000 n +0000032152 00000 n +0000031122 00000 n +0000032027 00000 n +0000151019 00000 n +0000033528 00000 n +0000032216 00000 n +0000033390 00000 n +0000151323 00000 n +0000034236 00000 n +0000033592 00000 n +0000034190 00000 n +0000151431 00000 n +0000034553 00000 n +0000034300 00000 n +0000034507 00000 n +0000151539 00000 n +0000035785 00000 n +0000034617 00000 n +0000035660 00000 n +0000151647 00000 n +0000036571 00000 n +0000035849 00000 n +0000036525 00000 n +0000151854 00000 n +0000037345 00000 n +0000036635 00000 n +0000037299 00000 n +0000151962 00000 n +0000037768 00000 n +0000037409 00000 n +0000037722 00000 n +0000152070 00000 n +0000038935 00000 n +0000037832 00000 n +0000038798 00000 n +0000152178 00000 n +0000040380 00000 n +0000038999 00000 n +0000040243 00000 n +0000152385 00000 n +0000041154 00000 n +0000040444 00000 n +0000041108 00000 n +0000152493 00000 n +0000041937 00000 n +0000041218 00000 n +0000041891 00000 n +0000152601 00000 n +0000042451 00000 n +0000042001 00000 n +0000042405 00000 n +0000152709 00000 n +0000043740 00000 n +0000042515 00000 n +0000043603 00000 n +0000152916 00000 n +0000044958 00000 n +0000043804 00000 n +0000044820 00000 n +0000153024 00000 n +0000045556 00000 n +0000045022 00000 n +0000045510 00000 n +0000153132 00000 n +0000046782 00000 n +0000045620 00000 n +0000046657 00000 n +0000153240 00000 n +0000047529 00000 n +0000046846 00000 n +0000047483 00000 n +0000153348 00000 n +0000048256 00000 n +0000047593 00000 n +0000048210 00000 n +0000153736 00000 n +0000049585 00000 n +0000048320 00000 n +0000049447 00000 n +0000153844 00000 n +0000050269 00000 n +0000049649 00000 n +0000050223 00000 n +0000153952 00000 n +0000051373 00000 n +0000050333 00000 n +0000051225 00000 n +0000154060 00000 n +0000052488 00000 n +0000051437 00000 n +0000052340 00000 n +0000154267 00000 n +0000053753 00000 n +0000052552 00000 n +0000053605 00000 n +0000154375 00000 n +0000054516 00000 n +0000053817 00000 n +0000054470 00000 n +0000154483 00000 n +0000055252 00000 n +0000054580 00000 n +0000055206 00000 n +0000154591 00000 n +0000056443 00000 n +0000055316 00000 n +0000056295 00000 n +0000154798 00000 n +0000057802 00000 n +0000056507 00000 n +0000057641 00000 n +0000154906 00000 n +0000058492 00000 n +0000057866 00000 n +0000058446 00000 n +0000155014 00000 n +0000059760 00000 n +0000058556 00000 n +0000059612 00000 n +0000155122 00000 n +0000061269 00000 n +0000059824 00000 n +0000061108 00000 n +0000155329 00000 n +0000061976 00000 n +0000061333 00000 n +0000061930 00000 n +0000155437 00000 n +0000062356 00000 n +0000062040 00000 n +0000062310 00000 n +0000155545 00000 n +0000063823 00000 n +0000062420 00000 n +0000063675 00000 n +0000155653 00000 n +0000064623 00000 n +0000063887 00000 n +0000064577 00000 n +0000155761 00000 n +0000065402 00000 n +0000064687 00000 n +0000065356 00000 n +0000156149 00000 n +0000065977 00000 n +0000065466 00000 n +0000065931 00000 n +0000156257 00000 n +0000067195 00000 n +0000066041 00000 n +0000067047 00000 n +0000156365 00000 n +0000068768 00000 n +0000067259 00000 n +0000068620 00000 n +0000156473 00000 n +0000069549 00000 n +0000068832 00000 n +0000069503 00000 n +0000156680 00000 n +0000070352 00000 n +0000069613 00000 n +0000070306 00000 n +0000156788 00000 n +0000070943 00000 n +0000070416 00000 n +0000070897 00000 n +0000156896 00000 n +0000072291 00000 n +0000071007 00000 n +0000072143 00000 n +0000157004 00000 n +0000072616 00000 n +0000072355 00000 n +0000072570 00000 n +0000157211 00000 n +0000074032 00000 n +0000072680 00000 n +0000073871 00000 n +0000157319 00000 n +0000074750 00000 n +0000074096 00000 n +0000074704 00000 n +0000157427 00000 n +0000076233 00000 n +0000074814 00000 n +0000076085 00000 n +0000157535 00000 n +0000077010 00000 n +0000076297 00000 n +0000076964 00000 n +0000157742 00000 n +0000077788 00000 n +0000077074 00000 n +0000077742 00000 n +0000157850 00000 n +0000078268 00000 n +0000077852 00000 n +0000078222 00000 n +0000157958 00000 n +0000079776 00000 n +0000078332 00000 n +0000079615 00000 n +0000158066 00000 n +0000080472 00000 n +0000079840 00000 n +0000080426 00000 n +0000158174 00000 n +0000081857 00000 n +0000143283 00000 n +0000143088 00000 n +0000080536 00000 n +0000081459 00000 n +0000081799 00000 n +0000151225 00000 n +0000149572 00000 n +0000150086 00000 n +0000150601 00000 n +0000151127 00000 n +0000153638 00000 n +0000151755 00000 n +0000152286 00000 n +0000152817 00000 n +0000153539 00000 n +0000153456 00000 n +0000156051 00000 n +0000154168 00000 n +0000154699 00000 n +0000155230 00000 n +0000155952 00000 n +0000155869 00000 n +0000158464 00000 n +0000156581 00000 n +0000157112 00000 n +0000157643 00000 n +0000158365 00000 n +0000158282 00000 n +0000158849 00000 n +0000158872 00000 n +0000158894 00000 n +trailer +<< +/Size 351 +/Root 2 0 R +/Info 1 0 R +>> +startxref +159015 +%%EOF diff --git a/src/axiom-website/CATS/schaum12.input.pamphlet b/src/axiom-website/CATS/schaum12.input.pamphlet new file mode 100644 index 0000000..7d5d77a --- /dev/null +++ b/src/axiom-website/CATS/schaum12.input.pamphlet @@ -0,0 +1,2870 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/input schaum12.input} +\author{Timothy Daly} +\maketitle +\eject +\tableofcontents +\eject +\section{\cite{1}:14.265~~~~~$\displaystyle +\int{\frac{dx}{ax^2+bx+c}}$} +$$\int{\frac{1}{ax^2+bx+c}}= +\left\{ +\begin{array}{l} +\displaystyle\frac{2}{\sqrt{4ac-b^2}}\tan^{-1}\frac{2ax+b}{\sqrt{4ac-b^2}}\\ +\displaystyle\frac{1}{\sqrt{b^2-4ac}}\ln\left( +\frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}}\right) +\end{array} +\right. +$$ +<<*>>= +)spool schaum12.output +)set message test on +)set message auto off +)clear all + +--S 1 +aa:=integrate(1/(a*x^2+b*x+c),x) +--R +--R (1) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 2 +bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2)) +--R +--R +--R 2a x + b +--R 2atan(------------) +--R +---------+ +--R | 2 +--R \|4a c - b +--R (2) ------------------- +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 3 +bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c))) +--R +--R +--R +-----------+ +--R | 2 +--R - \|- 4a c + b + 2a x + b +--R log(---------------------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b + 2a x + b +--R (3) -------------------------------- +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression Integer +--E + +--S 4 +cc1:=aa.1-bb1 +--R +--R (4) +--R +---------+ +--R | 2 +--R \|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 2a x + b +--R - 2\|- 4a c + b atan(------------) +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 5 +cc2:=aa.1-bb2 +--R +--R (5) +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R - \|- 4a c + b + 2a x + b +--R - log(---------------------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b + 2a x + b +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression Integer +--E + +--S 6 +cc3:=aa.2-bb1 +--R +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b 2a x + b +--R 2atan(----------------------) - 2atan(------------) +--R 2 +---------+ +--R 4a c - b | 2 +--R \|4a c - b +--R (6) --------------------------------------------------- +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 7 +cc4:=aa.2-bb2 +--R +--R (7) +--R +-----------+ +--R +---------+ | 2 +--R | 2 - \|- 4a c + b + 2a x + b +--R - \|4a c - b log(---------------------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b + 2a x + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R 2\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 8 +atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) +--R +--R - x + %i +--R %i log(--------) +--R x + %i +--R (8) atan(x) == - ---------------- +--R 2 +--R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) +--E + +--S 9 +dd3:=atanrule cc3 +--R +--R (9) +--R +---------+ +--R | 2 +--R \|4a c - b + 2%i a x + %i b +--R %i log(-----------------------------) +--R +---------+ +--R | 2 +--R \|4a c - b - 2%i a x - %i b +--R + +--R +---------+ +--R | 2 2 +--R (- 2a x - b)\|4a c - b + 4%i a c - %i b +--R - %i log(------------------------------------------) +--R +---------+ +--R | 2 2 +--R (2a x + b)\|4a c - b + 4%i a c - %i b +--R / +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Complex Integer +--E + +--S 10 +ee3:=expandLog dd3 +--R +--R (10) +--R +---------+ +--R | 2 2 +--R %i log((2a x + b)\|4a c - b + 4%i a c - %i b ) +--R + +--R +---------+ +--R | 2 2 +--R - %i log((2a x + b)\|4a c - b - 4%i a c + %i b ) +--R + +--R +---------+ +--R | 2 +--R %i log(\|4a c - b + 2%i a x + %i b) +--R + +--R +---------+ +--R | 2 +--R - %i log(\|4a c - b - 2%i a x - %i b) - %i log(- 1) +--R / +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Complex Integer +--E + +--S 11 14:265 Schaums and Axiom agree +ff3:=complexNormalize ee3 +--R +--R (11) 0 +--R Type: Expression Complex Integer +--E +@ + +\section{\cite{1}:14.266~~~~~$\displaystyle +\int{\frac{x~dx}{ax^2+bx+c}}$} +$$\int{\frac{x}{ax^2+bx+c}}= +\frac{1}{2a}\ln(ax^2+bx+c)-\frac{b}{2a}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 12 +aa:=integrate(x/(a*x^2+b*x+c),x) +--R +--R (1) +--R [ +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R log(a x + b x + c)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R , +--R +---------+ +--R | 2 +---------+ +--R (2a x + b)\|4a c - b 2 | 2 +--R - 2b atan(----------------------) + log(a x + b x + c)\|4a c - b +--R 2 +--R 4a c - b +--R -------------------------------------------------------------------] +--R +---------+ +--R | 2 +--R 2a\|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 13 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 14 +bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1 +--R +--R +--R (3) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R log(a x + b x + c)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R Type: Expression Integer +--E + +--S 15 +bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R (2a x + b)\|4a c - b 2 | 2 +--R - 2b atan(----------------------) + log(a x + b x + c)\|4a c - b +--R 2 +--R 4a c - b +--R (4) ------------------------------------------------------------------- +--R +---------+ +--R | 2 +--R 2a\|4a c - b +--R Type: Expression Integer +--E + +--S 16 +cc1:=aa.1-bb1 +--R +--R (5) +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R Type: Expression Integer +--E + +--S 17 +cc2:=aa.2-bb1 +--R +--R (6) +--R +---------+ +--R | 2 +--R b\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R - 2b\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R 2a\|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 18 +cc3:=aa.2-bb1 +--R +--R (7) +--R +---------+ +--R | 2 +--R b\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R - 2b\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R 2a\|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 19 14:266 Schaums and Axiom agree +cc4:=aa.2-bb2 +--R +--R (8) 0 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.267~~~~~$\displaystyle +\int{\frac{x^2dx}{ax^2+bx+c}}$} +$$\int{\frac{x^2}{ax^2+bx+c}}= +\frac{x}{a}-\frac{b}{2a^2}\ln(ax^2+bx+c)+\frac{b^2-2ac}{2a^2} +\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 20 +aa:=integrate(x^2/(a*x^2+b*x+c),x) +--R +--R +--R (1) +--R [ +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(a x + b x + c) + 2a x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2a x + b)\|4a c - b +--R (- 4a c + 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- b log(a x + b x + c) + 2a x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2a \|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 21 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 22 +bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1 +--R +--R +--R (3) +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(a x + b x + c) + 2a x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression Integer +--E + +--S 23 +bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2 +--R +--R +--R (4) +--R +---------+ +--R | 2 +--R 2 (2a x + b)\|4a c - b +--R (- 4a c + 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- b log(a x + b x + c) + 2a x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2a \|4a c - b +--R Type: Expression Integer +--E + +--S 24 +cc1:=bb1-aa.1 +--R +--R (5) +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression Integer +--E + +--S 25 14:267 Schaums and Axiom differ by a constant +dd1:=complexNormalize cc1 +--R +--R 2 3 2 2 +--R (- 2a c + b )log(- 16a c + 4a b ) +--R (6) --------------------------------- +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.268~~~~~$\displaystyle +\int{\frac{x^m~dx}{ax^2+bx+c}}$} +$$\int{\frac{x^m}{ax^2+bx+c}}= +\frac{x^{m-1}}{(m-1)a}-\frac{c}{a}\int{\frac{x^{m-2}}{ax^2+bx+c}}- +\frac{b}{a}\int{\frac{x^{m-1}}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 26 14:268 Axiom cannot compute this integral +aa:=integrate(x^m/(a*x^2+b*x+c),x) +--R +--R +--R x m +--I ++ %N +--I (1) | --------------- d%N +--R ++ 2 +--I c + %N b + %N a +--R Type: Union(Expression Integer,...) +--E + +@ + +\section{\cite{1}:14.269~~~~~$\displaystyle +\int{\frac{dx}{x(ax^2+bx+c)}}$} +$$\int{\frac{1}{x(ax^2+bx+c)}}= +\frac{1}{2c}\ln\left(\frac{x^2}{ax^2+bx+c}\right)- +\frac{b}{2c}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 27 +aa:=integrate(1/(x*(a*x^2+b*x+c)),x) +--R +--R +--R (1) +--R [ +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R (- log(a x + b x + c) + 2log(x))\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R - 2b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- log(a x + b x + c) + 2log(x))\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 28 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 29 +bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1 +--R +--R +--R (3) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +-----------+ +--R x | 2 +--R log(--------------)\|- 4a c + b +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression Integer +--E + +--S 30 +bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2 +--R +--R +--R +---------+ +--R | 2 2 +---------+ +--R (2a x + b)\|4a c - b x | 2 +--R - 2b atan(----------------------) + log(--------------)\|4a c - b +--R 2 2 +--R 4a c - b a x + b x + c +--R (4) ------------------------------------------------------------------- +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R Type: Expression Integer +--E + +--S 31 +cc1:=bb1-aa.1 +--R +--R (5) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 3 +--R (- 8a c + 2a b )x - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +-----------+ +--R 2 x | 2 +--R (log(a x + b x + c) - 2log(x) + log(--------------))\|- 4a c + b +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression Integer +--E + +--S 32 +dd1:=expandLog cc1 +--R +--R (6) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R + +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R + +--R 2 +--R 2b log(a x + b x + c) +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression Integer +--E + +--S 33 14:269 Schaums and Axiom differ by a constant +ee1:=complexNormalize dd1 +--R +--R 3 2 2 +--R b log(- 16a c + 4a b ) +--R (7) - ---------------------- +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.270~~~~~$\displaystyle +\int{\frac{dx}{x^2(ax^2+bx+c)}}$} +$$\int{\frac{1}{x^2(ax^2+bx+c)}}= +\frac{b}{2c^2}\ln\left(\frac{ax^2+bx+c}{x^2}\right)-\frac{1}{cx}+ +\frac{b^2-2ac}{2c^2}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 34 +aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x) +--R +--R +--R (1) +--R [ +--R 2 +--R (2a c - b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R (b x log(a x + b x + c) - 2b x log(x) - 2c)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c x\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2a x + b)\|4a c - b +--R (- 4a c + 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (b x log(a x + b x + c) - 2b x log(x) - 2c)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c x\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 35 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 36 +bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1 +--R +--R +--R (3) +--R 2 +--R (- 2a c + b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +-----------+ +--R a x + b x + c | 2 +--R (b x log(--------------) - 2c)\|- 4a c + b +--R 2 +--R x +--R / +--R +-----------+ +--R 2 | 2 +--R 2c x\|- 4a c + b +--R Type: Expression Integer +--E + +--S 37 +bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2 +--R +--R +--R (4) +--R +---------+ +--R | 2 +--R 2 (2a x + b)\|4a c - b +--R (- 4a c + 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 +---------+ +--R a x + b x + c | 2 +--R (b x log(--------------) - 2c)\|4a c - b +--R 2 +--R x +--R / +--R +---------+ +--R 2 | 2 +--R 2c x\|4a c - b +--R Type: Expression Integer +--E + +--S 38 +cc1:=bb1-aa.1 +--R +--R (5) +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +-----------+ +--R 2 a x + b x + c | 2 +--R (- b log(a x + b x + c) + 2b log(x) + b log(--------------))\|- 4a c + b +--R 2 +--R x +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E + +--S 39 +dd1:=expandLog cc1 +--R +--R (6) +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R + +--R 2 +--R (- 2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R + +--R 2 2 +--R (4a c - 2b )log(a x + b x + c) +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E + +--S 40 14:270 Schaums and Axiom differ by a constant +ee1:=complexNormalize dd1 +--R +--R 2 3 2 2 +--R (- 2a c + b )log(- 16a c + 4a b ) +--R (7) --------------------------------- +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.271~~~~~$\displaystyle +\int{\frac{dx}{x^n(ax^2+bx+c)}}$} +$$\int{\frac{1}{x^n(ax^2+bx+c)}}= +-\frac{1}{(n-1)cx^{n-1}}- +\frac{b}{c}\int{\frac{1}{x^{n-1}(ax^2+bx+c)}}- +\frac{a}{c}\int{\frac{1}{x^{x-2}(ax^2+bx+c)}} +$$ +<<*>>= +)clear all + +--S 41 14:271 Axiom cannot compute this integral +aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x) +--R +--R +--R x +--R ++ 1 +--I (1) | -------------------- d%N +--R ++ 2 n +--I (c + %N b + %N a)%N +--R Type: Union(Expression Integer,...) +--E + +@ + +\section{\cite{1}:14.272~~~~~$\displaystyle +\int{\frac{dx}{(ax^2+bx+c)^2}}$} +$$\int{\frac{1}{(ax^2+bx+c)^2}}= +\frac{2xa+b}{(4ac-b^2)(ax^2+bx+c)}+ +\frac{2a}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 42 +aa:=integrate(1/(a*x^2+b*x+c)^2,x) +--R +--R +--R (1) +--R [ +--R 2 2 +--R (2a x + 2a b x + 2a c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (2a x + b)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R , +--R +---------+ +--R | 2 +---------+ +--R 2 2 (2a x + b)\|4a c - b | 2 +--R (4a x + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b +--R 2 +--R 4a c - b +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 43 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 44 +bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1 +--R +--R (3) +--R 2 2 +--R (2a x + 2a b x + 2a c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (2a x + b)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 45 +bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2 +--R +--R (4) +--R +---------+ +--R | 2 +---------+ +--R 2 2 (2a x + b)\|4a c - b | 2 +--R (4a x + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b +--R 2 +--R 4a c - b +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R Type: Expression Integer +--E + +--S 46 +cc1:=aa.1-bb1 +--R +--R (5) 0 +--R Type: Expression Integer +--E + +--S 47 +cc2:=aa.2-bb1 +--R +--R (6) +--R - +--R +---------+ +--R | 2 +--R 2a\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R 4a\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 48 +cc3:=aa.1-bb2 +--R +--R (7) +--R +---------+ +--R | 2 +--R 2a\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R - 4a\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E + +--S 49 14:272 Schaums and Axiom agree +cc4:=aa.2-bb2 +--R +--R (8) 0 +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.273~~~~~$\displaystyle +\int{\frac{x~dx}{(ax^2+bx+c)^2}}$} +$$\int{\frac{x}{(ax^2+bx+c)^2}}= +-\frac{bx+2c}{(4ac-b^2)(ax^2+bx+c)}- +\frac{b}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 50 +aa:=integrate(x/(a*x^2+b*x+c)^2,x) +--R +--R +--R (1) +--R [ +--R 2 2 +--R (a b x + b x + b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (- b x - 2c)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 2 (2a x + b)\|4a c - b +--R (- 2a b x - 2b x - 2b c)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (- b x - 2c)\|4a c - b +--R / +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 51 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 52 +bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1 +--R +--R +--R (3) +--R 2 2 +--R (- a b x - b x - b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (- b x - 2c)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 53 +bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2 +--R +--R +--R (4) +--R +---------+ +--R | 2 +--R 2 2 (2a x + b)\|4a c - b +--R (- 2a b x - 2b x - 2b c)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (- b x - 2c)\|4a c - b +--R / +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R Type: Expression Integer +--E + +--S 54 +cc1:=bb1-aa.1 +--R +--R (5) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 3 +--R (- 8a c + 2a b )x - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression Integer +--E + +--S 55 +dd1:=expandLog cc1 +--R +--R (6) +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R + +--R - +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R + +--R 2 +--R 2b log(a x + b x + c) +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression Integer +--E + +--S 56 14:273 Schaums and Axiom differ by a constant +ee1:=complexNormalize dd1 +--R +--R 3 2 2 +--R b log(- 16a c + 4a b ) +--R (7) - ------------------------- +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.274~~~~~$\displaystyle +\int{\frac{x^2~dx}{(ax^2+bx+c)^2}}$} +$$\int{\frac{x^2}{(ax^2+bx+c)^2}}= +\frac{(b^2-2ac)x+bc}{a(4ac-b^2)(ax^2+bx+c)}+ +\frac{2c}{4ac-b^2}\int{\frac{1}{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 57 +aa:=integrate(x^2/(a*x^2+b*x+c)^2,x) +--R +--R +--R (1) +--R [ +--R 2 2 2 +--R (2a c x + 2a b c x + 2a c ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R ((- 2a c + b )x + b c)\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - a b )x + (4a b c - a b )x + 4a c - a b c)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 2 2 (2a x + b)\|4a c - b +--R (4a c x + 4a b c x + 4a c )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R ((- 2a c + b )x + b c)\|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - a b )x + (4a b c - a b )x + 4a c - a b c)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 58 +t1:=integrate(1/(a*x^2+b*x+c),x) +--R +--R +--R (2) +--R [ +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R 2atan(----------------------) +--R 2 +--R 4a c - b +--R -----------------------------] +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Union(List Expression Integer,...) +--E + +--S 59 +bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1 +--R +--R (3) +--R 2 2 2 +--R (2a c x + 2a b c x + 2a c ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R ((- 2a c + b )x + b c)\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - a b )x + (4a b c - a b )x + 4a c - a b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 60 +bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2 +--R +--R (4) +--R +---------+ +--R | 2 +--R 2 2 2 (2a x + b)\|4a c - b +--R (4a c x + 4a b c x + 4a c )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R ((- 2a c + b )x + b c)\|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - a b )x + (4a b c - a b )x + 4a c - a b c)\|4a c - b +--R Type: Expression Integer +--E + +--S 61 14:274 Schaums and Axiom agree +cc1:=aa.1-bb1 +--R +--R (5) 0 +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.275~~~~~$\displaystyle +\int{\frac{x^m~dx}{(ax^2+bx+c)^n}}$} +$$ +\begin{array}{lr} +\displaystyle\int{\frac{x^m}{(ax^2+bx+c)^n}}= +&\displaystyle-\frac{x^{m-1}}{(2n-m-1)a(ax^2+bx+c)^{n-1}}\\ +&\\ +&\displaystyle+\frac{(m-1)c}{(2n-m-1)a}\int{\frac{x^{m-2}}{(ax^2+bx+2)^n}}\\ +&\\ +&\displaystyle-\frac{(n-m)b}{(2n-m-1)a}\int{\frac{x^{m-1}}{(ax^2+bx+c)^n}} +\end{array} +$$ +<<*>>= +)clear all + +--S 62 14:275 Axiom cannot compute this integral +aa:=integrate(x^m/(a*x^2+b*x+c)^n,x) +--R +--R +--R x m +--I ++ %N +--I (1) | ------------------ d%N +--R ++ 2 n +--I (c + %N b + %N a) +--R Type: Union(Expression Integer,...) +--E + +@ + +\section{\cite{1}:14.276~~~~~$\displaystyle +\int{\frac{x^{2n-1}~dx}{(ax^2+bx+c)^n}}$} +$$\begin{array}{lr} +\displaystyle\int{\frac{x^{2n-1}}{(ax^2+bx+c)^n}}= +&\displaystyle\frac{1}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^{n-1}}}\\ +&\\ +&\displaystyle-\frac{c}{a}\int{\frac{x^{2n-3}}{(ax^2+bx+c)^n}}\\ +&\\ +&\displaystyle-\frac{b}{a}\int{\frac{x^{2n-2}}{(ax^2+bx+c)^n}} +\end{array} +$$ +<<*>>= +)clear all + +--S 63 14:276 Axiom cannot compute this integral +aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x) +--R +--R +--R x 2n - 1 +--I ++ %N +--I (1) | ------------------ d%N +--R ++ 2 n +--I (c + %N b + %N a) +--R Type: Union(Expression Integer,...) +--E + +@ + +\section{\cite{1}:14.277~~~~~$\displaystyle +\int{\frac{dx}{x(ax^2+bx+c)^2}}$} +$$\begin{array}{lr} +\displaystyle\int{\frac{1}{x(ax^2+bx+c)^2}}= +&\displaystyle\frac{1}{2c(ax^2+bx+2)}\\ +&\\ +&\displaystyle-\frac{b}{2c}\int{\frac{1}{(ax^2+bx+c)^2}}\\ +&\\ +&\displaystyle+\frac{1}{c}\int{\frac{1}{x(ax^2+bx+c)}} +\end{array} +$$ +<<*>>= +)clear all + +--S 64 +aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x) +--R +--R +--R (1) +--R [ +--R 2 3 2 2 4 2 3 +--R ((6a b c - a b )x + (6a b c - b )x + 6a b c - b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) +--R + +--R 2 2 +--R - 2a b c x + 4a c - 2b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|- 4a c + b +--R , +--R +--R 2 3 2 2 4 2 3 +--R ((- 12a b c + 2a b )x + (- 12a b c + 2b )x - 12a b c + 2b c) +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) +--R + +--R 2 2 +--R - 2a b c x + 4a c - 2b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 65 +t1:=integrate(1/(a*x^2+b*x+c)^2,x) +--R +--R +--R (2) +--R [ +--R 2 2 +--R (2a x + 2a b x + 2a c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (2a x + b)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R , +--R +---------+ +--R | 2 +---------+ +--R 2 2 (2a x + b)\|4a c - b | 2 +--R (4a x + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b +--R 2 +--R 4a c - b +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 66 +t2:=integrate(1/(x*(a*x^2+b*x+c)),x) +--R +--R +--R (3) +--R [ +--R b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 | 2 +--R (- log(a x + b x + c) + 2log(x))\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R - 2b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- log(a x + b x + c) + 2log(x))\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 67 +bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1 +--R +--R +--R (4) +--R 2 2 2 2 +--R (- 2a b c x - 2a b c x - 2a b c ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 3 2 2 4 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + 4a b c - b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) - 2a b c x +--R + +--R 2 2 +--R 4a c - 2b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|- 4a c + b +--R Type: Expression Integer +--E + +--S 68 +bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1 +--R +--R +--R (5) +--R +---------+ +--R 2 3 2 2 4 2 3 | 2 +--R ((4a b c - a b )x + (4a b c - b )x + 4a b c - b c)\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R (- 4a b c x - 4a b c x - 4a b c )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) - 2a b c x +--R + +--R 2 2 +--R 4a c - 2b c +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 69 +bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2 +--R +--R +--R (6) +--R +---------+ +--R 2 2 2 2 | 2 +--R (- 2a b c x - 2a b c x - 2a b c )\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 3 2 2 4 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x - 8a b c + 2b c) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) - 2a b c x +--R + +--R 2 2 +--R 4a c - 2b c +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 70 +bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2 +--R +--R +--R (7) +--R 2 3 2 2 4 2 3 +--R ((- 12a b c + 2a b )x + (- 12a b c + 2b )x - 12a b c + 2b c) +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) - 2a b c x +--R + +--R 2 2 +--R 4a c - 2b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|4a c - b +--R Type: Expression Integer +--E + +--S 71 +cc1:=aa.1-bb1 +--R +--R (8) +--R a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 72 +dd1:=expandLog cc1 +--R +--R (9) +--R a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R + +--R a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R + +--R 2 +--R - 2a b log(a x + b x + c) +--R / +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 73 14:277 Schaums and Axiom differ by a constant +ee1:=complexNormalize dd1 +--R +--R 3 2 2 +--R a b log(- 16a c + 4a b ) +--R (10) --------------------------- +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.278~~~~~$\displaystyle +\int{\frac{dx}{x^2(ax^2+bx+c)^2}}$} +$$\begin{array}{lr} +\displaystyle\int{\frac{1}{x^2(ax^2+bx+c)^2}}= +&\displaystyle-\frac{1}{cx(ax^2+bx+c)}\\ +&\\ +&\displaystyle-\frac{3a}{c}\int{\frac{1}{(ax^2+bx+c)^2}}\\ +&\\ +&\displaystyle-\frac{2b}{c}\int{\frac{1}{x(ax^2+bx+c)^2}} +\end{array} +$$ +<<*>>= +)clear all + +--S 74 +aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x) +--R +--R +--R (1) +--R [ +--R 3 2 2 2 4 3 2 2 3 5 2 +--R (6a c - 6a b c + a b )x + (6a b c - 6a b c + b )x +--R + +--R 2 3 2 2 4 +--R (6a c - 6a b c + b c)x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|- 4a c + b +--R , +--R +--R 3 2 2 2 4 3 2 2 3 5 2 +--R (- 12a c + 12a b c - 2a b )x + (- 12a b c + 12a b c - 2b )x +--R + +--R 2 3 2 2 4 +--R (- 12a c + 12a b c - 2b c)x +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 75 +t1:=integrate(1/(a*x^2+b*x+c)^2,x) +--R +--R +--R (2) +--R [ +--R 2 2 +--R (2a x + 2a b x + 2a c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R | 2 +--R (2a x + b)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|- 4a c + b +--R , +--R +---------+ +--R | 2 +---------+ +--R 2 2 (2a x + b)\|4a c - b | 2 +--R (4a x + 4a b x + 4a c)atan(----------------------) + (2a x + b)\|4a c - b +--R 2 +--R 4a c - b +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 2 2 3 2 2 | 2 +--R ((4a c - a b )x + (4a b c - b )x + 4a c - b c)\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 76 +t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 4 2 3 +--R ((6a b c - a b )x + (6a b c - b )x + 6a b c - b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) +--R + +--R 2 2 +--R - 2a b c x + 4a c - 2b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|- 4a c + b +--R , +--R +--R 2 3 2 2 4 2 3 +--R ((- 12a b c + 2a b )x + (- 12a b c + 2b )x - 12a b c + 2b c) +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 +--R ((- 4a c + a b )x + (- 4a b c + b )x - 4a c + b c) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 2 2 3 2 2 +--R ((8a c - 2a b )x + (8a b c - 2b )x + 8a c - 2b c)log(x) +--R + +--R 2 2 +--R - 2a b c x + 4a c - 2b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 3 2 2 2 3 3 2 4 2 3 | 2 +--R ((8a c - 2a b c )x + (8a b c - 2b c )x + 8a c - 2b c )\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 77 +bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1 +--R +--R +--R (4) +--R 3 2 3 2 2 2 2 3 +--R (- 6a c x - 6a b c x - 6a c x) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 2 4 3 3 5 2 2 2 4 +--R ((- 6a b c + a b )x + (- 6a b c + b )x + (- 6a b c + b c)x) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 78 +bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1 +--R +--R +--R (5) +--R 2 2 4 3 3 5 2 2 2 4 +--R ((- 6a b c + a b )x + (- 6a b c + b )x + (- 6a b c + b c)x) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R + +--R +-----------+ +--R 3 2 3 2 2 2 2 3 | 2 +--R (- 12a c x - 12a b c x - 12a c x)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 79 +bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2 +--R +--R +--R (6) +--R +---------+ +--R 3 2 3 2 2 2 2 3 | 2 +--R (- 6a c x - 6a b c x - 6a c x)\|4a c - b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 2 4 3 3 5 2 2 2 4 +--R ((12a b c - 2a b )x + (12a b c - 2b )x + (12a b c - 2b c)x) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2a x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R / +--R +-----------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression Integer +--E + +--S 80 +bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2 +--R +--R +--R (7) +--R 3 2 2 2 4 3 2 2 3 5 2 +--R (- 12a c + 12a b c - 2a b )x + (- 12a b c + 12a b c - 2b )x +--R + +--R 2 3 2 2 4 +--R (- 12a c + 12a b c - 2b c)x +--R * +--R +---------+ +--R | 2 +--R (2a x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - a b )x + (4a b c - b )x + (4a b c - b c)x) +--R * +--R 2 +--R log(a x + b x + c) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2a b )x + (- 8a b c + 2b )x + (- 8a b c + 2b c)x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2b c)x - 4a c + b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 4 2 3 3 4 3 3 2 5 2 4 | 2 +--R ((4a c - a b c )x + (4a b c - b c )x + (4a c - b c )x)\|4a c - b +--R Type: Expression Integer +--E + +--S 81 +cc1:=aa.1-bb1 +--R +--R (8) +--R 2 +--R 6a +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R + +--R 2 +--R 6a +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 82 +dd1:=expandLog cc1 +--R +--R (9) +--R 2 +--R 6a +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R + +--R 2 +--R 6a +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (- 8a c + 2a b )x +--R + +--R 3 +--R - 4a b c + b +--R + +--R 2 2 +--R - 12a log(a x + b x + c) +--R / +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E + +--S 83 14:278 Schaums and Axiom differ by a constant +ee1:=complexNormalize dd1 +--R +--R 2 3 2 2 +--R 6a log(- 16a c + 4a b ) +--R (10) --------------------------- +--R +-----------+ +--R 2 2 | 2 +--R (4a c - b c)\|- 4a c + b +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.279~~~~~$\displaystyle +\int{\frac{dx}{x^m(ax^2+bx+c)^n}}$} +$$\begin{array}{lr} +\displaystyle\int{\frac{1}{x^m(ax^2+bx+c)^n}}= +&\displaystyle-\frac{1}{(m-1)cx^{m-1}(ax^2+bx+c)^{n-1}}\\ +&\\ +&\displaystyle-\frac{(m+2n-3)a}{(m-1)c}\int{\frac{1}{x^{m-2}(ax^2+bx+c)^n}}\\ +&\\ +&\displaystyle-\frac{(m+n-2)b}{(m-1)c}\int{\frac{1}{x^{m-1}(ax^2+bx+c)^n}} +\end{array} +$$ +<<*>>= +)clear all + +--S 84 14:279 Axiom cannot compute this integral +aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x) +--R +--R +--R x +--R ++ 1 +--I (1) | --------------------- d%N +--R ++ m 2 n +--I %N (c + %N b + %N a) +--R Type: Union(Expression Integer,...) +--E + +)spool +)lisp (bye) +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} Spiegel, Murray R. +{\sl Mathematical Handbook of Formulas and Tables}\\ +Schaum's Outline Series McGraw-Hill 1968 p71 +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/schaum12.input.pdf b/src/axiom-website/CATS/schaum12.input.pdf new file mode 100644 index 0000000..b24e1d4 --- /dev/null +++ b/src/axiom-website/CATS/schaum12.input.pdf @@ -0,0 +1,3958 @@ +%PDF-1.2 +7 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +10 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F1 +/FontDescriptor 9 0 R +/BaseFont/XGVGVP+CMR17 +/FirstChar 33 +/LastChar 196 +/Widths[249.6 458.6 772.1 458.6 772.1 719.8 249.6 354.1 354.1 458.6 719.8 249.6 301.9 +249.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 249.6 249.6 +249.6 719.8 432.5 432.5 719.8 693.3 654.3 667.6 706.6 628.2 602.1 726.3 693.3 327.6 +471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 +693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 +458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 +510.9 484.7 667.6 484.7 484.7 406.4 458.6 917.2 458.6 458.6 458.6 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 576 772.1 719.8 641.1 615.3 693.3 +667.6 719.8 667.6 719.8 0 0 667.6 525.4 499.3 499.3 748.9 748.9 249.6 275.8 458.6 +458.6 458.6 458.6 458.6 693.3 406.4 458.6 667.6 719.8 458.6 837.2 941.7 719.8 249.6 +458.6] +>> +endobj +13 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F2 +/FontDescriptor 12 0 R +/BaseFont/EEFPIB+CMR12 +/FirstChar 33 +/LastChar 196 +/Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 +462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 +734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 +272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 +544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 +489.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 611.8 816 +761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 +299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 +761.6 272 489.6] +>> +endobj +16 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F3 +/FontDescriptor 15 0 R +/BaseFont/TAMYWG+CMR10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +18 0 obj +<< +/Filter[/FlateDecode] +/Length 180 +>> +stream +x%=@ wE#r1j&o3Ĩ^86> +endobj +6 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 20 0 R +>> +endobj +25 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F4 +/FontDescriptor 24 0 R +/BaseFont/IJTCAF+CMBX12 +/FirstChar 33 +/LastChar 196 +/Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 +562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 +875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 +675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 +687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 +343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 +593.7 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 +656.2 625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 +812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] +>> +endobj +28 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F5 +/FontDescriptor 27 0 R +/BaseFont/EBENTK+CMBX10 +/FirstChar 33 +/LastChar 196 +/Widths[350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 +575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 +869.4 818.1 830.6 881.9 755.6 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 +863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 +319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 +319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 +511.1 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 691.7 958.3 894.4 805.6 766.7 900 830.6 894.4 830.6 894.4 0 0 830.6 670.8 +638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 +575 1041.7 1169.4 894.4 319.4 575] +>> +endobj +31 0 obj +<< +/Type/Font +/Subtype/Type1 +/Name/F6 +/FontDescriptor 30 0 R +/BaseFont/CSSXYP+CMEX10 +/FirstChar 33 +/LastChar 196 +/Widths[791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 +1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 +888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 +1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 +833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 +1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 +1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 458.3 458.3 416.7 416.7 +472.2 472.2 472.2 472.2 583.3 583.3 0 0 472.2 472.2 333.3 555.6 577.8 577.8 597.2 +597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 +791.7 777.8] +>> +endobj +32 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/omega/epsilon/theta1/pi1/rho1/sigma1/phi1/arrowlefttophalf/arrowleftbothalf/arrowrighttophalf/arrowrightbothalf/arrowhookleft/arrowhookright/triangleright/triangleleft/zerooldstyle/oneoldstyle/twooldstyle/threeoldstyle/fouroldstyle/fiveoldstyle/sixoldstyle/sevenoldstyle/eightoldstyle/nineoldstyle/period/comma/less/slash/greater/star/partialdiff/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/flat/natural/sharp/slurbelow/slurabove/lscript/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/dotlessi/dotlessj/weierstrass/vector/tie/psi +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/alpha/beta/gamma/delta/epsilon1/zeta/eta/theta/iota/kappa/lambda/mu/nu/xi/pi/rho/sigma/tau/upsilon/phi/chi/psi/tie] +>> +endobj +35 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F7 +/FontDescriptor 34 0 R +/BaseFont/PFTUWD+CMMI10 +/FirstChar 33 +/LastChar 196 +/Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 +750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 +762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 +388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 +298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 +465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 +639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 +570 517 571.4 437.2 540.3 595.8 625.7 651.4 277.8] +>> +endobj +38 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F8 +/FontDescriptor 37 0 R +/BaseFont/XQGLQC+CMR7 +/FirstChar 33 +/LastChar 196 +/Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 +323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 +323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 +874 706.4 1027.8 843.3 877 767.9 877 829.4 631 815.5 843.3 843.3 1150.8 843.3 843.3 +692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 +323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 +600.2 600.2 507.9 569.4 1138.9 569.4 569.4 569.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 +877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 +843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] +>> +endobj +41 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F9 +/FontDescriptor 40 0 R +/BaseFont/TAMMEO+CMMI7 +/FirstChar 33 +/LastChar 196 +/Widths[719.7 539.7 689.9 950 592.7 439.2 751.4 1138.9 1138.9 1138.9 1138.9 339.3 +339.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 585.3 339.3 +339.3 892.9 585.3 892.9 585.3 610.1 859.1 863.2 819.4 934.1 838.7 724.5 889.4 935.6 +506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 +1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 +594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 +530.4 539.2 431.6 675.4 571.4 826.4 647.8 579.4 545.8 398.6 442 730.1 585.3 339.3 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 693.8 954.4 868.9 +797.6 844.5 935.6 886.3 677.6 769.8 716.9 0 0 880 742.7 647.8 600.1 519.2 476.1 519.8 +588.6 544.1 422.8 668.8 677.6 694.6 572.8 519.8 668 592.7 662 526.8 632.9 686.9 713.8 +756 339.3] +>> +endobj +42 0 obj +<< +/Type/Encoding +/Differences[0/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/arrowright/arrowup/arrowdown/arrowboth/arrownortheast/arrowsoutheast/similarequal/arrowdblleft/arrowdblright/arrowdblup/arrowdbldown/arrowdblboth/arrownorthwest/arrowsouthwest/proportional/prime/infinity/element/owner/triangle/triangleinv/negationslash/mapsto/universal/existential/logicalnot/emptyset/Rfractur/Ifractur/latticetop/perpendicular/aleph/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/union/intersection/unionmulti/logicaland/logicalor/turnstileleft/turnstileright/floorleft/floorright/ceilingleft/ceilingright/braceleft/braceright/angbracketleft/angbracketright/bar/bardbl/arrowbothv/arrowdblbothv/backslash/wreathproduct/radical/coproduct/nabla/integral/unionsq/intersectionsq/subsetsqequal/supersetsqequal/section/dagger/daggerdbl/paragraph/club/diamond/heart/spade/arrowleft +161/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus +173/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/spade] +>> +endobj +45 0 obj +<< +/Encoding 42 0 R +/Type/Font +/Subtype/Type1 +/Name/F10 +/FontDescriptor 44 0 R +/BaseFont/RJRYYM+CMSY7 +/FirstChar 33 +/LastChar 196 +/Widths[1138.9 585.3 585.3 1138.9 1138.9 1138.9 892.9 1138.9 1138.9 708.3 708.3 1138.9 +1138.9 1138.9 892.9 329.4 1138.9 769.8 769.8 1015.9 1015.9 0 0 646.8 646.8 769.8 +585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.6 +646.5 782.1 871.7 791.7 1342.7 935.6 905.8 809.2 935.9 981 702.2 647.8 717.8 719.9 +1135.1 818.9 764.4 823.1 769.8 769.8 769.8 769.8 769.8 708.3 708.3 523.8 523.8 523.8 +523.8 585.3 585.3 462.3 462.3 339.3 585.3 585.3 708.3 585.3 339.3 938.5 859.1 954.4 +493.6 769.8 769.8 892.9 892.9 523.8 523.8 523.8 708.3 892.9 892.9 892.9 892.9 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 892.9 339.3 892.9 585.3 +892.9 585.3 892.9 892.9 892.9 892.9 0 0 892.9 892.9 892.9 1138.9 585.3 585.3 892.9 +892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 1138.9 892.9 +892.9 1138.9 892.9] +>> +endobj +46 0 obj +<< +/Filter[/FlateDecode] +/Length 999 +>> +stream +xK5 | +wŒ%?8U\!d؏lӳ.{~R`͔7+6؜~5!9zʏWo͟7o_ 5GbXHn^/tFRGitD@2@|y: L|O]612`n ߙ<ӠĀL:h1Tݴ_f?oYx׾KouDxte+?: M wkpV#pڜˀ؜!6wTl q7QF]VBnɪ6_a +*(#,W ;@+)Rm>"V'-iՆ4VђVMˀiRSkD-É9CG@-<3BgSkGaCCPs{q6\a/8K9^,)OeQ e|e]e娆*)R0`ݘiq=ԗ?q+erˮ/dž2t؂ʎ, +EiSuyE펗^sVy)횧_I- 7V N\kt +l.i*3YOV<\D-YZo<6\PD"Sc/t#6ݱ[d9Rw>q$X3pس$֝% E+otUA"H-1]%pS4Z۩=Sv9`p!|O:N.4eDeQ Mq !Uy]|vj,X4Ḧ.pjhkKEGHfH@abtEKE.VZF#mku?}VUtwy#z}4[}7&F] +endstream +endobj +47 0 obj +<< +/F4 25 0 R +/F5 28 0 R +/F6 31 0 R +/F7 35 0 R +/F8 38 0 R +/F3 16 0 R +/F9 41 0 R +/F10 45 0 R +>> +endobj +22 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 47 0 R +>> +endobj +52 0 obj +<< +/Encoding 32 0 R +/Type/Font +/Subtype/Type1 +/Name/F11 +/FontDescriptor 51 0 R +/BaseFont/IAEDAF+CMMI12 +/FirstChar 33 +/LastChar 196 +/Widths[609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 +489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 +761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.9 772.4 811.3 431.9 541.2 833 666.2 +947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 +380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 +334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 +699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 +652.8 598 0 0 757.6 622.8 552.8 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 +589.1 483.8 427.7 555.4 505 556.5 425.2 527.8 579.5 613.4 636.6 272] +>> +endobj +55 0 obj +<< +/Encoding 42 0 R +/Type/Font +/Subtype/Type1 +/Name/F12 +/FontDescriptor 54 0 R +/BaseFont/SPMOLI+CMSY10 +/FirstChar 33 +/LastChar 196 +/Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 +275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 +611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 +820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 +666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 +500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 +444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 +777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 +777.8 777.8 1000 1000 777.8 777.8 1000 777.8] +>> +endobj +56 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/suppress +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/dieresis] +>> +endobj +59 0 obj +<< +/Encoding 56 0 R +/Type/Font +/Subtype/Type1 +/Name/F13 +/FontDescriptor 58 0 R +/BaseFont/RKAXVR+CMTI10 +/FirstChar 33 +/LastChar 196 +/Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 +306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 +306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 +525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 +743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 +460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 +460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 +766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 +511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] +>> +endobj +60 0 obj +<< +/Type/Encoding +/Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/dieresis/visiblespace +160/space/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 173/Omega/arrowup/arrowdown/quotesingle/exclamdown/questiondown/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/visiblespace/dieresis] +>> +endobj +63 0 obj +<< +/Encoding 60 0 R +/Type/Font +/Subtype/Type1 +/Name/F14 +/FontDescriptor 62 0 R +/BaseFont/CQTQCY+CMTT10 +/FirstChar 33 +/LastChar 196 +/Widths[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 525 525 525 525 525 525 525 525 525 0 0 525 +525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 +525 525] +>> +endobj +64 0 obj +<< +/Filter[/FlateDecode] +/Length 1193 +>> +stream +xXn#7+[rSܚ!8HSFZ1 K-# +Oqm3.&^)! A=~A?-Q@;$)Vâ@˟o2:)eEvCobvmq-FZJ܆/oAiVp,)6AC5 +r1BE|ߢ6 3T'oK$00?$Ki+|WWA- #x)C~J+g!fn(DžHb!UT*0sV-~7$6K Z֠XjƛEܳ) SM٨1p#=*RE@!nW0caIGkpK+`bA< +Ɩ X:įyd*1@ `=}҄ݳ' +QA1adN/Dh1jBP vvXQ]vo֐>hc’4LB_8RԕWCqHҮL= +05m8EG~`v(C3NX {m[UpխV22yGN G{B#>%'|2q'W^RD_Z~NG$=ޥr6X +j{BrW{0w[rҢdVt*hȚRX㓤łk6(c-EA3{'uwk) _b)axUGޝ\sѴk0#.Wx-35G!S"rFY>]b +&0wI58(EJK>R9vfo aF@26WrC<:ޟOp<ն%اZ wU2i +endstream +endobj +65 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F12 55 0 R +/F10 45 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +49 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 65 0 R +>> +endobj +68 0 obj +<< +/Filter[/FlateDecode] +/Length 453 +>> +stream +xڵUN0>fѸ޲R/r %QP[ԏǵD}qlyc# Asd[tfT eWQQ!Q'`>' `rх;QgOh*GxC”t031ʭxnMH!K-|;e-&C* Dqp~lD< R{QRݔi]Tj@blyk$_q2|%dL8[tZrawm1/M?"o"Oh300ZZ|_+R@t7PD/ ]2 Y]N}`S.,&}>~\탂>MAKG[!M' ؕ,rPP:> +endobj +67 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 69 0 R +>> +endobj +72 0 obj +<< +/Filter[/FlateDecode] +/Length 517 +>> +stream +xV=o0+8JHb.E[mQp$\?QEeF$N=QB)Z!XIdըzD֜oƿrlQϱ0*?ͶpNNr"`tuoӇ)qʉ!Sf24QuIdb_2XdE;Oe\TX W=v5/^O1Ǡw$zivۑ6.Y 8 +x*'v3}w`to:jbAwic~je:nJW7oX,W˷|w?ԩbo4 am&C=zeʑ^I(ͅ IZ݊5P;+ Ok)MZsU4W}L&Tg#CCA.d7&r| EIj4T I_*pv'ϘDh's%8zuW7h} +endstream +endobj +73 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +71 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 73 0 R +>> +endobj +76 0 obj +<< +/Filter[/FlateDecode] +/Length 510 +>> +stream +xڽAO0 |[U$M$. Gr1=i JۑHg8'[Kr^..@ˬ&1 39)%ޤTBΓwޗׄ +lHh'UN]jms6PIis oOϛ;jnCw_kyzVL +c cFە!.%.Y,D1 1U)<@H[l3~wUBJl"q.0c6LCF(CnKd K@_fd~aLh  IX:E#R˝V532Ukמl+a**a>cEךXQQyˠ! mWh*;cȏBi1q5~K]M'd:BPSiedLc_GoBX.~_5eRZVB +endstream +endobj +77 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +75 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 77 0 R +>> +endobj +80 0 obj +<< +/Filter[/FlateDecode] +/Length 539 +>> +stream +xڽV]o0}߯ R(soHlӦ=-}H"1@iLꏟc'4!qVꌄ}ls  g!n1*T$?ġJJ|@} +9AG>YAZ +bf@%MƋQ{h3תsZ@P<^ZXa*/U7٥[z +0Qa[ɻJ} +endstream +endobj +81 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +79 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 81 0 R +>> +endobj +84 0 obj +<< +/Filter[/FlateDecode] +/Length 401 +>> +stream +xڭTO0Wbeii[I<~?Xt˶ $ rMGyIa3_9oʊRNYпڡ2ϳom+ڵinnBRODWzqB@֢)#fP)?4 +endstream +endobj +85 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +83 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 85 0 R +>> +endobj +88 0 obj +<< +/Filter[/FlateDecode] +/Length 963 +>> +stream +xڽWMo6W,R0KhSrv:m*!)J.Z37oސZ(c׏$\R!QTMs~{VvE,ʹp. +. ǰBQ+H% &ݦ.)yE4MTP_q|$`d.(FL5Hc~F@*2!˻nFd׸7P6L61S=cS⬦#U\3*q*Z!-&\h5&jRQ@rԿ<%͔UPи j'SJ,fDCF).gW҄,+'lk &6 "azanZFERp guI *l[c|ޚ I0CL ǡ]N5zW}fW%D:偰ϽQ5Q+ Gr]ed.s){쏇qSx%ǣ/ ЫcXFﶽ~s|{lM]5E{+ ڟzUկ&;)x+dk̢9㗻 ,JˢƧ 陴6YK <,DÔ}~z7 jrbl79COu?lbXj=ClLBF2VJ[L <3̻uūV2x5H3q815Q%*yUd}?.DzGzNyԌNh\5T> +endobj +87 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 89 0 R +>> +endobj +92 0 obj +<< +/Filter[/FlateDecode] +/Length 527 +>> +stream +xڕUKo0 W(Ǒ"ʒzvڼSvH|ɔp"9/H"BA|.HI<R3M/eT~'0bBrmh~iնjCaah5ȸu杉w1\'O:P +$ƗU,X^X +(܏tzѯ@+lXg{0~PGk/nQWc"_|ƼLn&ȌL5"AP5.BasL\?c@݀Bԥvł#܄,NX~/Ĩae#YFeVC !ŧ,fSTqHK,aBY2o͝sYZNwS,mY[{zsO u 觃U&v|1(X}4I@Q}g6^&UgX<$ǡ :yf-xNmY~ +endstream +endobj +93 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +91 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 93 0 R +>> +endobj +96 0 obj +<< +/Filter[/FlateDecode] +/Length 550 +>> +stream +xVK0+|Cv3~ƕ"8Bn*v{R<~dӤvk{f<7F) +EnxV{H-Q) +(w_?@")T +an3>wGѴ6FuB}~vk?#S2Coc 0rj)ظ]I]&jgs$A,ڱ> +endobj +95 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 97 0 R +>> +endobj +100 0 obj +<< +/Filter[/FlateDecode] +/Length 441 +>> +stream +xV=O0"v\"!aHP!jO4%uTH"ž9`BXsnє +`Q }bMR k һS4k@bsRydmwZj>"O4_7M+h:_6ŮHu63xE2*DeFS۠RDק$y> +endobj +99 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 101 0 R +>> +endobj +104 0 obj +<< +/Filter[/FlateDecode] +/Length 504 +>> +stream +xV;O0*#~TbQ 3$!$hQ R81ws@̀I>>#h$X2 D*A)1JbZÏqju4/A +!XnF#@Z8\i$|. n;l<$6ⵘzI"(G3%[=M,ȁ]*[[;7MX,~*}uTxeYV___YjRu]]D}WUlrT$DY2(Ȥܧ짫 O,Cg>-fcVƠRΜ~1>O +endstream +endobj +105 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +103 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 105 0 R +>> +endobj +108 0 obj +<< +/Filter[/FlateDecode] +/Length 150 +>> +stream +xu@D{bˣe`K#-uby$`bV32 01Cl`FJrO:K^!qP/DQ5͞ )Zli}H ժoØ|y_S_u<B-)eC2 +endstream +endobj +109 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +107 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 109 0 R +>> +endobj +112 0 obj +<< +/Filter[/FlateDecode] +/Length 990 +>> +stream +xڽWK6W(BR)cSV M'I=1ćZ7|3 gG/_OǷŤ"jBbBoq,+SArћI!Iht 2 8`2HjHeXu?T$&ʆ?56/QE:[cb^)q6>!jxiSM֦tA%7Lw R e+zU*{$ADux6v56#k)}޶|}zh#k}Ksx(놛ThT>75sm m.4]R> +endobj +111 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 113 0 R +>> +endobj +116 0 obj +<< +/Filter[/FlateDecode] +/Length 565 +>> +stream +xڭVM0Wh 6VKlժ-= "6TeW *w0$|dU_g=cϛP@mϩJh"Q!"9UJ`BX##IO<@J&=P֘8$~m5Κ>) +7@T +7yv>vii8o}2R +.; ;l(UJP,J.pxhN߽5;`Y۾,aA)'8uy&l_dCV3VknAմ;E%Gn`yD/I yKߓ4h#~%/T`1yg0P8CMF@14gjǓrߖp pmya2Ж*6qcl1Sqg:SA2RW:f8o|<+3(jdrت a!s|/xcb`ک?EcSb'&sh:w5s O| \X%OE +> +endobj +115 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 117 0 R +>> +endobj +120 0 obj +<< +/Filter[/FlateDecode] +/Length 529 +>> +stream +xڽV=o0+8M1@Nю05 +NxPP$HKDĻ{=VU(@Bb)$} 1.ԕMNNC#)8LLA$*Krx~RP2ٗŔr/&eB*#+fTo7\0io> +endobj +119 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 121 0 R +>> +endobj +124 0 obj +<< +/Filter[/FlateDecode] +/Length 526 +>> +stream +xVK0+|LƎq% 64-ڤjEql'ae& Fq @wM6H$9V@`$0 @.SH }=!#,XtC}+ V}v4 O*y%G%oѩ Q./TK7k/@;U5Muh}ǂrp:SIes…Y_wG3)6 J2-f6Sќk\jwm}lbV[ +Ӿ&mx='K-y4B1wbihxdgGPKN5E;"k +endstream +endobj +125 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +123 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 125 0 R +>> +endobj +128 0 obj +<< +/Filter[/FlateDecode] +/Length 913 +>> +stream +xVK:_͕ 9Gbb@ (HRR+͏8v7 tc<ʒ}a=]?9p-?3pVh(^/ +ʪLW ڗ~X +ȸD1tEPe~>u$X媺/NƓUX\8AcQfoA񲹹]mMu4%8-{ႴP`sn@ +" n.&>,S{dQS]. $θԓe;FHweofz51?GLz[A}$O +dYf"WWC)pPpX +A*4XLvL3^AatuS{Z)c;Ɓǃcz[4$N0 yM11נ-Ezg0nO᜴\ -mДВFΡFJdy(MBɇh@b>(eMU.xlR>AAHPeVLi\[*Jky4 :zM@Ψ4: C KnoinE7:ѶluM%a~ T_Wh:W%h Њѩ%13:oH+ҩ0.o,B?EhkTSlA? J jT i2ŶzT-Vu}UvϥH!jg6\^x>i6׻׻ou8|܅Ƴz;fu}8J*k>Ϋ>k>b~uj z:=T8t(hvS/0'*(f"-YxO~^[uAܦDHNZʥu5Ǵ4c}mh]4 +endstream +endobj +129 0 obj +<< +/F14 63 0 R +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F7 35 0 R +/F3 16 0 R +/F2 13 0 R +/F9 41 0 R +/F8 38 0 R +/F10 45 0 R +/F12 55 0 R +/F13 59 0 R +>> +endobj +127 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 129 0 R +>> +endobj +132 0 obj +<< +/Filter[/FlateDecode] +/Length 958 +>> +stream +xWn9+xlC A9&:ŝZ'|K7 -{Atika{H QB)Cq_K$F6HnÌqܰokz}cHS%z0*AAX]z2$p%VP5399YN i,5uiO"7PHkhH:?|eฮb2/DV1-I:@CF, hbyp` +<ތ:B"26,"ov &r vɃ'֖<̚hdosAA2')،<#Y ؈ /XMZt 3~0g /_*W=v_%(&Hh:rҿy{p5l5UWß=^ uC:$i3Ɵ^.3`Tf]c0*c%RrJ# ybRٴ8Z}zҹE1~-MteJ6'kx )Mҧɪlxv +|uQiٍin7TҦs+]#bQqڂq_ӰzSeqLZa)DdMUtoJ@݋ZI1 ~/K(4<x8?J5__> +endobj +131 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 133 0 R +>> +endobj +136 0 obj +<< +/Filter[/FlateDecode] +/Length 546 +>> +stream +xڵV +8$ؘzZuOKV#7TeW;Y 1f&Q /D忐TqDRAUϏH%l0H;7~]GgDpjϼO5ο!Tw^" !혏«8Ut{0u(RHy)5SXN ܕ8`u +ELu#9{wqS%DrV?y1E='ELyǀ"!DNqδuB S_;6|P1(Ûyߊ'm' drQΦW58$Ձ1)Ɓ8'[WABy2T+Ga.p)Hk- Px8&az=[#z{ouj5 pI9$Kw`!cc=i;6fQ6OF( +=oO_gS/')`4˜W +endstream +endobj +137 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +135 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 137 0 R +>> +endobj +140 0 obj +<< +/Filter[/FlateDecode] +/Length 545 +>> +stream +xڭVMo0 WhǐOK*˰t؎oAҢGnb'fl,IQ#S&R!ؖ>{iXHCGd$Je燈KKlTD '"qF1;yKUV%%TZ[x n?XHDs¡6^݅Iji͉V$=Wšs4#;5Q{}i䯯` Z4:HcWGm5QWfY0s qMoPf+xRY bxjeR86Gu+۫r_Yrb OTrZNZ#Ȳp?L3M7J3-gF\;-?i; bVp +endstream +endobj +141 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +139 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 141 0 R +>> +endobj +144 0 obj +<< +/Filter[/FlateDecode] +/Length 499 +>> +stream +xVn0 +~)ZtjU,Y5 +tP||K& isE"J(E['t,ϘD80bšPGC1^8o 0cE7F̔QU[vQS JnNi˼\1?u+>^F(9 |5TN哹 0sgzK.&R |4m+;X`:]H(BeiQxww _}I9Hߏzkoqr z&E\a0Z cd^JZ6FAEM.AxX\uڠQ=e&4(0ZS{I+ |H\Np˞ ɄCg?ո]r[#ıdDf"ø_6_/1˗噸05~)G _4R +endstream +endobj +145 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +143 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 145 0 R +>> +endobj +148 0 obj +<< +/Filter[/FlateDecode] +/Length 521 +>> +stream +xV;o0+8R1( СVue1`KJ_VJ:A#{>QB4-&28S(_ bQ<aBFI-qUEψ"Xe$`T x0 +%nfu2sDG&4xYfGЃ1Rp6^Œ\x Gceh-x$v-B@8ˆ"M0-p8|81L4"4rx8[2I]fLr#&9tE$/Y3+/d%d8"/^8uw^}R$ΘSY$q11*ʻM[ Vp{!u&v]ݗv)׫7gcc/Т S9g;_;W KO P \?:690T@\4 +endstream +endobj +149 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +147 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 149 0 R +>> +endobj +152 0 obj +<< +/Filter[/FlateDecode] +/Length 1055 +>> +stream +xWKo6W([+C_ hSǮOn +,TIɢtj`/4|7=ľ?r3f5;p_] uuޓb0Ͻ ! +)L +5yLi5}.#U^r+Ycw$=}2/NNrc>m.XCi2+c,cphJ9&[͕d= Up0}Z.v#~ԄU9QSh"Թs@݁\xb ІjÝq1Gz6I\hVGKi ŝ]5% 7.^/uNU͙ڌ<{R0cd+a4b*e1;X5h*#&^rO 4k`56PFraK!ƕ4+!F/wwqm 10W "}*& 3A!*2Vm88q*-tQvw:?v_v/| B4Qh &qҽKVph7onOkSkwM /kj*9ܯLFH6]&-iiw}!%_K}`h,Vu3R{ +#>E߇!% xx$~HSY}XpcR@m_G,9FvL6Ip(DURkbQv #㡄(X69 +N> +endobj +151 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 153 0 R +>> +endobj +156 0 obj +<< +/Filter[/FlateDecode] +/Length 585 +>> +stream +xڭVK0W#6+R5[iDDHUvp`mH<7 +IүoKu9YDC:~{a^`c`Ss} wʉx(X2_QG^T}8gŭJPn,Jp}kU5[^CV; +Ֆ3eT톙P|u{˻ρ:y[}ʯFE$SੲQP͉ @mSW̜X32Yd-3L6Z>=6^hxbwiM;N-5Yi] +t<9ǵ7[ALjzߨ[{56>iDl727^z6KU~}hصi+cK{BlNȏn -4rOٰV!Rz08|2̼k5%=#x?3TH+'!qd?| +endstream +endobj +157 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +155 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 157 0 R +>> +endobj +160 0 obj +<< +/Filter[/FlateDecode] +/Length 550 +>> +stream +xڥVM Wpa2+R5[ַHvV\)?({6"!h }Gʑ.DRPa ;g”"B$̤!"I ` +8NZ?"O0*Hn IIOO"!O{Lz?Fs Վlf&in yu-^&L*LXzipQuj,yoA;r hRysQUD;F&ͮٞiDPh ^zpE wݖ2T>e.ygm +endstream +endobj +161 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +159 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 161 0 R +>> +endobj +164 0 obj +<< +/Filter[/FlateDecode] +/Length 497 +>> +stream +xV=O0"]"!fhR!!@!Hxm66,swwb%X7\j4 hHbA.&e6kP1#'XSDܨ<#a2Rv>Lsxf=|~cRUw4oϯ[7\#Ho>|95prˇɸ#h3$iOO R<,# mlŴ +lbh6m2EzcY#+bdԠ$w DR;R{*hOhNո;5ҮB ì.x].yǒ?)yI>xAšgB0au\_npYEz b!-oG1l,nMbJf:͎kJF,]jjkj\j4K)io)IL/ +endstream +endobj +165 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +163 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 165 0 R +>> +endobj +168 0 obj +<< +/Filter[/FlateDecode] +/Length 546 +>> +stream +xVM0+|tڎcǕ8"ⰛCRTmhw0 CAi(b + i u>0@, +D βGdz,7]L"`f8owpX7ժڻO4 +%wf[$(K2{S.?7+eAܞ%'<8*U2E=LB}"rڳ lTpi, x% S6L,F0IIːpx2l#lF6wŷ`F4ٚn^.)hpS?J]EmKʞWwnB> +endobj +167 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 169 0 R +>> +endobj +172 0 obj +<< +/Filter[/FlateDecode] +/Length 994 +>> +stream +xWKo6WR@e uC4JyMXˆET?CQn\VJ8Gqq}a\A +( ,EVOόDPgbk'?>e"b)o +c #:_ x?wu~Ww_vK~b@*C. +Y<񊤄Šc!ZPқ0A1$UsFs!ưt Mi02QHqNQL&?(Sa"Fb@9I'Pf 2)\ueܭ1s@>gpp P:9ۅ^\Mʅ ЧJS,%ȀICUGflj8y6#18eV]4YoUzt dՁڟ#K%6dloԍ6_Nģorȥ+&F M'\绖IBnei*W' UJjjaS C`MMZOV" ζ7z. +endstream +endobj +173 0 obj +<< +/F14 63 0 R +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F7 35 0 R +/F2 13 0 R +/F3 16 0 R +/F9 41 0 R +/F8 38 0 R +/F12 55 0 R +/F10 45 0 R +/F13 59 0 R +>> +endobj +171 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 173 0 R +>> +endobj +176 0 obj +<< +/Filter[/FlateDecode] +/Length 1026 +>> +stream +xXˎ6+G!|(@6E]6(dw: @0@%EԃOE,>9ͤ=x}wBά0@aw?7~Ǖܫo +>|޲Nt6(Ž.JF Gэ& @7S[/e2( NG! 9A@CFZɸ}1 +@(L/xVVɷ-k-KϔpFxQQ]IJ:P̭ ԜO _%eh?=mO F xs@x_kRz s ~A(?GBFh@>C1} +z)KW:Oê -bCY8G640of/e 6 njT/U[ŠA]uXQ+BsШ E{1¹3E 4Yx)6ݷV؂\ a=4\fZtcQ >cT`QG$#5oV0S+crta& x.-tӀwu b cMj4BG90"L}޾7o'h7>SY3?yŗ\ghy(0x;m$#6bF&nCQ Hs-2uش<_m %cOjn@<#ںh˪! +lLɔN9b0ҙf TģM[SZI_U+dXO+18jU^hՃ]ht>%p^Q5]+A00?)$s>ms-KnNEևW] Ԁ3AEdI[Eip)C]V6愃%\Uf`A ^4|yYPz}[3PmM"^q ٮu",Hm8ƃ`;R񧹞VB +endstream +endobj +177 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F8 38 0 R +/F12 55 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +175 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 177 0 R +>> +endobj +180 0 obj +<< +/Filter[/FlateDecode] +/Length 583 +>> +stream +xڭVM0W!6 Klժ-=-Y)D4TeW *w,6Uxy s#zB>=D$c"/KP%XGO+m|ۚf)ƧcVڼ02n}J_g{:οN(z +kTw&PxV˱:Pj_uKXۢ^B :tڣ6qSWam͓E;7)I[1 FoPyBXI i h+eyR{A\#۽=X"㖞cÈ~bHf1dP`xa2r^ѱGҲHq}C Ba=+l `Wt^[qeKNi7L0xd8i;3y>ĀMFPBL]w27zS,XgچJm8Alb4'4Rc!@*z2nK'l(@[k˾] fgI.]}جGʭ3 j*{ySbif,M4٭ +endstream +endobj +181 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +179 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 181 0 R +>> +endobj +184 0 obj +<< +/Filter[/FlateDecode] +/Length 594 +>> +stream +xڽV]o0}߯ 'Ƒ2-Ǎz JISZyȤkB$=܏s FCksr,9*pDrAF;Lȏ(#4N~Csj{f!spJWAZk4 n)kÃfxY<`zYaQMںoHߨ2,%[j6b#!dHg̏F.se*hE9 Сpǫ>vzg<3&BxSe!\󒎏ܳX~!] XV4wva^&zJA'9V{8]_ha +bzy ojz;8l +I-o7Qu-7,jK=92(_-I}/\2s[EZ{{S}ܖHs"lRX0*4DzkfzlU?ᇌDUҽ%ն8LF/_뒉tC zF%[]zc 'K>*I]+E7Cy`W61-&9-ZZfQ~K! +endstream +endobj +185 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +183 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 185 0 R +>> +endobj +188 0 obj +<< +/Filter[/FlateDecode] +/Length 534 +>> +stream +xVMo0 Wh7cQvq1@m?v +3a()||ԋ([AZ(#b~ +tPx+ϷYǦ)@*Y}J7K}zS*mVgA2Fиg7n\( XNwƦɥ"e͜3WsA1)/A)k)\Ti$퓝HP~7NJq15,W #|kIG)tqL%!Rl\9C3-O%QDG}rq3uCi"#Ό'F^MΊ{s0%2q̧ĊˆXls!ؼ4:{XDk +eM,z`hm4f4NDB.k7|~?n{i|߿^6qtհcH3}m5BwgBi!S !xh_3t)+ Ɍ +3@,o$e]<7!6aU}lw +endstream +endobj +189 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +187 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 189 0 R +>> +endobj +192 0 obj +<< +/Filter[/FlateDecode] +/Length 397 +>> +stream +xڥO0=vYZ$4ѣ 7@_6Fb>NnW'q[۬R/bYn>[4ղ7Ukc0CElSb FS~QTY*ᔹ(.]$ +endstream +endobj +193 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +191 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 193 0 R +>> +endobj +196 0 obj +<< +/Filter[/FlateDecode] +/Length 1014 +>> +stream +xWM6W(B.9KѦ@OY%n8),PwH&AÛC,KμfD8'$^ o*"!F0 &:BćhV>}kg!,S20}U Eb>vTZ} +=fDx`59Cpi]LJnfSZ%}ͤ!jnj O:>۴i5އa<ee +3+ Xg%@!+[S"g>J>+Q66b0e~<^DTLcvnæa\%XO;czCfݿ臒gXU~]S9U]]rV0' `Q MپX-7~ՙúf2B5KbVvk0. P_)XD`BEDs LHFI7͋VTPH-T5J t5 oPxô_BQͲl_gZGOdL4Id$*b8=wfR"ϩkF9LJێj|m|zЍ7ߜðN~Thqy(0kx;NpyRɆq1z.x\0Oe**mo.m{ iӷ> +endobj +195 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 197 0 R +>> +endobj +200 0 obj +<< +/Filter[/FlateDecode] +/Length 601 +>> +stream +xڭVo 0`*2-6zJvEJ|I9`{/`BR4k @Q(@a%@ "!J j Y(~,W Qu[m=-Md!+rtY2JLC[t\IO(eGnFdw3 y<덵3w(gN?@(&jzIO8Utڏ^j`Cr:c,:-?7#̛j}[֫ cl"8ִ'>v‚^KU+땁45gTq؀g;{ƪS@:a&T6i`(X\!9Pe1RS:FΐCWpuBzE$$0ioTnD? pןq?&;{`13:AfʢwS^2.}t.mSC.rjM||o4S(=Fې9sPx_㠐Aq1'> +endobj +199 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 201 0 R +>> +endobj +204 0 obj +<< +/Filter[/FlateDecode] +/Length 575 +>> +stream +xVAo WpĶp˴tڎoc(&MiIԦ1zs= ZRv5ЇfuҥP)V*H5|AJ}0$6,5H FmABAdDڗ7ov*ip훰sfQ pf#"+ SDZ+W%3*/vgs@xq mHC1otA7&3y!mipl +&;FWxp<2=Wi撼i&K@4h=v}>u/5:iruܼ'w&r,m!,7͏wP􈾨tq`%\q_$/oLOӗ=/qVsR_Ӎr{9/na}guCf +:pjG*7e%T)q{k K*['ɪ]ֵ׮u/L> +endstream +endobj +205 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +203 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 205 0 R +>> +endobj +208 0 obj +<< +/Filter[/FlateDecode] +/Length 458 +>> +stream +xVMO0+z\ڵ]?V/F0O$&x ?ޮA@]}J[pFʁZ(H2Ho!Bb*ar Wuټ-nQuX,ƺ=5U]9E)ݰq|`B AX ʘ{\n0Mrej C>TY3c(Ҿm13Rݴ`Ӧ_ն ; +EcNidٶMD2I? 9 }+DS xh> +ߖ +픙{ۙWS}N1sY.'cEVӆJ x\ #qأX.IS%-ZҶ0?HOJ\˽S6:,~blf3s1j=ڀ,)"IO@ĉ285Nk`^| +endstream +endobj +209 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +207 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 209 0 R +>> +endobj +212 0 obj +<< +/Filter[/FlateDecode] +/Length 523 +>> +stream +xVMo 7̇îv{Vzp')$UbICZ.1y p1X;߳a@Jl$%HXr]@DH$It Bbudr5'W"ঌ08$0qsmL)>X'BZ&l2,՞fyr6j&vpN4hAurk.[ 6 u:Z@ &Mk_Ԏ"Tr*٥'@}z%7(Ɇө$)i')}FPg1OC,{ ˌJ4.H8QOׁþ}IQ`L[́>9z8)`v)F87b[V,Ţv?i+ov62qnsŷzYrU.{_S}^Qdt1֛UQ|WxNjј`bBo:˧|P4'OB#Cx#?$ mWëBS ̫ q? +endstream +endobj +213 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +211 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 213 0 R +>> +endobj +216 0 obj +<< +/Filter[/FlateDecode] +/Length 1073 +>> +stream +xXKo6W".9|ȥhSƧX :NM +IiEQ{(_diڄQ ?ȯpI$(I9'=4:A5kT#wܿQ J. +&:@#.0Y()pF&ݤwp@~4$cQ%W yo2b +o֧**5aAQ-d`+x[vqe)l]{H,}h\SxsGIj.:yQv& 3!|a;OT9fQ9$#ZkL@b⓼͝T rTbxV9O=bK@7`:0|wgCAE\acykCe3 A&qI@}!a $lFYkݰ%`UY )28 Ug$|wk.V_0 p3`-1uB Mt)"`ITXFC|^!ΗhɩHpa`$:$S + QI]a<^Fؗгa2L=w%4_.+q̆)!jB׽Be&b^7珰Gxuv_7|2 +" +ŐQ NJ7#֞ G>zi$=JjhN^C2} .9@w:kx.1Y1Ө&x2~X"_& wre[N.ޫr*B:MK[PNYL4om}"'2' {6i8PePz[7v;; A +endstream +endobj +217 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F12 55 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +215 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 217 0 R +>> +endobj +220 0 obj +<< +/Filter[/FlateDecode] +/Length 613 +>> +stream +xڭVMo0 WhǑbɲleX:lةNU +E"GIqIIԣDR'I |) SgA)D!B$4 i2DxI߫GErKx2#b#j#d/2ȆϥZ8S„c=y"ւ$ +Xo`)@m﹤lUaV@kfcedu)i9)qVL-ry6WZd!j>Ӹ1l.O< +endstream +endobj +221 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +219 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 221 0 R +>> +endobj +224 0 obj +<< +/Filter[/FlateDecode] +/Length 600 +>> +stream +xVn0+xŇH1@/E=E QpwIJ$kABkwHqCT[‘ʔ@$aA3Y]{1I!X{yD{ s%ի&١yG}OzwLb\Q_A*ek7;px GLX3b%Q@>oS먜ðs uy*M>aB$pt,$T- fuip穌 +NT0aG´i<#:WxwBĎ6SF#̼BƝLuXM͚6mZAe U7힞//??]ӷCL>N匶75=4iwҥ7u$bCFG{ +.)]N$\{ +)^qgEOt:γ +ỶֆۚK~}ɗesjΟŲv-dx:ez}=\W*?mJ3nnٟhR*+Kkf[ w +endstream +endobj +225 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +223 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 225 0 R +>> +endobj +228 0 obj +<< +/Filter[/FlateDecode] +/Length 1080 +>> +stream +xXKo7WR`ee.|hQH=Q d AU?>>}(N-ˮyqH2{V>~f?/ߢdf?A0R#O4JD$^P΄af=?yq^~8nj^O>aTiuU%Q"Q s VP+d2q= \맧;aϵ|+JȤJZ', D2?HLtIMT*֬DlY>Ӣ2 x낥]i] \bs0phl_+I߱)m~:ڕ+@eDP_v%0\ Ǟ4^D{Sk]*N˅5]P˼Ƹ&2b1:\hJT[Ȑw`AV5@ YZB(&o/K /zРiAk|b')T"i"*2jC*D4Um\Hƥɏ$gFBϛyoAj;:4 F .ȶ-zٰL2"v=P;]lHlʻ5969*(:"/(/WFQ亍zp-I~EW!=~ǜ糫jyHE_otyq1`FWc iPi4OuDOL{aShĂeqWjӇY>iK׎70ue߉ pNIYm9}(K +endstream +endobj +229 0 obj +<< +/F14 63 0 R +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F7 35 0 R +/F2 13 0 R +/F3 16 0 R +/F9 41 0 R +/F8 38 0 R +/F12 55 0 R +/F10 45 0 R +/F13 59 0 R +>> +endobj +227 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 229 0 R +>> +endobj +232 0 obj +<< +/Filter[/FlateDecode] +/Length 945 +>> +stream +xKo6zñ8|ȡE"=l/b@llٰԃzl( p??Q+,{ Roq@M!pŅ@]o/hZza >dB]~M(@VJЊq>M9)a;Ve5mpz0V<2b(QbbrC(òId #7ux]U1_U2mNL +Aj*Y\l - 녪bYao)ۙVF̚))\haB*1naMkX{ 7G8CeleP‰@7:.vHTs0dCivBti8CnvHIs)>fA ϣDB)UK'S+zfB{]:pOh?H I!æ>`C,q4#d\bx!@o']mAI2!GZSìAbcҶٕC?Rnu'<܋x ڏO@L RA v /8H?(g&ijz昝+4쬉KQ7a5}77j _'+.yk=xUxpQΫ>;^V1dWO4MqE'6)?%͵d\W\rӄ&kUP_g޻PŠΣ*Wg˄aXx@xxK X*_l]4*.GN_r[.rF0ipiV݉(! +endstream +endobj +233 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F3 16 0 R +/F7 35 0 R +/F12 55 0 R +/F2 13 0 R +/F8 38 0 R +/F9 41 0 R +/F10 45 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +231 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 233 0 R +>> +endobj +236 0 obj +<< +/Filter[/FlateDecode] +/Length 1042 +>> +stream +xXK6W([> =6>epZ P;$%Q/[WHj^ +GJ~bHޓBC8Uk +- +[(剂"x!x?-7'`F{Ls&m \ˊ@Pr!P)#L5ȽkHJ hu0(e\UeI:͒qDp0=TjH0#ڄ㡝 +}o5. Ao<* E"@TA.):1A;6m}o EƕlLy5U*L :φ>}0`iȘ6iA6L0Uןڪz` >.֫@^=0:{|1ur}:}qC7ہ[<$k9tz__?<?wԫٝv/ f5Tv-EpO +SÿF] +endstream +endobj +237 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F2 13 0 R +/F3 16 0 R +/F7 35 0 R +/F8 38 0 R +/F12 55 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +235 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 237 0 R +>> +endobj +240 0 obj +<< +/Filter[/FlateDecode] +/Length 639 +>> +stream +xVK0+|Lڵ?╸  ‰J)*U%]=?vh$Dr2{7a v,|HPH  II#ĐQE@B(E ldCN9hKɣ@cҮ?epD*EH*Ð{c4V^6џLj*S3Y_ÉMBY qtG"\Czujd~7P>M +\RcmR28 mL馇5`^āی*aDQۍ1,D~ nlj`2Q˃oMʈP,oHɦb1ć`[ڊu{$uEO]C +'>U3oK6VzY6I2SWA>̥슨>‘$!*ׂR,Y9p׌zp~y63{n ;馈K|OӏM'v,.Fa5LBbn3Y5$O!+Cn.?`]v=.BB[_4E8W,LMy[DdzfQ%2XZzLIp2OV(ˌq˖ +endstream +endobj +241 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +239 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 241 0 R +>> +endobj +244 0 obj +<< +/Filter[/FlateDecode] +/Length 626 +>> +stream +xڵVMo0 W(Ǒ"˔leX:liNU$A"GJQKM98&)||qySݦiUTiD`ʏoC%MS[!Me.!!{2$'"RH|ȼaјUĭr島~ ~tus2 qQ P9O 6A'&Z70[2[ h| @LƜ! m9ݧ!Eߌ`ʃ~() Q,=+UʙϭL;(VMliW~eh/[ {؟3RBgXK=aUԓ7 pk;&%={4]U_P9)͠Wkwz,^-Ϲ,JL-̦qB !@@hC;:Y]dB'75c 8?jaSup ,zkGQs7Yptu>f i|m_c#WOެSmf~i'k*2y}ǵ!̐jbbRrR%u]< aAfWT*V䘬fEa?R +endstream +endobj +245 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +243 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 245 0 R +>> +endobj +248 0 obj +<< +/Filter[/FlateDecode] +/Length 564 +>> +stream +xڵVMo0WGll*UO 9TZvDYTc {Cx oga ,<# (I$ +$_?C(A>FA.%=aʄdA W$SP].3=6j"[[]nN]IjũKdDp[e3g"l sC-|d*Hs. 2L|ՕS.Q9~@Py$fQPcVH(O56B/VRSMF hӤDOǃieL\fZtLwݛp<LӜ['6 \4P^B@t|oAyi=eƔ/$:*o,vOgk%s+NxA1Vy<vcӼGkn{AM%ַ7iT`#$IUf1j~Ӹj逥aTDbTQMYal[1Mdj_f|ԌH˒:_u@FԺs,.(z +eAŔA? +endstream +endobj +249 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +247 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 249 0 R +>> +endobj +252 0 obj +<< +/Filter[/FlateDecode] +/Length 610 +>> +stream +xW;o0+8J(ocѤhB[!6\@Iȏ/y%S")(dﻣ#zo G5ߑ""K*_+ԘUoog!LHk΄\QQ;dĔIʫO&i 7fNί8:Ls'&Q\ȫݰl"U[[yP$BK[X 'C<9eĝN0MJEAqیP.Mέ +ᦫW9œP#=Nk2PyHï++غoRKZ'1y֙ȗ})_/WԗA[').mO.ͬ=IѥrI7Hfa;iWL9Kwg'&Nܭ=$z> l$PJJG)9J'`}e7G''3}tjxt)D;e֋Wb͠S|]2Aqե{pu) M˸e8ȓ1M~U4 G ?e(c>sr2 +mF$."v|oQJ;Ax|qw;?|sƿ DV+iw#7z +endstream +endobj +253 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +251 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 253 0 R +>> +endobj +256 0 obj +<< +/Filter[/FlateDecode] +/Length 651 +>> +stream +xڕV0 ,@6[ޥh (+lNAH19iAoJN/h(’5EO _/ x{Jܲ:(m:`b +V)jꡚєăц2V7}7ejsĴUma֔Pw6kxnKm/J,]#MέL}aP +%\BwLjOg A#:e Kl34gQǧ8%g f|qfu7IԆ.[̸-r]n=;O\A;A kHM +(6sqq> +endobj +255 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 257 0 R +>> +endobj +260 0 obj +<< +/Filter[/FlateDecode] +/Length 683 +>> +stream +xڕVn0+tJ%襨SV$5 +NR\PR| #C#5|>#QEdQ){f0'A=H9Y`,Ms*.zЙͤwU"0/ ~2cweeɆGDzMS{o5b0c݌YݘiAo|:X5 $q3xNO FO?kA!`i̜Dnf OùT$ಒX^Nп<_z:^}"&0k?t뀮#Q8=Mܦ/ui% 败I+Qczy<" S4Mg$,%t9Kʒm{_7T+#N>6:|sH>Jy֞B8"C1&flt{k^kDǭ +_1,"\I˂;mEV m%ڙq8T hjH"aLڬ*/`Y0mNٵK)f -XkYҒ$;eZ'c E dC{YT{m/2_X1SH;{ٮay + c^}ò .]Q]G2yUȫJ93}C?P{i +endstream +endobj +261 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +259 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 261 0 R +>> +endobj +264 0 obj +<< +/Filter[/FlateDecode] +/Length 648 +>> +stream +xVK WpCƬKl[֭GiTʮvsHvpq^0RE0|B=S'ҌhpʼnVa5nj*J3o 0cUUqf+,MQ^n;A+kl Xr#M?\xc;q'J[~x'yĥۉ0> +endobj +263 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 265 0 R +>> +endobj +268 0 obj +<< +/Filter[/FlateDecode] +/Length 531 +>> +stream +xՖn0>Gi))ڱe (P$A(fH9Aҡ@ß( efYb5 ÈakNB +oUY_E1bZs1s᜶fTӱ9ߏK<~NԑS-4Ǡ~ev(:mDHgJ&KÃ@i#a*mod`9ȘBALUQP8x/Lݙ3@,F\bpwOO?߻1 ֯} {.v.>-aXPʀMiK ~s DQUڈKi_;>x*DXDTK@Q`#ZfGS\KPwx[DKvmh뜶v9CiO.57@%c_a/eWjkܥK#2y a#A99.4{XRUDIH?[ +endstream +endobj +269 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +267 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 269 0 R +>> +endobj +272 0 obj +<< +/Filter[/FlateDecode] +/Length 573 +>> +stream +xV=o0+8J1(?D)ZmUŒd.H:Rt~==PX|7S #AGI$H? !Y@2[#hv6 um39!_Hv틄 }ڕ37}y8ʌTrU]IGݛ]t7pXxlvyU|Wb&h,PFqcxF0A <21LH5*ӟ :)daǨ>&\cA,"ڡ  #XtDr!Tp~J cN{ݷDi& eR}ڭSϢm2|/Ln(> +endobj +271 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 273 0 R +>> +endobj +276 0 obj +<< +/Filter[/FlateDecode] +/Length 133 +>> +stream +x=0 Dwc2؍C7!PeGt{:p PcB _A'ȻA> +endobj +275 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 277 0 R +>> +endobj +280 0 obj +<< +/Filter[/FlateDecode] +/Length 1081 +>> +stream +xXnF+8IR%H xNm`f,+& `J6c`](~UUay"+tG$'9E~~qS΅=o0v^NoRGr|L,($%}!< $G`5Hr#< +.IrbY)"E١ۭ@ԄEy+j T/6p LuVb{,l}drrϕS7I +X1eK}fz`'ffEQKq&֎F]! LS:Akж~')Vp;er5I#XO', 1arr|q`p`]@!X")#eXF$OȫO'B&6\nɌta)jO9nxP /2.6:. @CsJ BB)n#tkp{"YzC&՜ \272`B zA%V 8и) /p ̷I1˗v[R0^,Nf'c4ZxXY^3+lxlokowj}|r];r?xJC +TzЈȘ_Bk.|v3$WS& +c~q"i-/5\!]1w+/]%]ǭQIWܐx[kS6j1jta+~O|D0~`?hCRCD.,SeGl9FMv[g8KXnbߍq; Խ\a8l#09edJG4c.dDzsa%TlkS-C[q6k,ݏt*H6^5QyȋuR%o6{`U.4Kfd%-HF*EK+ԩL?c$ +endstream +endobj +281 0 obj +<< +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F3 16 0 R +/F2 13 0 R +/F7 35 0 R +/F8 38 0 R +/F12 55 0 R +/F13 59 0 R +/F14 63 0 R +>> +endobj +279 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 281 0 R +>> +endobj +284 0 obj +<< +/Filter[/FlateDecode] +/Length 611 +>> +stream +xW=0+TBVLrIqL+\GZX亸~H{f=3\(՝aǟBmq#ko%7+]bůgW]Tc(w:,*-*7&*A$atjz+xeN cՖ%VMne}ްǥacL-#h'U0uD2.,c +^Q<n_҂5*kc +ߋs@ijvZ;Ƣ #eCCk:$J I48Dy6 $Qn{(tiM#kj^>kEJ8 +nW]bF7"w 9&9zD~wR浥S{gAe*],Q⢆ +qG;Rڑm2EG?mb@/P%3I@^]fTJ^b/%1nx]um<(tT&S*fMfdz&[˸Egbw1 +endstream +endobj +285 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +283 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 285 0 R +>> +endobj +288 0 obj +<< +/Filter[/FlateDecode] +/Length 692 +>> +stream +xڵVI0Wl;Lժ'&=Mf$@!U8P_vf'L -s B62˗S>,RP(I % P(Ho"!CLA ` U<&z%3s3q +fޔ@ +endstream +endobj +289 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +287 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 289 0 R +>> +endobj +292 0 obj +<< +/Filter[/FlateDecode] +/Length 711 +>> +stream +xڝVM Wh'Y٪UO]t$JHUvJ㋁+`;=1ޛ`B}d/ѧbHy$Q;(h,1B?D%v J!G?/ְ*NY[eߝc$oX^w]]t'6 .PyZ_v*K3g 7rU dQvuFD,U_'<Y \L4@H5vSթ)0]V}Uk̞k bdҝ&?x> +endobj +291 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 293 0 R +>> +endobj +296 0 obj +<< +/Filter[/FlateDecode] +/Length 689 +>> +stream +xڝVMo0 Wh;oYvvZvhrɒ*KII"Tl |.>[ +(߅P%/O?KWʺoC(1Ò 0^70%* /,Juk8R;t;]OW d.Bq1%vx,yr)&o ɟl}(Q|")NjyfG>$N }N.td +mg)$LF9V*D$욹kCJM">MfMt+46%sTg +endstream +endobj +297 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +295 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 297 0 R +>> +endobj +300 0 obj +<< +/Filter[/FlateDecode] +/Length 675 +>> +stream +xWKo0WpVfmDj-JJU%{R~|,/x{fH@JS`ObD' +_ffQ<2(>~  яK@XYeN% +8lڈ0 +]/R8aÕAdK`+L0S3w3JmB !~Ig##2=|!V(nd2B2}Hv;2`J_l@rJ4!,C/)^J—fRY:CQ!x0k͗5B,uLܔ0B<ٝRhn` +C(@:g%249"3F62-z[ܬl}d`f(h&ЛX^'}׃{zlaWQ@\_kTaE}M̦#Lx2?LK6v[i Ԭ6OǓ YE:79"[5 +< 2̓o/#LL.LA.n;+_\ZDݏj9ZRlzuxߖ:Hߧ]gxh//t|z!O97ǖlQ=a2l6F?wWe}|f k#> +endobj +299 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 301 0 R +>> +endobj +304 0 obj +<< +/Filter[/FlateDecode] +/Length 631 +>> +stream +xڭW; +(hy 6\fRfE)d5\s,@uo}̧'*D3i?R%_5l1ơYaiDW8i)𘘓I-sh+ȌK\y=b^;%P|:TO}7NtL5@0k-b"܃+ČK ~9"(Y/dw. sq&cqƮ +V(r,09M$eɔf{Jy!R +`\`zZT]A:*^scy +,o3wf6v/u%0Nl{R)(jy8rbYHKSy2 t=_"Gm#.,>w>GP@A$r r y_:&W[vvditTJVɠG'o% *l]+¥ 嘁R'eTbaS4=ܲnSˣ'߹Ld?3O\"-͟H! +endstream +endobj +305 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +303 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 305 0 R +>> +endobj +308 0 obj +<< +/Filter[/FlateDecode] +/Length 713 +>> +stream +xڝVˎ0+XanfvfWZ 4TeF3YPi> lH,ÏsyYFOч}YT絈"s#$H.y=Fk$_owHh^[7%|]G#\4!&n'ɺ +i6дmB α2ӆBrV8N4I <IUl0]L7yPn)*S +VA= +ۢ +4@sXSX*2#|p +D+Y28ٲpK}4W% +¸,>Bі$8q%а5rOΆx# ƿmd +0 +O-%-w-I\l]McS]$2pIݬ\IvCM*eb*MDfY6iz gUX{K$;yJKo1 @+d;?e&}lnwa32x;"zyUA0J +endstream +endobj +309 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +307 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 309 0 R +>> +endobj +312 0 obj +<< +/Filter[/FlateDecode] +/Length 713 +>> +stream +xڭWM@ Wp!7Kl[n JJUvk l0m<6 $Mc˧C}"ȓ\ů@DӀ(h|ʘ <˰MDh*pmA.F/G%HBi[F-akօCne9U9Oqe +rS@ _ŖUfy/+ l`lH"(}\YkKE&:h1@^uR ]02jyBBUnf(>(_L;xqǎ l1>7F./#1" ^1eyE8j>l\$ep +n9H%.JFʮ3("KT6e g)S|:Cw$7ou--}0'qPFe2>>ӄu+,a+xKQLI8ˇ>: n|cy`3?LuR9 ι)#L0{=8ȮY;Nlp +P.iR )0dnVcyۀ@su/٩dk)M{B,%@2 t釰> o&]b6 >o{{~ä# PLC͓,Cm%îxl +endstream +endobj +313 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +311 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 313 0 R +>> +endobj +316 0 obj +<< +/Filter[/FlateDecode] +/Length 601 +>> +stream +xVMo0 Wh7b}[vq `?]ۡkK(I9>O+3A,gjTWrjJ_:krwS^"[vvCvb0I$־. +Ђ;y"õU? +>VK8n JCi(=}(WTSw`` +taEj)pX-Gn&&k|J~=qu~-p%TEtt "^VO >y"hB#QxgGzu [#?wq~ބSB!cvc0N[f +- i[ z>9Ne)=9xO%2_&\ 9XI TXG1mC9QӍ%57#å^B,Y>ݗE7z#.yO.}tuvK9;Z +endstream +endobj +317 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +315 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 317 0 R +>> +endobj +320 0 obj +<< +/Filter[/FlateDecode] +/Length 463 +>> +stream +xV=O0"v\"d % j!H8N&ŎZB\컳߽<p1gnu6t%ހ""I(gcZCdDH[ޔc QOjZ6vҿPJAhum3iٲ8eA^G +CbPԮB#D v@ev Dl8>\Ra,u\}1wbV|̌%{RO=)^r2>,f Ȝ>DED}Z qɕQN^F,}uE*@Ы+Z/v^$LBN,=6%N'> =FNh0`2Pdw*XGl$?RRzHPLr/ֱr<@ ۚhI,xK3gc!B&M'iꂤry +endstream +endobj +321 0 obj +<< +/F14 63 0 R +/F3 16 0 R +>> +endobj +319 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 321 0 R +>> +endobj +324 0 obj +<< +/Filter[/FlateDecode] +/Length 1253 +>> +stream +xXIo6WR@G %@-)2 ;Jb؃:yE֒d&Ӣ( %mB%a%k-AF&DH)T2CeWLPj6ɨϨnjq_|oOr7[:7,vWԻo N2Bβ$guYw뇪X-*[y7OeOfRd\`-GHekj}{'~rᆩx;;wC>EF0=ɠL#bvJ nFgkb0SS~yE>!@ qCy:{ܔgby(vߗx0N qYH:""`b>g@FqLްѲw#C{7Ɯd OL(H$ j*a# +*qj3J;e*$2:.WnS@yڷV *\Yح@Li_>S0eyK=fuYcl`Yu$B! 2l_`$`{i?9v1H*5H4 $Ϡ͑G l(g4 EZeíAuР!;g@u]IIv7+XcOr.MbYc]^FDlISNzx +%(S|cDua :8P>闪gx=tmbۋ'{S~U!G'ċcAz=?PWa@FHp$hhd V<YC= +1/ Rd$ 3e +P(} zrN[M&qEp8;QDs`‰B ֈE[oࣚwWFu%@dHFUIclW^wW3VAnb(Rq"/I&޿C{4|11)\ +3{g@)o["6'=  okZ81*ލ<.^Km>YʢR#4_x|16ˢUͧ]//^Uj^gSr$O5OS_~=10NP2RNJh^nL'\ •흸.Q.tMNgTG ?$oBò.XjdYW}|Zn7~#ҧ]H6ӰLR/ +endstream +endobj +325 0 obj +<< +/F14 63 0 R +/F4 25 0 R +/F6 31 0 R +/F11 52 0 R +/F7 35 0 R +/F2 13 0 R +/F3 16 0 R +/F9 41 0 R +/F8 38 0 R +/F12 55 0 R +/F10 45 0 R +/F13 59 0 R +>> +endobj +323 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 325 0 R +>> +endobj +330 0 obj +<< +/Encoding 7 0 R +/Type/Font +/Subtype/Type1 +/Name/F15 +/FontDescriptor 329 0 R +/BaseFont/EVJXTH+CMSL10 +/FirstChar 33 +/LastChar 196 +/Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 +500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 +750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 +680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 +277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 +500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 +500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 +777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 +277.8 305.6 500 500 500 500 500 808.6 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 +277.8 500] +>> +endobj +331 0 obj +<< +/Filter[/FlateDecode] +/Length 264 +>> +stream +xePn +V +aZNT)@\X#CUƸ0 po025>C+=$z&}My(TROt•MH{,N*>uպtt}5W خU(nK,D5Tc +endstream +endobj +332 0 obj +<< +/F4 25 0 R +/F3 16 0 R +/F15 330 0 R +>> +endobj +327 0 obj +<< +/ProcSet[/PDF/Text/ImageC] +/Font 332 0 R +>> +endobj +9 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-33 -250 945 749] +/FontName/XGVGVP+CMR17 +/ItalicAngle 0 +/StemV 53 +/FontFile 8 0 R +/Flags 4 +>> +endobj +8 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 3966 +/Length3 533 +/Length 4517 +>> +stream +xgXۚQ)B"BStI$tiҋCAHM^H&Ugf3k{YϺ}\p# +D 9! +x4aU"+ <@`DZNBFN\)\G_Y +$ E.!H3Ġ ޢ d{;{QBa ͤǁ(׿ZhStAaA(=@LwqP=\Y;p8{A@A8>O6]4 +&A°hO 㮆BdpvGC\13uSuSП&]G bz鬙_U~fC+291سD AF7[! Yik$r>{v6^;X+Hh0/w:/IjS摪9x[ˁyRF +/|ŮeRXOw AqfOB햙vܾyD!~chJ*\!ERd:R- +TP}԰<Wq"'`j 0=Puc֢1{5vC`Sb{=LƷtFؤҸH[ ͒]Z=Cρ݇}{@TnRRx7t?4 91>*O3>.ŧl9@UOhnR3KKK*d*J& Yˬ\WG 麗nhlw +jtd+OǾ $e"Sc曰ñgs?$#cwpf +5?BU#魐RgN!X0p+2d1?! H?+ˠc>{^o3'nS 7ZVE\TT'urClKsۣplΑn;pkB9l&fjz8ΞV0f'ǻJMчIiaKqٍ؞vۑz˃wx ?6x^AdZ6FCwQ4. Ik^m_/9קx@)#yW ޤzѩL7ޙe&M7:;tFozqݺNjygu2U# +R%p;1gi(7]%OS޴', 5m'6 ",H%8#<}!^_-:N-0l2AxJ Fk+4e?Y_dvM`ţnXч~~^ң +?lh꣝P)idI >kGuwi-N +(-`] $ip96u }'$"kDf./@:xw  +endstream +endobj +12 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-34 -251 988 750] +/FontName/EEFPIB+CMR12 +/ItalicAngle 0 +/StemV 65 +/FontFile 11 0 R +/Flags 4 +>> +endobj +11 0 obj +<< +/Filter[/FlateDecode] +/Length1 714 +/Length2 4386 +/Length3 533 +/Length 4937 +>> +stream +xgXS뚆%(HhIG{oR $@$ M  +ATi""H J " v{9s>g7׬z޵xLThg +&%. ͤ)qI:"^0,HK~n$ u"# hoԅpT= 0aC\`(D`qBfl?.IIp pF!@0z[p?\oNa7%p+H4o1Cp-?Gs6E`C4!{W C!]TP@/ 髅 DMXwE#=?$45LtD5M`H/_= 2m4\p`yaRSCb7y99 B!t5eT]0Ͽ}Y"ODs眮sin8nj-^˸W<~E)>q76dg$1@[9:Ҿ؅ñE\Zv!IDa:[ruDb]h`GJ-xf7[XO؛)8VMdBb3eL3@?U4ik@nȊf 9V qy_ܳta! CޥEvquLljԅc=* +G ^fQ gFrbH9X~H~!_F,m#T by#߰*VP!!:'^X&;7ug4੨wR+n<8}|ɼ05 +|89U3-N{1V̜Z+P^6)?svٳws"9Od竌m'vɼ;s{2:mO/Nל8z-9s SrC/uu_Z?# jY[".W>5rtQf^{͒DžhЊvr*R ֲاmdltԖ[>."c% HcZzfEsXsjQ*YVX[T>04o730ڨd!DكӝxAY^>cu(NE699~6-D&'K+)F)LC_핽Fo}g` ዆]Nrdvmsd%9'~VE\y C +L HyI9xD=n)Kݣ}FXtghipW"{!Y}M٭z$Y*B&\=1PpWbټLK{aLSV-|cX=&<$zx6ی#8?r&ɪ>_f!z˘6k$gM){!qW8~^}ζ)k#jIJE3$"4*ۀqd,AoImt>14F|S'GԛD3&ݪO`A-_acw%7?%c,0)40]>rP_?rf}odyhl C"[HUUaF:|7,C$讃aЁl3uk#<nO0]>ؾjlIR8.V&W^fP:7ka&럌~xeJҘCWTSՁRfxh-㸁_ꪝT +f/nk2T"w~OYmqÁk0#4va +c:/w^K6k!aqKOʚ{nE0Qk]l$a+᳧Ǘȃ8A1fBۃro{U6詫߂r{i)AnO/uf1tϬ2WYQlTc+qK5 zX_ +R/ud9xZu)xEl"or[N\YmᬒD +m^4T;x"quF~/M|,C8J;{ܿS5;Tʽ]wfC[p4C/oӁ$sN1>G"j]wpp9p.RӳȖW3T mV$#?PK:x!C~<ᯯ9]P2@ +տf&jSs&t3JWW2U&" _^@)/):h_gXu7 45 +ƀC9/õ 4+{3+>v}ѽO~+TRءH7*׶h{bFZLS^'0^=r6ak~܀iX8n^|f YFQ[jUі ڔ7̓)Q #Xװt ǀ(~f4=-ItcM!n{:@JNoȶ}qm ;/|ү],Xy@O& ^˄:(t?^*Y;޻#28t,!i|wA'+&^Ŧe2qn@g"a;:aQ7Z-~jz९]lR^٧tM pFK_OkNH.7q8Umot.j!͎ +=:(eKBPZƟɄ- Akh{&ܬgT:ܴYNqͬSJd%_\jpI~<Q+ +o2}FUs;i9:=>V1yku﶑lu G 1׸YNq9n H)i_PWR:>yo١l8= !S;'<'Zb-ǻ.LJ$EIcsuBq/ZZ:L~0EdDu=B6em.ן' cOm~!e' +__U&]U fON_];2wUrjV@Fp85ޠLq"860PKרl=N(̃ +Gy+mm#xK0"VGa %<ܝE D*a=gw]xe'n|: +cz&l>/q.jaUgT-t@qJ +&&4(e&BᶶEqj*;^A];Z%lZW<Niۿ]eguAv׸苼a❫RR(k6 +twZ5SEU Ko)e^XՖ. 8d-ɈQy1YM|X l0'f0N̦ר[;WA ב|sVBtWȗKݵvxTOwǪk>;[HSYaP!SJ)V:y! ` F%pG^e˒xx豟_WEEg]3H;G,0;n}qv 92GH H[%:w5~Uu_tT3? b&u4 +4j̤lK/Y2MY> T=dsC0]J.{Mi:OK7!NfƝu i0I!,]&%Hlp&2.JzFs-tp1]$} ]Aow+~RPɤ<5sPǽ$Ӂ_7,ߺ`V qasHO!gwS^WǜH(}fFܦ65墇ۇ} n5$p}Qfܞ91#<=e?kRx@LX #Eg~ v߄m;7r N)%}m&f bLANl㲚6bGaojy#B- u*]8\"Į"Oꃖd3|QؓDىY +)Y +QnTŜJgz(ÓQ.DSΙ  dP T> +endobj +14 0 obj +<< +/Filter[/FlateDecode] +/Length1 720 +/Length2 8955 +/Length3 533 +/Length 9509 +>> +stream +xeT\݂44 8k&hڸww<[p'rf}e|5:_*zj5Mv))D-QpspqI8B@Ζv g[X 1;d=-X8dHB-@P2b dд38{pR66Ѐ8A]!`44nn` +b E 4?KG\2r60Sz4`7sQoeڻ8Cv`#ߥ:)C.^UpXIA@\JY:YCjfsy;ONG뿊j K3lg?qt|_¿?g,l tA G%;;qq W%(Ϭ#ϛw[1CTWf:aZ&"2.c` +}. +|yהUx3(RoȄWo|x]:(63-v>y.rWubmlHqQQa +mT#T[l.4SO n`2Dd}'$Ab,c=cy·m,jvMr)nCBфdu;5ƒ +A |=~_C%3eI߶=vX4pCW$~zTGЖlNxxlM{Y~TY_A }mtWRiRVꇌ<%a{[c=]͒G0C=؆ k叙Rj3&憶B]TzkJ3ˑIԀ}-|4敐=TL +\S^$Å|?y%˫ fFě >v/EI5׸N_(9>pUz*cy%7eVʒEo.Ia/߶W+ |b,'$g%#_)UASO%i6.U+M5R>5ˮhP\8a(C$_[9qȳzpoX)n S~t\Fx8%\/q͐oE HtdEV=g32[dͫ63<2r' + T2 6H)"YnyyU,"\;_1t;B*aBUq" +o^/wrG; MED^zޑY;F\㈱+}/æ 7v:#D`)cc1Mԥ5~tWr :DtzP)7+ݐқ64٢^ͅEX.og%Ƹ5S\gaD[v䄷E%WQA~-#~:s$LLiczgZv^߾R+sI)>WJ줛2289̭>| {N^LmE8PSdd,.19 ;jgm&ʞZsr9-vzu20d@AІZ-#p=`=$7(t‰3Y$<}Qh7 +B9wF.c:Ϣdjs?6m% cly4u |`__UNiT? rhxz}h'&},2zc`. I`b nk9!5Cpߞ@٪9/IMYڎsh,ߖ1b}q?v?qTe)òa_~>ܶ\LDoucD;)iwȚoP1B˥#Y{-4Wu17y̖+xC!|vGD5Q&];b\hC^ic[ƿYӂcV\ 嶃xQNRl^,5+H)nFs,|C"G&nnJϵml˫#UyYI zqfňMA/]}O$d6b6Տr0~F=nˈ8.QY-U>BUi.6oqJ|Ol(07]oLf~9oH@BPeMR^6L4j.7ׄy_{>X`B/;y5^9dCֹ6j}8o)QeWBYCRte턣%0dic)U!s㴡 'M$EvוhRObf?P9ӊ3Q8TjQύxꓝcPha( Y#*?Rg]X`VZx5v]ý%6_NAتi2i-G"/zG1sЏS~!@l룰~pswY鯕z۟^ ;=,3f+e"^&\GK|dYhG|"3y)zʪ`K +f%Ԩ4IX?%[n\b;/6NPg63>Ŋu&钗<++K]L3bFq0+՚~ +ɏ4z{W^J .6߈xQZ[~=y$i2@2UZEetRE;8etAlKmig}j7 8CDNςFI +cJ0&FUszF1p/>ӎs!^ ާ(l4a*v~M5Fpw~?Ix+3獃W/*ߜ\;ϝo b 7كXHљr]^黫Nl6ʞYc$s +]YsdR\ i6Y%. +]Dhӊ^&$Gt-Uf߼efzGu8'BC^0l%BmY)*R)Y]QaG5Az@G޼^r0?eZجsܩCM'5R. RC!7ÁRiD¥v=(97<8X9_0n'U5=H9=yd_ m/M]>:qi_ng^ +-2E Omq F7Yc ْ=[I1rjt$8LO +E򦼐i[\aTw3+ CK[f-{qy9qVyӵm'UZrP82+ kq}$@mҁB "{(y}W\Ԧ=qa1pGqiWͥ b1"Жmj8Ӎq瓙) 7C$GM, $ =[d-: )7 uGNK&cqp> ӎ%xx>M~ıM!/үrˇAH)wr'AV enRAb3>G7|&Y-z[7&BY|{h"E#g쵋!YEwݙiz^)gr0$M]&2#_>~VkFo6;.#o]RΣh zCw5R;W E5HH׭4: ,ԕ̄8P~K09yjW7v6D u@XEOXKZyN"Zd'Ǹ)|$Shf.Es69Em1f^P;w$1! +_;hZ{Gygn#2 +w$Q!0÷pXiK;鐠0Fqsu2}|:Jؐ[v|ȭg<20DI/J + ݀]xgkm񘥒RRQ+ɁǬxto 3O2k8͠heF™Ȕv^~K FzZoXM;O9#ulRYT1``mEE ck.| +!ZAz +3 nG ~GDc`κʡޜ)ل_qo&#Ti11Yծ'e Une1V<\od# L]HRi0#RX\!Ԇ?^lZdfgF۾o(3{m|/YWc0q -ࡨ{Yy߰[I4Vݗvxg{wrE" <W SҼ'%̶@~}'GaY!GN*v2=Ҽ O tPyOR̼kbj*#iW4d +M1BU= JyQϦV;yoY23F"(7t޴>(%[CRS)\Ge9ŚO6avniji驏"qa+Djt7ٯ<~%MR'%f|jQ]uɌF&}XLT6\~WP`kN؊.=wL۸NφMSuo%">'yzkS'r֢Q$fbC:1z\g 'gfp|{uDJNJZluOo)K#Gui +h~!\@vXo9_RgÊ\)~1n94φS1*Ncab"k `:.6F[WԞ#@XotUpӬ҂D#KTr]'Z_I +[oi.6^ NS~QA\p4Ky'Nj~zd _"vk\ڲG:xm4+"`nZ6VK +ѧpSOs t #zVmЕa NIyxi[tTÿonm9E>G_J9*dwP ((ǰ޲~Җn7R"HKLl&2 j4'G^vl)~6b>I[='*L̴CKɎYtlk%Pr!'4ZLy "=Oڔ_"ktEXvIzRd^]wkT!SQK + $+ J_t GJ@[GFzTݞE'V=]# 7\, p|ZW7l+}?"~4{8T}OXttdK+y3ꅆ}lyIIAQS!dqx^XBʅ_':/47RKQզ*^$Q`mhu0~Gڌ\n13W|δ]^2d0o`nҵжQޚc=}En鳮D*d=ߩ/Բ;hgF eޮaUI Z=SRE%wgZ^ ND3F֍ܚ:Wܳ>O$NA&{= +lɜcv G7TDM]"6Yi|Y҉6EԻ9L!|> V>)w\-̱iգl~0TJxw_j6}u9th1-Vvͻ +mfY-ߠ81g5c1šW.9kw&ŸŌ`> +endobj +23 0 obj +<< +/Filter[/FlateDecode] +/Length1 716 +/Length2 4421 +/Length3 533 +/Length 4967 +>> +stream +xgXSA$ Rz %THh-HA^ D.H9;Ϝ;_o_zoy9LEHmW V* +i[@APQW Ǣ\1p,RԼ@TZ^BR^Jif}2^B$at`&?{d}|(6TC%6@!\9 zX*nCdX2u8Oϖju8djFTZ;OխF;Lj'"Ōh hqi\B$®̏TẼum$PwV~KM6NRo'~Ͱ k2|̜֐s8;;3sW(Ϥ9Pl^, &94kCubH]\}CUw1G}<{D VJέ.q=z_Q6S\]YQނ&8\w|ig<ŝsR7 "T"pc'7HloR9=(*fsC,<H֫Y%BG"(FζHs}"HwsvăXuM}}QttԙZgJ`.8Xc 6Wu[%w.({[ 4hH,zA%&/su#K+(QⵜKS512J~W-w,'| mrbMҒ,h^ zFLw[URVu 5R:Q/ tG61,X[w4@Oy#EFJ5+0= ++t˧v8A*J4"_I%11n ׎Uy R=)UR28Ls^3(1Mt#}a~ +}ٱ58y5>.Q{/_}a)rTk +QfR5MqbP +ű响ew]9g5`ј]o$~4q􍹋q0Ӝ"ylXqQW}N*Ya> +z7@md f;=ޞeI~sO>5xeKU~z#$s}-*{ KWK?rhLKl@k_9ic[AVlUKۖV7?kޛ+Yƨ#eu>_{g@]lrPOsIf4TsEWg.{d8paZolY4'y<#8H͹|=~Ow*h༝6 HU*DTj:ߑ?eoHpfbk_ CBvO6({sہ&ݞnp-tƗX +q6u+@$J=HK~r`)_ðnj"'Q_IvD]hIWۡ8Y'B%,Gr@+G0=Yر69“TPDZ;Z1|4r ArXwdoV&W0jXǴH! S2{hjQ > =ݍ~8=ؐP.wOdjI>ì4Јb w VCIJ4&'ȿfF69O{tid/.y{p *R3nN:7>T[&~~{+hY2k wPU9l˳R<&'%/OΓ5tyl4c;D_u2z4[Ze+yT3<WU3\q (M="{Zÿ<+AuklHT)sw\ңn||avqh$f=iBqX˒sx8#6l:/@w@;Ҙ[똕z5PGk#)S#[e!g*{Wܑ)rܘjUnXyh1+7}0״HZvn:f jkD{ػ WSĺ߫6:شH5sNo)nG#i 7\$;԰)„Ksmɛi: 8110|h)͋=W*瑈lbhcJ٬L;ήRh=$(c9 M7W="ӷJa>~,Sݩgq £8Aֹ[PYa\s>`d[FXh(+tu6hC=Zvj\]Il\ CZeFZK.:Q˲k5h4 wE*|L聴K6/ޠ6)>~7حV# "uL/)ɠ}M[S M+]5$gsO1M wa%6Lb7 .єٕ \'֡#z]L<bq,0UDi|w'u0}Ot&\W! ,@Ҩ~U¶]j`~mHn2x+n|IqB)sk^66KNLC}9:VZ>(=*%䖩ǣy tk8CL1q6rو‹>4U~mڪbkusWų yzx"V𤆢bk0ifA{7oC }ҼTE j"Y 'H\˃8':&)cfxr#fUYnj%{ +ӜZ,E7\p~',K-TkkWV?iY1z *Gryw=eһ#{pܾ®fcD]O +/Nڕ^J|L,h|]Bvu%u!똆l$YZM;p |]q0u:`[j~|Gcw6;BԖjKps#T]^qK/cmyeĴYQ }G4#YvʼnJy uSC;T{sQOt\6+wwPqŽ'f|#مA,hiU WII^)/0 sMNro`{h7$M\^^za|8%R%[ڠ8)3(t,ECpG4wTYDɒ!Ч(SUVJQm> +endobj +26 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 4447 +/Length3 533 +/Length 5001 +>> +stream +xg8\mEFmh0%:Qcme!j!E-JH-"DH Z"Ǔ}s=_u?k^[RBuAb18 iIi%4(- i}0 ! Prxd@PtEET)5+ 4< W +huE"p@& +_㏀K@8tA#1? 0nX_i?K .oRQ'A7-E? +u C#QP`^~8 G`."¢BjbQ W!q@7;p1R:Z:[U׿|32xt1_ ϕߺ`\p$ha0N _I]3iyY DVU 7r HA^w  y1 " +47!2 +bu.1~Zr[RN^~\+|Ы> :cltZݫ:9 +5TJn0z kj[G {dOo9ZF_Y3RT:h7E4FD5Œ8xRX98<^)4-L/(t MΠ6Dt B +ͮ 0WE Yuz)EV'&yݻ'KiC1\Zi-@as}|׬ q{90K{:OG+% n*zwG9.+m|1{ +Q|'+Wc1 +, "- _'L9\3|׫W} @FSxZ=8>=z^|FD N)֤0=:& \%2[y[ebhsrwEQ&$ȓta4c&/sC%xJ$Ð@O + ~3*TRe@cM+"O0"Öc[vfoj; $)Cߡbaχ\]f&l#Fvn%T*ffyz $ +w7$ Tڮh[}:6+GFwDoI Xlqv֒`ޢ[ +-6u?2_?>]˰k+ݚgN]jTҁ$t=.m +."p8a7/Rqo}i7KfgM}9qvQ2$("OFvMg:pǪ3{, "E%gQ1iSIM؃ C*2(r^ ]0ݪq^8nޫ@p2'`Kv2]5yKD/ gBbmh{.;sr>}!S;?J.ιj?āڸyR/clIlV"xKՠ>xHZ֟?y0c!ƯSMOi  + j]?֕ l~0*H[6($^p#)`+;dJQʟiMJ|F3#ˆBQ%a}8-LBѯM݁C[ +.gk!"!qrgDM˦b'Tp\%KCԛ7䠾2 י)Z:"l h%㤝޼,$deo~vT뮒Q Zc7`q_jR29o{ϢrΊ稑WZOWq6GHs|O.{탖$ae士 ]?ځ>oGjEb1K屻÷yCÑ-dǖ#ट2mէdiib߷nWE|cD(]=b=1(eR%^`KmjI1td22.:o.y= Y*ȩ)[#EcȈ<[Tj +#͹Fguq(ߒqT93H8QJpQ!J:Q6>?aQ9.7Rp,;Ɍdt`e{SwO(uH[jٍl;i 'T5Mk}OjF (K>e=*0|I S)P0^{iG얡P kf lX6pP/_FZhTyOhN꣛b/k% w}kef5`Y}weql}| +DrI*h%ki[LOYe5Pv@UxB|!]bR,~#PZN`;1dr:+MfOzKFЫd"J#^#r3ePP=ޝZ+-)&p[)=;TqDR-{5g 8!zU=)8k|SZߏ"pڦP8&*#3|P2HFi=y+u_SK,cD +fDa*fnr+D>yuz}kT>r9u&a\4)ҫ+yRj#/(J?Y:wc}+BJge VwjxLjz^?LRACrwhk͎FCEo;>^;+{h=U^pvBGˁ~Jӗ2h46)N15I>1ϩbmP'۷z$bh"NfFOP8Ҽ|4;'f҉RGvnFNHf NڡHgmoD D;}m/{)PA OUIJr5gƏ ^N9ngrȱ|dD)UC41Vc@ϙ}Os\Ws2nǨtgqP+&Sd_};{&:QbG<> U SIpAw"Bh֐dd%7IiE4LLaD**+(IrL/Zn3olIsTpkKwO]!U1WG*M) ;u`2$/ݖW&;XeGsWH;k3#g$*N$+;udTaxf_׀Nz%-fN eM!LLBQ@m1$ccˠLc (6pZ[d|lZf3ovlE7xq2y֓aFvԃyc{C_Usnp TR|߬b٠l=#0ub=sz *9'Bcg3^(*x@<7Kn x!]/ft;QW 6^Cץzg僢ݣoH U&I|*L8`Oq֛K)nJ::VJ|P_w _fKغlڼdzK8t͠+B~-Y?6MDAXYlKnc: +Oxؒ 6?8==޸!,iA.D0 eT,u%e7mTv:3ޘR ۥfno5PAvKS)*mYZl-hKyj7|L25;QQZpa2Q,mo\uwQ2^GW%Beg?w ԞȒa 7f{&N#EKUFe,CDWNE-G!9Rqꖍɒ mf"%MIjgwWWKDSRfdK4 O0  +endstream +endobj +30 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-24 -2960 1454 772] +/FontName/CSSXYP+CMEX10 +/ItalicAngle 0 +/StemV 47 +/FontFile 29 0 R +/Flags 4 +>> +endobj +29 0 obj +<< +/Filter[/FlateDecode] +/Length1 984 +/Length2 2363 +/Length3 534 +/Length 3036 +>> +stream +xSi<{bk()m̒ ;![PcY4F %Kv$"}X +hBRt-t:~{|yATЄJC*M *p8DNΐbD*K5IDh"`H =耼¦J'4"K,t/*Ò;*҃T@Dl7S[*8:z)ئ+3 + +ߩ ͏ 4lR d}[?7'_FK&)d_:H,xFY~5g Y3:DSI,3EH8tBh,RUջ:@qw9MQ @֌Ǒ"ۧ4-SRS+,]K *ˉ~qɦ}E^܃Ke5E +MNsY%(MQNKj?-}K!"vU u.ۉyszQ3RYFP'ƫG m5{7ܼ-䡤M&C%b; |=4=m׋bu.!y%NiJ5sN,Mサڙ=u`Rؑ9j׍IEOSDd/t=@ߑbWʝ7EBgJ aI {F5!XGzm] VV&=F=eo#Xnw}:ePAp{[mUNrF퐳Ӌ +^yk7nv}b"u`/VƤwl)9`Nʇu;P1Sc,>=.\_w><;)G#D%|wpgJ;hrL *II V4xsطm}G'R|Cz+8k悗?(kt `s *—’cF_2x Qc^7UzpܘMiuGW^ Tp8НG3- ?XNb'rfd-|3GJ>~[!)%cHGt5ݎ)/^i"+'ޢ!ف464"+ *NIjs!>3Q`;ℲW}rg>JII+nriao:ᖵF{6}d +ز.R>rbMh"#rf[\S15{ `(:Ď~R蝊gy &lcI#TA-GcMHе?)'qy}jAW%l)a\A-,tΪL@$.s};:v#۳~C2]m܌ +JQ:b5Lw}鶂;Q2]i{/%J{g2[m׮j +-_];pqXa4{=t-UW5-s]Z?L bEW?۱,!K +w%+wŦi^ U%~O\ڳg5D +PA-7[sB19 ^ãe^vxD?>Zaf,bv5XVHZ@}wξJMie}|䎪ѐKA[j\ONzѪَ1x Z#oi] ,Mnbԯ%(8¥%:1բT#{z`pba[%kn eI +=pQ$c;,^p%Dq[ [+{?kť򊪎0Ul5$M9c_)ˏF(3fck~4&Wϩi0DTBÏQē55-NroXMbo9+NO^<V2; G']QlsU9_+n̓^0+ٵ)EcUgw'^(_[`Q)lN[+M [t; \\9#I8awNҐODXU&]y0 +tzZlm5q%(G4ɽ˫85^v[.s^m 9Oo;uSR&m5E'Cu;NΙ)o%K9Gv2Gcq0iEQ{vnDZ1395Oc~FojXrOG罟q,tw-ZDjtl./3l̺';oR$5l_I03O#YҔۅש*LvH;POko7Z!US񚮴ӆ%#҄{^ru06Ae왫_. ϻD]0L72v?ws a$Z7A/3]|9:ąZ0H3 {|=rL膭5yzɣJqxLWIkڙBQ}~9}Jh6h +Ⱦˍ4f{ꕦ݇!4!8ѩd,6B +endstream +endobj +34 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-32 -250 1048 750] +/FontName/PFTUWD+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/FontFile 33 0 R +/Flags 68 +>> +endobj +33 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 2538 +/Length3 533 +/Length 3083 +>> +stream +xk8TǍt&Ia"f"3 I$cfd0fDCJHȱ#*$2HFHRN Elڽ˾}a}{~x`AupzǺpITY> ssr#E!}Jqi0V%3-:VQtJ@c̵=EU{'G8|"^xo^ʔgԒs(]BD)4ڭ[k_ESжR^ӹứTwɑ=$Ҟc~ɔkHXúO +b` -$uxr(etʬ:N /U |sKs֩:vuj!V-2A};w䮪Rsi% Ghԋ_Ƙ ږ87*gll2X٦XjU']Kb] -S GT@T1Jbkޜ3=4zT"x~3/~D;LP!.8Q"ki[gnIo":*|Ssӝ(ku{m~VS֒B=xK=-S̯}-FEwdۖ]լ@5 +MC|dCh3$ xTHYC9|-hh[,Pq -//" wNl.ohЍL@iTMұ' ^Z3PCr>g>fK?SyP;x1d6py"m6B'jnL2֕ҞٖEC%_E2ņ*EGQFj[_LW +v<28}all'@sBl`Zpph2CT=ɝUu+[ȟnLEĝ3!=ÉvC!w}"7 |֟@ܽz> 1+>1lv g /_4p^QSz@' aӖ19O}xDZDŤ%DK-Vo)kp^xQ& ȝaa4^ IF c ^[5W9ʓM)l?I.Uq+5};gpe*Wks?M~\ (d@b2\d'XRt1Ժ +Zs>nQ;/$ƾʳ9Oo2.X]+|7EY8tjwb\rv+;Ƅg]L;T\f;>W?R~ӳ{lZ'B6y4*BBWRJC4nfdˢ> *[6>E(o&I"`w֗-| +sXN~a5n-Iyg/'dOS}4(3 +endstream +endobj +37 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-27 -250 1122 750] +/FontName/XQGLQC+CMR7 +/ItalicAngle 0 +/StemV 79 +/FontFile 36 0 R +/Flags 4 +>> +endobj +36 0 obj +<< +/Filter[/FlateDecode] +/Length1 712 +/Length2 1508 +/Length3 533 +/Length 2043 +>> +stream +xiXYi("(&!$ + +QLXd1@IR!idiâ((QhQD*.0YDq=7Tss/ʌmoS cp*"o`@ +'cd(@x[j2G P/ 0`A"#`.TE1!X#V GEA8 WUׯYk#!81a6Sg&''~t5X 'F_ n8DBɊ +AX@`4B7 ^j"_MK' Q[(]#ܹ)Iᴷ^ҎǺ}qkxǸ%9׃&( +6ˁ?ӮI +1 Ef&Uwz%VunkjV(,.@}c%~,/quҌzkMa'`:]FڶL1-{bk{Bzׂ<]='xE\NoFB[ lMte_3sZLk|D1t3|ELȭsZmVLnNCAk˦5rW);e=d+Izr"t"{<~%3HPGd*47$FA-?w®ejLqi:Ɣf)(;4ޚf7Č쬃OF?Xs/zBwn;@@`΄.M?Zk=,^p}ak0mC<[4X[%r{G*~/{T4dLRE<IK{}pm3N)eԏ~2=%ҽŸ s6[(XSʘΠD>[f8)6bز3"l(/>B3ڍvI\O>{RlE[_*~9Pslu[ș9p3v*cOazG/nS}ZZLZ|.6uN 1ÒFJ +Tu!nOFLvc_߬A%|i͒ +Y8/S_ӥ~"}$ R|{SpzG8p_Tj9|'|0v2,B$ϳ$#%1ʠ=O7<{֭Yɟ#ESdr7˩ cT둟\ar[ۃD 2">) G ]>l +endstream +endobj +40 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[0 -250 1171 750] +/FontName/TAMMEO+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/FontFile 39 0 R +/Flags 68 +>> +endobj +39 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 1820 +/Length3 533 +/Length 2360 +>> +stream +xk8T#bF""L32&3QKeLY3 \ƈ$P)T\"5$ +ʥB'~N9ywz}oUQf4$@, +d2 \]݂ R8 eIFP qv7m/ !G.ye7Rc riTudMx".!5*_5R߸>G>|Z|]ᛪme6WvUJO 4p*o,^<ֿP^,X_<mf&GWa-6Yz>2N)n^*VM9r6CDžY訵}H4z"#TsT,Osfۄ9PzY%9e})$dw],W;,a2#cOq&ٌ^_HMO,t1x)D]+_*@^ot_jCh `%4~퉚 o>P1P?9_oPlbC)c;l +hzF5GTUmB}G&rp)~ǓZ] eE<3}1hj`/5}-U&]d'fw|7syFKp&" 0|=}|UI`Oy9>+ZmFjmwpMRP1H323?~˦cm:`!,^0i{β4q.w'bMWq_MɪC]O]':}2b.ϻZ'j[k[g']b\ŧfEg;[g"T+E"CIj^_h?Uy"n6ޜ.}HC Ptke7.7!/zG]96KC9/\_zȐnQQN~Fx6e\N} (=u ؅twIs.gōҼGv7-'.n/0誴96x9zvn'YE ~&WX +=;;!yEJp}3zK?gr|BD۞Uf J=6~ަPr׊:r9\3Jn~X5[x|®.3 k|c~O?jp ;b +5{^dO,_-)_SQ$FoS"t\jd$qΈYF[,IpL>3Jrqwk8#D5|~-(ԜK2)IPnwRp^ݦޝ:ZN  jrgº<lWij{wovY¿SN; Xc"-NJh7IhKcy8{T⵵P4cÚg"C&nbR?M7F=dE:9~$ֆc"5OQr}im4jTO\XНѱSˠߙ"5_y#_tŴ濼2A +yQ?V +endstream +endobj +44 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-15 -951 1252 782] +/FontName/RJRYYM+CMSY7 +/ItalicAngle -14.035 +/StemV 93 +/FontFile 43 0 R +/Flags 68 +>> +endobj +43 0 obj +<< +/Filter[/FlateDecode] +/Length1 721 +/Length2 599 +/Length3 533 +/Length 1109 +>> +stream +xSU uLOJu+53Rp 4W03RUu.JM,sI,IR04Tp,MW04U002225RUp/,L(Qp2WpM-LNSM,HZRRZZTeh\ǥrg^Z9D8&UZT tН +@WT*qmKdgaqn99~ A!S U[PZZZ4<6Ԕ\tYϒĜdǼT]C=cSDf[fEjJ@fIrBZbNq*X<5/);D?+(2Wɀ̼ʂTj0RQfB!P!Xh%d+$$0_Q LC +FF +F +C2 KS=]L , ɥEEy%0 ԊdsD3ud&|9pU)|׉s77Rd(wirkSsk|^1=6Zsas_y2-3%^ Jړ}9_+l5_ ?ܛ%a{TĆ6ႮԦ,؉v3k02<[RZlez_ 6n? qܸs)_Ǵ3٩F&dL淖g2)D^c]Q,'$'Z㛾 l>uy;Mwָhl49"K]9h\8?Lj#oY~8qo{ jVf4HOc_s&z򏲫۽;|]}xNezesC&Ꝧ[֭fS!ES:ZK8sJhOOʝv2+ìRZޖ(ynY҇3 +=m^un)[TZbeQ9E%E\\x +endstream +endobj +51 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-30 -250 1026 750] +/FontName/IAEDAF+CMMI12 +/ItalicAngle -14.04 +/StemV 65 +/FontFile 50 0 R +/Flags 68 +>> +endobj +50 0 obj +<< +/Filter[/FlateDecode] +/Length1 727 +/Length2 3040 +/Length3 533 +/Length 3590 +>> +stream +xynH( AԁffFy HH0"#"Ձ55e/(++)@]\IJJRjcxHQQHbF~BZ# H  'ݐ(,@O,#P/RHG,:@}CP_43װàp`pD$h@Ɀ[!(_]#" kc=H,DVKG(a"=04KGb6TW@?j?)Q$#CG+v}(І"`x NC +Ue@X^W-uiT(*Rx<K?u4$$Kt&P99 !gη9rA iiĮ:ɵD{1NrK7q2􌲽}aGu$S>I㾽ХuږP~xW϶G=w⑪It7F8+V;Uq*иb6|^mSmLrHIL|I\x{`xFRԽ0j@m>H! u"ջg%&ji߇X3x:RBX~p.鰕̳>.wbuK/3n;ʰ~υbw9e! I2T\˃vQ4.\-Q\eͣL %\0{c~A9+X}޶~ jp?w2}.W {;{u>g[K*F +E4[G6˱6~MW9~ޜ)獏`r#r@NqDD?X>(=ԺS.j:ˈ7É̕jg)P߽3eW]U^B]:عu%u`Hy3<_9do]6\+(O(ScL U{xˍC6}څӫ*wSl!wDkS,9.AꔮVg:}xbrIF {x-xҊKF[*h!5 ,KImƳ|0uZ +'ɠ&욣*s֖ZjSK_(C/jxܥ\e$dnU*Hw,3=]MIJy nck&XoeD4gۗiDm0qq'd/"/k6s׼x!*X.LgU%t3AoW Wf|bҴ`?vOR"&xb\ner9uÊd{V { ^&#Uz0ޚ3[R^avWT]oL~O(VP`x8oi~[ݻ0fr۾4?砪YM?ౝ4a +,74Wh"+Izm!SYIn緆jg?%32 +=#ǓJ*TCu3P| %m&0\;ro +w5 =-})e&=V)jNJA]ݱIߤtZR0",x Ri;>S/w/l8A5D^AHY+߫G=4YO ε ̏5%s7E <9(U +kl;x7H 1Aog|Gvz޲,42vg_ǨQSA?HF÷@r߱YN./1V ~jD 9#mxܴnM֤Aߣ|[=db2 >OS},WHARj[6>0L[ y{ lv5]9(Z諻hdP0E^g*icndr.Tfv#gWt*pAi6ʖepSf93_69Soy_\$(q)*nw:{՜"ɁhAv#j3/#26OY} b<+ +젊Mg2M~Nb1>t6MTaBxĀXq '"}鴖@)'#LU]jf7]uar 5m'͎INO(i( )]q9 +yNHB?WT`A`͆)yX~tF8كEOPk?LY%l#Y.MX"z#.pbma')?1IFvi_~>U?( CIUSpYd@@·߈tyѥ 5UVu^ԕ!_(,/uskoc'?nM8Z o,ќ:}' f+;tijDq$Xwf ñ\L,f eV ~aC+ZZRt +O +2핀-`aRbCC +Tȝq}E˫p"nt%ޮW1nB6?yRoq.iQrXH3=aI!(‰S*]ظ 9h]-~Tv@ym< +\%Pnbk6f_S3 jnC "+K1?Y| f<Ǥ_N_v9-_٧Y > +endobj +53 0 obj +<< +/Filter[/FlateDecode] +/Length1 724 +/Length2 1132 +/Length3 533 +/Length 1670 +>> +stream +xkTHQ9ճzK 44$\ Lfd"bUDTjEZ˥U*Z/UE4BmWiuuu|λM3 r`"&p@ n| ^`SD(NeH>[Cպ1 +B!Q.&`J"G*wwB͖mَA {c&)'Ȥ0( +Dpj:vGuSB" +?|]co +kwZؕD_ў:vϸyXڥ'| +#s 7w5u_Zp +2%-x䗷zSC5z9@鉣?&F~۴^F_ 2> %3XziñCscU3ݷc'5Mfߺ.o.ݾrg]ٔ墢w{z_?0$H :s$wD:Mf1 S]i!\ϙs6hg֞b5[[mJQ ̽ QEe؎+ 8.|ziz>Q-{nKǚ׋-JDq3Ͱ[)F3Q %q;f6k(aV趬Xυ|p?nPՁ>L/*~ajzZya]K6C"9hv1努e1"zsX"wϩoM*v dυYsil˒~ZkŶE4aLyh[ra": 8qX&*DIxJ&Np6ҋhύ#ZyPs4:ףO<4I) zUGc^%nkZ".{V~m:{u>1HD +endstream +endobj +58 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-163 -250 1146 969] +/FontName/RKAXVR+CMTI10 +/ItalicAngle -14.04 +/StemV 68 +/FontFile 57 0 R +/Flags 68 +>> +endobj +57 0 obj +<< +/Filter[/FlateDecode] +/Length1 728 +/Length2 1814 +/Length3 533 +/Length 2357 +>> +stream +x{8T%aO ːDD0R2f03&)*0;J)vKH6xPLڝ<~hz@F Ġ(%{`1#ttpLȆt"ƀ(^KS3KLqȯ- b$"AM^o]"Lg{GB/RĄ#?8f(͑Nb0D:HdNeoψaL#cSqn6,,s \S cnl™L^:O^aqJO3er]ŮiE*=RwfQ$>v ҧƥ3.L^ [M^Pƭ萚?(%)p촟9 Sk.7 M?h)[^_z9Q Ck#^{j/ZxNM\xcHc4k>\}B\[a>: +j)7hRdKg/vy:3PïS~?^1T=+|7,v)Pu%*&p cƯEFozAWz9T`]ؗY~syA>4vsPU؇]xR?J=ՑKZ8@?Uٮ[ #ѫ̽|dԨf_ueNۢWWSCyVv +,\z4;q biǻ]I:GL}9zC9~6jkyb "JoE*5Z%(}aRg*H^[![mv-䧫$qi#{VV65۰X_J777|zs32c:J%>Ʒ7ԫj{QsL/2یSɧ}CX6nlwٴU"Rc +Zz(]='+ݪJS=ܓ}\6 +fn (2.ǽ)^ P%l 'rs&|aޥ rZuLU7q*^5𱳜sڴP& $dpbrz%/ƚEe1ed/C]Tw.ԌjuGQז7,{w!.~,PKTlTn,'@k9"Ż1v=ԩT'ڑ_jZwgsDƎovqHc\߲Lk~ZvKR;Zm̚E=;4qH:8.ɫISz[[H229e(x<izt1ֹނ釉#09)_~t~%rr*D|B66#2) ):JiLk=ڕտW#TF zV8.gla{t6`X7|9Mq35.-jӶE`˾;&c{rdR兆C%[/[Qק4r!tn~tBЈˎd&<I Co}h +[`WQ&oF{|tu [wLRn5#!ΙO)mwߕК6"V߼~ɰy!?b +l A Y +endstream +endobj +62 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-4 -235 731 800] +/FontName/CQTQCY+CMTT10 +/ItalicAngle 0 +/StemV 69 +/FontFile 61 0 R +/Flags 4 +>> +endobj +61 0 obj +<< +/Filter[/FlateDecode] +/Length1 719 +/Length2 10142 +/Length3 533 +/Length 10697 +>> +stream +xUP%qww6.ni]76 4nӸLssLTC˕IEMQLޕ *`ebaAu63rr3r5Ž 'A@:8z:[YXhEۙ9[\-TL\=a[[?>q(92! LL\fV7wp+m +rϒ_.?I9Mm=f +3K ws ?٬V7# `jlR ɛZ*jdke"loak`WE%dϴ3? ETDǺUl!g?qm0_?m4q{S+{ %;7#;bcp25{+' Ϭ gln9fff&*Jgk8,8ԴAoA|j\kq-;>hm|80 o~Np3eNHu%x]# +)<]dAT0N i3w'~,nT\}9e`ABA~H1R$yLk=:) ++p +J^g:$rgsb|>4.5)o{|7ԺbC%P$b;̓&EP~u3k(i2,Ij%{&?C;Nݘ"6CY \?ν Y\,}}m2O-ycW +Bgmz'Hz%^y92rA4~*(rg<'b УY'O{fT$0*Mp9I HT xEN_PbtXxM{*oQ=yW`f!FD.2nWҭ L$~.G;#O/.1/onA5 d}jv?{[-i;(Z%?rQ\2PlXD#F=1d| Kn ]@n cFY_expXI`lQb(ua֨w|J1+b@J˛|&+H]g b҂$b7} +A{9us\.(x9]ʴؙBаv)2raNlLNYE8Ӏ9pU*+Sٴ)MI[C㯲?/o+xz*:&7͔$Ktͩ99yc+F!h3K&LγhI!`=jяKGrg%jQ䞉~V<{U Cn|AUhY@x2JI ;D4ieYgx)=J +sWQlAdQlr, N-E0,-5Wcs<(8ݎqHHE]COf? +xc/ G\Sg^<~a"1i#rmk)'GҬ)iD nq5 VDU>wtϷ41WĎ@c-$L74bc|+=|2*? 3x|KX*.=CDK/ hoj\X PW |P;f*˘o"8[uz'X5/.{"@ d8|K|$ڦp5XAl;ښb0868x9%y:#pd%2/q'8l)t +$"%<ЏiFvhQVGRXUVLgJ0ƽ[y:NL/3d{+4>y%%E[[c5ƓO'^4 HGsp|ھƢ-md=ghJڎKen|wi#`c[ӆ#[*4.FjaXCvxk#&PP_ośԡ%RZ~;%#/ l/SbnȜ{xmKFlW.*(ՇEȓ A wpX90X\ o?6))<ѵɪ(m>>:;R8^R7":9yç2@{oQVr9rŘ2r:.yDWxbFf>pv 5wpk6z,v +LK-hC,J뢒h[Ktevf.qWԊ<+AЈ1Sd:V2hHS]"bEljf_+s.J{TgphSEYw#<<7@dd*o&ڭ~/ *=`Rm6lj5G0OVV4FԾ~ǧd ~hyus޴WDะV>U/nV|s׽dHcϯI#?_`K>D|P3[Mx6}8Լ-Փ ]X^JCq74YuYH3Ж <[:Aݨeus϶N(;X>BdZ('<(E5ӻA!LrNaٵ:炆I{*k(:8dk<',d ? VnMo$~쉎O2n_5@wGoa +ϞMheqMKr0qUpV։Ӂ&F[)HG'Cf +ى= lRпl2[9A7KBwΡVezSiJ|wd4C_8Db tzNk+4lvȄG_ө ;ݸuo俻L__!HeSSLPWư~?o-z 4s̮j#8o靟1#lR^d>G]!!ڽ=z|tqQ+"f^WH vXZ E+JN7?)HdAhVC QjjhdжM}>i4 +pB@,W  $4'C$ avf~"l69p!s#9H$[*^}zLE8ϯF=cVUs,^pq/qZ^9#gRhߌ!Ӱb.edUJd$SEt^j&qeGvn/T@{cg[Uc}[."!59l2!,l ew=,=xW_pL0َtoƽcR BG] Q?S*dF&wJb$ɀWu;@|Tl:GtuC.fn/`MT׽ּ(ۺ_OlA&>|9pwmKAemi>Mu]soaO[3 td3H}}+װ.ZV}pK`f +|{^p;q2 +‚WzűL-W--G>i#$Xh{>32/W^jHЪ&_]b~kF>rUSF٭.-8muǚ $&r"q}1fy10oP[ +$'g-(-8#Kk%Rq+e{Zqͽ|)&Zަ.l+m(#_t@B(¶)gmY*^Dc='=$mA#]S;C K7H ָ!l;n3FHgjnLCe)umFBl}|lʲ!YY g=wsfV @"K4pQ;9J^y eb^ W\MD^ϣS+Wc" ǔpfl?zR>OrQ'kjyhYT3r# uHexpᖅIP=1;|F <Rm[Yk&M6rOZN_|ScKQQp=?ƄZQ$]fjcmKzYaXgf۠u! +{+A :^pZ^fzSL*ϥRuH_ũCa[֓D_!E'spcmk oiRQ5 og!xfqQg[G1eކZf׏yc8^Z-Kѱ,va&Y2l`EKuSТTɑ1šh3jL +ߵ^bTR8qI@TЎYnZ_Kq`-B`i^o|:[N*WX(Mds ZtNfxqcXrτ<8-gy;v]rY+FZ N +KrtP7xG'z:\$"dH)y_>[5sxiFDT,d:qټ 0odqqۤ^Fq.!,P_KUOG-.dG꛷J +Zy^ FA i=]'Zh܂;8>T;E;9iNtQ|A𦠉nOHO'1]SUb՚< l|-Ч3-X(îaEWwx|ʻ\< +~E_x^yBtg鵆;o{Kwl1ao4BKDywos]tJ=I)PY:w|͵oRf0 ذiep\ ' iL}^ОQVdUpT̏*7tdʙ:OD +_ٰ33. o,͋EϞzV7v5ұˌ̦#gY %cb^/^C8>L{tfI2 xE@$bΩ{)UfR^ӟB@<4iRDMN\pt(,Q_~ZrgR OOzB1 SKwe⮴#ٯ[}"QBe0r5e x=PlXAb4PNAV]MAKb}C9hlj}23u0q~FiW,ɦ0(B#n7vq^ >P`V2?Q /fUwoԀ417VQl_lNuT[eN瀢Tm`̟L}[AԤ|62QM%H( >|"or}J֝GXo#+gUgㄸACF2zN{&;rJ>T~ilRN{~H>u*#> ǔT_"zf\:V»IhδG\Hgb"TQdg*"m+A$vu?[+,{k׿[aK+se?A3jƞ9ˊjp/G ȃܼ6zͪzEmBzpDT9?y Y3IQNu*4;#x&yi}dRA$ѺHM@cq6 +UBg;Mm9w^H$7-.g +Fk 50Ohm[J X~14-% 8)b.:+^N` 7.!)l7YxcB3\֝ +ul: RLIC&9 KP\WEz璎?4E_|Vʇ,ta[$ͮ(ؚ}C(?#^1%@ɆQ}tZA(s܎I!{B$f G.x |ayv3z irw9-~~^6-/(xѦdZt0owr +Pey*~BXW`e6cK>"09x {m6k#q 06X¦}$zj{T~n_e~'(Y,{\倥[Җyj1+w5wy +s[tp^t ?w^@dˉɿ̂TBP_$=u`nˌ\]UW&EMnss'B"@,:V:c9>i˵z;{N*ZWn:@it=3fnZJPy'^(T>3W^q +,x;UحF'b헓Uy-c,:{)(Q@jm[-MO8mJl' rFbk$46-SrGyGfKЖx";Bi)JrW-Ě0.ʟE׋8׃xl %kݹ۔QQUD>w0CIx\ܺ6#5_pFG`,XZ,V ]K¹~ft@3Y/}*ΩH QO19B80$i#ffټ=o>іPx+?] +r W/pQ$k*j㯧fP^UxW*Z鞾J|+[^VOF$h=:+"Ep逧~W/Kɿ #KP,qL4\*d ئ:tAfH_/tjHh=F2'ZN JpTǎ@/PC{領?gk0ڠ +6s>Xwb!z<R6&-ڂMCIF:+-xx 32qS|ݐ8[U>{{(ݔ |؁1%(D50?Gw\>@؊}w$ nغ;lsb>¹fWޑ Sh{@r^bmmpV 8[ +.]*f̖u=K7cQ < LU~26-~&Jj\:Hi1K2 +LQUOnp{UXLh}RW!1&|&<\>ZU0%_ qb & [Wkݯǣ q +Grqg1M38ޮH896ʕ'F;BѣN TCͮ!!28Fp%+c^^"ص&F!뛯_j^`>LC}?6pa ݜZyDBW-O|0&֘T9m1t(SCNB4_;RI|U8 RN_&uEڷ2'fUeN=9*uI]U8փ.ԙe!D*͝)'TO_-;Lj)s_C˙﹠*g +cW?t`7_ΘEw)=IJְ8b6.~Zϓ/3 / ATzz*'*y4u/yA#`=?˱Iژ^r[-8b#W@[K*hBI4S dSPgU2k{ڏMO/?Lbm`RP JD!9G :0wS<@Gw|yö&AtP(I5Fo՚&M@ӄqv2ajEdBD!㙏URϕ{oC/0Ғ_GƧ<\6F,7ѭG +endstream +endobj +329 0 obj +<< +/Type/FontDescriptor +/CapHeight 850 +/Ascent 850 +/Descent -200 +/FontBBox[-62 -250 1123 750] +/FontName/EVJXTH+CMSL10 +/ItalicAngle -9.46 +/StemV 79 +/FontFile 328 0 R +/Flags 68 +>> +endobj +328 0 obj +<< +/Filter[/FlateDecode] +/Length1 722 +/Length2 5038 +/Length3 533 +/Length 5592 +>> +stream +xUT\ۖqw N + +wwww¥@p 4@pNsoK~{s@!vȻ8@@0@FMG0d< V0 " R^v>0/07@jg0˰H9C<6V.5+=9 j@W<O7 ` ` `pb +K{ |0?s).N~0Sy53뿡{VP'8\ݼ`+w/85 j#bpyP_X +Z9yB!.࿃<O N9}eC]EؿVP/5_<. |oɹظ.v ¿SIKps87 _z.Pw/,K@HOs3<?k[ _ lb(;ۥEKaBBLAX4E+9Ee㝻6R$pЉQj#(J 1t6ښr }xE!߸];'|BYEBH}U:p,ϐ:DmVK0d +cz;®!X8ʶq.f3 Ϫ\3H#3 I=+OEFԬ^4\T@vt Iu{}z.ԮlWp"v4`wsجIZet汝Wl$uzIȎt5۞ۨ^G%}Trg_™o 2Dv>}Bu| ѽJ(j2Lҭ1Ѩ8,Wv;w8]1^e|Y?kъ=(`WuI5n\vo%#b]@򵍡SC::99R+k3"$؋/C$1ƯM{ +d +?dnw@2ƪ fŊswY&Iuxe9Hx" P_AC| P_rv;߿i8sCI[&eW7;$ 2hOuƧ%#h r +A_: K0M1M0?6"7_4haݟgT=A[lڈc.ޫMvգ3<=*+t0rdL!.6*Φhك/AΘ6!",xgEztW޸ptӶ?'ffb U`δh0$Z#ۓa^ =09m.r[ʠ@4:FɕmU/6ihҺ&ϓZ~u-O6O*GrKlgVR8ȿh)?L.vp)1FY"Kk{'Dr_= qbi\.PO%r,u8߁mI7u=~2͗n)gP"qiKκ[]uw1{962I HWܛ*z@ih|?,>$@ qΩ24wT$\Sd#$Bȭ7\/u-ƨsO͸j7|:}ڤ [DO EqN|m[X9dxl]45K&$`}!k:mAkŒ Cܺ^`zQs%8T y}0*7EoH؆V5ᅆ cKZ1Pr—:a݅SPK9<.)nۗn+JG}~g=ϼf+{ELAy3qX2·F,pStajߝ3Eɉc9"61AkWėyX{$GG/+>)g}["መu?J)dM^җ6_U$ :\a^6U?IylOtͤ6SI$R&s>-͌c{LITB}NVx}Jh?TvK%c +Qm`!7gjKZW@P B,{A!Չatd9Jo$G>:9S1PgrRiYVJg/BdLfl- d}u+y);JN: :JוG"Bu|=ƩBvxj >0TcokDiۣ>1Vi-_w7L5TB֬Dfp"^e]Wģ~=q?,^i ^a=et+\1Jb7HGpjfUJ|1m6viŐ.iG} +#)ם?cM,9ԣY{u,(Et:ԋւ*&VXE4b4}S] g5(u-~NQ:ap >O7Zq'J,Xׅ-ɟh"kz0p36w}CXAf!parCD7}ůęRIO霬^Q­H㚇NA`og*~Qᒭ3FaT):bԤ<*=R{cF-S8%@3`YgX\㣨`~I>ƃzyTɋDLtFcc O>7 ym*~a@2˽7R@Z嚟8d>X ŏ,o?xum_՛Z2"p{f!5J㖪\#ߋ4Q؎6AGbg4(Bp176vE.>H-0mΔDrJ6κ V27rDd;uó?֛Z!<̠baտ'Oa U]t`QMyOS$;, ָ?7(ZAn<Ǭ{>-&w"ۃAd JOz/],VJM7 +i_)у~t6Ouֆ3l_.ߌwܥ|';SgM6i"-H%(.w'3uhr*F?dVxCЇZH (|6]A۬A;FSj\@Tû +_oeH +ʲсsurZ֮BJ TZ +Es+wqa-nFx|TArMtIQH _φy)7hNo z-tu +aLy:Ä!{,״Z.?0mB<)N?Ҵt O48b,jRݞ+dDJSTYC0tR\ʾMckQB)as".j-8|q3ʭ 4WZGe:;%H+F弼["eOPmfQ'M<Fa)FUfJecɚ~ d]m +AW󠍁W:ǰڗL#jLˆYs| hwKI('=+ :(QyJ#I'8JE't8~QOJ*|)O +-XS<+A@LҜtW?v8涝/qцL|q0FG>bq" mJz=dX%$ZCC`X}L!i>劉ҫeM15M@W +VoQaB F%RloD%SDǾjJ2|fM4i1̠lhVZ4rQQ>emQBԈ_>@A.ā!*5^X oUx^~.6-L;xvJxB~%[LM uX_G@bdG\щyz 9>ث:M;H=J2ub8džC$x_s,^Ĵ=5fztogU(pkqRL#ˢ m-F ~'圕^vDVj4B42O2rFɮt?os:Ǵ6bVZf\6<|냍 jզ0>tG݂о߁Ң鱿[OzM |,aQ|Kqw,xB]PRp֚2kf](Ϣ6GyQe j$?a@T­R0&, $p|FW +?P qhEJ|^>6ؾ2 m;{.bo=\kMh,ص!ǣ< 9s6-nL,]bEii=ٺY/N" 7Ł:_p{ |cY,4?TD3N K>vO|)X呣F yc.=h|B+v8Ҟn6G'[1HMҜ;?F5v}̽]Z.G<%-CSo[/{R:U_Ci,q78p]P8ͲUn@lYL,ʪd ߅yV׾ O +F̈#( "Ň -gb3՞C*.kذsy ?Vw.5l62 2 +3;@N/}wz +2_i@~n/KG rE` +*;GR 9Pu VΈ&aL!Ĕeڑzhsgr~tczEm _`4K5dw@cO`D04o!`Bj7>dņRc.dmn.XEQO>U͑-#@X¬;FYT>hGn?fGgH7\69]_J +ILBB)j P>>,krژ|ڧ54 TnO$/AI;ْ?D_iyjIh͚ǟj1[1hFw@_6ͥeG(^80 >KzVTr//?`:[y8b` +endstream +endobj +1 0 obj +<< +/Creator( TeX output 2008.06.15:1852) +/Producer(dvipdfm 0.13.2c, Copyright \251 1998, by Mark A. Wicks) +/CreationDate(D:20080615185350-05'00') +>> +endobj +5 0 obj +<< +/Type/Page +/Resources 6 0 R +/Contents[17 0 R 4 0 R 18 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +21 0 obj +<< +/Type/Page +/Resources 22 0 R +/Contents[17 0 R 4 0 R 46 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +48 0 obj +<< +/Type/Page +/Resources 49 0 R +/Contents[17 0 R 4 0 R 64 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +66 0 obj +<< +/Type/Page +/Resources 67 0 R +/Contents[17 0 R 4 0 R 68 0 R 19 0 R] +/Parent 334 0 R +>> +endobj +334 0 obj +<< +/Type/Pages +/Count 4 +/Kids[5 0 R 21 0 R 48 0 R 66 0 R] +/Parent 333 0 R +>> +endobj +70 0 obj +<< +/Type/Page +/Resources 71 0 R +/Contents[17 0 R 4 0 R 72 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +74 0 obj +<< +/Type/Page +/Resources 75 0 R +/Contents[17 0 R 4 0 R 76 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +78 0 obj +<< +/Type/Page +/Resources 79 0 R +/Contents[17 0 R 4 0 R 80 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +82 0 obj +<< +/Type/Page +/Resources 83 0 R +/Contents[17 0 R 4 0 R 84 0 R 19 0 R] +/Parent 335 0 R +>> +endobj +335 0 obj +<< +/Type/Pages +/Count 4 +/Kids[70 0 R 74 0 R 78 0 R 82 0 R] +/Parent 333 0 R +>> +endobj +86 0 obj +<< +/Type/Page +/Resources 87 0 R +/Contents[17 0 R 4 0 R 88 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +90 0 obj +<< +/Type/Page +/Resources 91 0 R +/Contents[17 0 R 4 0 R 92 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +94 0 obj +<< +/Type/Page +/Resources 95 0 R +/Contents[17 0 R 4 0 R 96 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +98 0 obj +<< +/Type/Page +/Resources 99 0 R +/Contents[17 0 R 4 0 R 100 0 R 19 0 R] +/Parent 336 0 R +>> +endobj +336 0 obj +<< +/Type/Pages +/Count 4 +/Kids[86 0 R 90 0 R 94 0 R 98 0 R] +/Parent 333 0 R +>> +endobj +102 0 obj +<< +/Type/Page +/Resources 103 0 R +/Contents[17 0 R 4 0 R 104 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +106 0 obj +<< +/Type/Page +/Resources 107 0 R +/Contents[17 0 R 4 0 R 108 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +110 0 obj +<< +/Type/Page +/Resources 111 0 R +/Contents[17 0 R 4 0 R 112 0 R 19 0 R] +/Parent 337 0 R +>> +endobj +114 0 obj +<< +/Type/Page +/Resources 115 0 R +/Contents[17 0 R 4 0 R 116 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +118 0 obj +<< +/Type/Page +/Resources 119 0 R +/Contents[17 0 R 4 0 R 120 0 R 19 0 R] +/Parent 338 0 R +>> +endobj +338 0 obj +<< +/Type/Pages +/Count 2 +/Kids[114 0 R 118 0 R] +/Parent 337 0 R +>> +endobj +337 0 obj +<< +/Type/Pages +/Count 5 +/Kids[102 0 R 106 0 R 110 0 R 338 0 R] +/Parent 333 0 R +>> +endobj +333 0 obj +<< +/Type/Pages +/Count 17 +/Kids[334 0 R 335 0 R 336 0 R 337 0 R] +/Parent 3 0 R +>> +endobj +122 0 obj +<< +/Type/Page +/Resources 123 0 R +/Contents[17 0 R 4 0 R 124 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +126 0 obj +<< +/Type/Page +/Resources 127 0 R +/Contents[17 0 R 4 0 R 128 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +130 0 obj +<< +/Type/Page +/Resources 131 0 R +/Contents[17 0 R 4 0 R 132 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +134 0 obj +<< +/Type/Page +/Resources 135 0 R +/Contents[17 0 R 4 0 R 136 0 R 19 0 R] +/Parent 340 0 R +>> +endobj +340 0 obj +<< +/Type/Pages +/Count 4 +/Kids[122 0 R 126 0 R 130 0 R 134 0 R] +/Parent 339 0 R +>> +endobj +138 0 obj +<< +/Type/Page +/Resources 139 0 R +/Contents[17 0 R 4 0 R 140 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +142 0 obj +<< +/Type/Page +/Resources 143 0 R +/Contents[17 0 R 4 0 R 144 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +146 0 obj +<< +/Type/Page +/Resources 147 0 R +/Contents[17 0 R 4 0 R 148 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +150 0 obj +<< +/Type/Page +/Resources 151 0 R +/Contents[17 0 R 4 0 R 152 0 R 19 0 R] +/Parent 341 0 R +>> +endobj +341 0 obj +<< +/Type/Pages +/Count 4 +/Kids[138 0 R 142 0 R 146 0 R 150 0 R] +/Parent 339 0 R +>> +endobj +154 0 obj +<< +/Type/Page +/Resources 155 0 R +/Contents[17 0 R 4 0 R 156 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +158 0 obj +<< +/Type/Page +/Resources 159 0 R +/Contents[17 0 R 4 0 R 160 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +162 0 obj +<< +/Type/Page +/Resources 163 0 R +/Contents[17 0 R 4 0 R 164 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +166 0 obj +<< +/Type/Page +/Resources 167 0 R +/Contents[17 0 R 4 0 R 168 0 R 19 0 R] +/Parent 342 0 R +>> +endobj +342 0 obj +<< +/Type/Pages +/Count 4 +/Kids[154 0 R 158 0 R 162 0 R 166 0 R] +/Parent 339 0 R +>> +endobj +170 0 obj +<< +/Type/Page +/Resources 171 0 R +/Contents[17 0 R 4 0 R 172 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +174 0 obj +<< +/Type/Page +/Resources 175 0 R +/Contents[17 0 R 4 0 R 176 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +178 0 obj +<< +/Type/Page +/Resources 179 0 R +/Contents[17 0 R 4 0 R 180 0 R 19 0 R] +/Parent 343 0 R +>> +endobj +182 0 obj +<< +/Type/Page +/Resources 183 0 R +/Contents[17 0 R 4 0 R 184 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +186 0 obj +<< +/Type/Page +/Resources 187 0 R +/Contents[17 0 R 4 0 R 188 0 R 19 0 R] +/Parent 344 0 R +>> +endobj +344 0 obj +<< +/Type/Pages +/Count 2 +/Kids[182 0 R 186 0 R] +/Parent 343 0 R +>> +endobj +343 0 obj +<< +/Type/Pages +/Count 5 +/Kids[170 0 R 174 0 R 178 0 R 344 0 R] +/Parent 339 0 R +>> +endobj +339 0 obj +<< +/Type/Pages +/Count 17 +/Kids[340 0 R 341 0 R 342 0 R 343 0 R] +/Parent 3 0 R +>> +endobj +190 0 obj +<< +/Type/Page +/Resources 191 0 R +/Contents[17 0 R 4 0 R 192 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +194 0 obj +<< +/Type/Page +/Resources 195 0 R +/Contents[17 0 R 4 0 R 196 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +198 0 obj +<< +/Type/Page +/Resources 199 0 R +/Contents[17 0 R 4 0 R 200 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +202 0 obj +<< +/Type/Page +/Resources 203 0 R +/Contents[17 0 R 4 0 R 204 0 R 19 0 R] +/Parent 346 0 R +>> +endobj +346 0 obj +<< +/Type/Pages +/Count 4 +/Kids[190 0 R 194 0 R 198 0 R 202 0 R] +/Parent 345 0 R +>> +endobj +206 0 obj +<< +/Type/Page +/Resources 207 0 R +/Contents[17 0 R 4 0 R 208 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +210 0 obj +<< +/Type/Page +/Resources 211 0 R +/Contents[17 0 R 4 0 R 212 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +214 0 obj +<< +/Type/Page +/Resources 215 0 R +/Contents[17 0 R 4 0 R 216 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +218 0 obj +<< +/Type/Page +/Resources 219 0 R +/Contents[17 0 R 4 0 R 220 0 R 19 0 R] +/Parent 347 0 R +>> +endobj +347 0 obj +<< +/Type/Pages +/Count 4 +/Kids[206 0 R 210 0 R 214 0 R 218 0 R] +/Parent 345 0 R +>> +endobj +222 0 obj +<< +/Type/Page +/Resources 223 0 R +/Contents[17 0 R 4 0 R 224 0 R 19 0 R] +/Parent 348 0 R +>> +endobj +226 0 obj +<< +/Type/Page +/Resources 227 0 R +/Contents[17 0 R 4 0 R 228 0 R 19 0 R] +/Parent 348 0 R +>> +endobj +230 0 obj +<< +/Type/Page +/Resources 231 0 R +/Contents[17 0 R 4 0 R 232 0 R 19 0 R] +/Parent 348 0 R +>> +endobj +234 0 obj +<< +/Type/Page +/Resources 235 0 R +/Contents[17 0 R 4 0 R 236 0 R 19 0 R] +/Parent 348 0 R +>> +endobj +348 0 obj +<< +/Type/Pages +/Count 4 +/Kids[222 0 R 226 0 R 230 0 R 234 0 R] +/Parent 345 0 R +>> +endobj +238 0 obj +<< +/Type/Page +/Resources 239 0 R +/Contents[17 0 R 4 0 R 240 0 R 19 0 R] +/Parent 349 0 R +>> +endobj +242 0 obj +<< +/Type/Page +/Resources 243 0 R +/Contents[17 0 R 4 0 R 244 0 R 19 0 R] +/Parent 349 0 R +>> +endobj +246 0 obj +<< +/Type/Page +/Resources 247 0 R +/Contents[17 0 R 4 0 R 248 0 R 19 0 R] +/Parent 349 0 R +>> +endobj +250 0 obj +<< +/Type/Page +/Resources 251 0 R +/Contents[17 0 R 4 0 R 252 0 R 19 0 R] +/Parent 350 0 R +>> +endobj +254 0 obj +<< +/Type/Page +/Resources 255 0 R +/Contents[17 0 R 4 0 R 256 0 R 19 0 R] +/Parent 350 0 R +>> +endobj +350 0 obj +<< +/Type/Pages +/Count 2 +/Kids[250 0 R 254 0 R] +/Parent 349 0 R +>> +endobj +349 0 obj +<< +/Type/Pages +/Count 5 +/Kids[238 0 R 242 0 R 246 0 R 350 0 R] +/Parent 345 0 R +>> +endobj +345 0 obj +<< +/Type/Pages +/Count 17 +/Kids[346 0 R 347 0 R 348 0 R 349 0 R] +/Parent 3 0 R +>> +endobj +258 0 obj +<< +/Type/Page +/Resources 259 0 R +/Contents[17 0 R 4 0 R 260 0 R 19 0 R] +/Parent 352 0 R +>> +endobj +262 0 obj +<< +/Type/Page +/Resources 263 0 R +/Contents[17 0 R 4 0 R 264 0 R 19 0 R] +/Parent 352 0 R +>> +endobj +266 0 obj +<< +/Type/Page +/Resources 267 0 R +/Contents[17 0 R 4 0 R 268 0 R 19 0 R] +/Parent 352 0 R +>> +endobj +270 0 obj +<< +/Type/Page +/Resources 271 0 R +/Contents[17 0 R 4 0 R 272 0 R 19 0 R] +/Parent 352 0 R +>> +endobj +352 0 obj +<< +/Type/Pages +/Count 4 +/Kids[258 0 R 262 0 R 266 0 R 270 0 R] +/Parent 351 0 R +>> +endobj +274 0 obj +<< +/Type/Page +/Resources 275 0 R +/Contents[17 0 R 4 0 R 276 0 R 19 0 R] +/Parent 353 0 R +>> +endobj +278 0 obj +<< +/Type/Page +/Resources 279 0 R +/Contents[17 0 R 4 0 R 280 0 R 19 0 R] +/Parent 353 0 R +>> +endobj +282 0 obj +<< +/Type/Page +/Resources 283 0 R +/Contents[17 0 R 4 0 R 284 0 R 19 0 R] +/Parent 353 0 R +>> +endobj +286 0 obj +<< +/Type/Page +/Resources 287 0 R +/Contents[17 0 R 4 0 R 288 0 R 19 0 R] +/Parent 354 0 R +>> +endobj +290 0 obj +<< +/Type/Page +/Resources 291 0 R +/Contents[17 0 R 4 0 R 292 0 R 19 0 R] +/Parent 354 0 R +>> +endobj +354 0 obj +<< +/Type/Pages +/Count 2 +/Kids[286 0 R 290 0 R] +/Parent 353 0 R +>> +endobj +353 0 obj +<< +/Type/Pages +/Count 5 +/Kids[274 0 R 278 0 R 282 0 R 354 0 R] +/Parent 351 0 R +>> +endobj +294 0 obj +<< +/Type/Page +/Resources 295 0 R +/Contents[17 0 R 4 0 R 296 0 R 19 0 R] +/Parent 355 0 R +>> +endobj +298 0 obj +<< +/Type/Page +/Resources 299 0 R +/Contents[17 0 R 4 0 R 300 0 R 19 0 R] +/Parent 355 0 R +>> +endobj +302 0 obj +<< +/Type/Page +/Resources 303 0 R +/Contents[17 0 R 4 0 R 304 0 R 19 0 R] +/Parent 355 0 R +>> +endobj +306 0 obj +<< +/Type/Page +/Resources 307 0 R +/Contents[17 0 R 4 0 R 308 0 R 19 0 R] +/Parent 355 0 R +>> +endobj +355 0 obj +<< +/Type/Pages +/Count 4 +/Kids[294 0 R 298 0 R 302 0 R 306 0 R] +/Parent 351 0 R +>> +endobj +310 0 obj +<< +/Type/Page +/Resources 311 0 R +/Contents[17 0 R 4 0 R 312 0 R 19 0 R] +/Parent 356 0 R +>> +endobj +314 0 obj +<< +/Type/Page +/Resources 315 0 R +/Contents[17 0 R 4 0 R 316 0 R 19 0 R] +/Parent 356 0 R +>> +endobj +318 0 obj +<< +/Type/Page +/Resources 319 0 R +/Contents[17 0 R 4 0 R 320 0 R 19 0 R] +/Parent 356 0 R +>> +endobj +322 0 obj +<< +/Type/Page +/Resources 323 0 R +/Contents[17 0 R 4 0 R 324 0 R 19 0 R] +/Parent 357 0 R +>> +endobj +326 0 obj +<< +/Type/Page +/Resources 327 0 R +/Contents[17 0 R 4 0 R 331 0 R 19 0 R] +/Parent 357 0 R +>> +endobj +357 0 obj +<< +/Type/Pages +/Count 2 +/Kids[322 0 R 326 0 R] +/Parent 356 0 R +>> +endobj +356 0 obj +<< +/Type/Pages +/Count 5 +/Kids[310 0 R 314 0 R 318 0 R 357 0 R] +/Parent 351 0 R +>> +endobj +351 0 obj +<< +/Type/Pages +/Count 18 +/Kids[352 0 R 353 0 R 355 0 R 356 0 R] +/Parent 3 0 R +>> +endobj +3 0 obj +<< +/Type/Pages +/Count 69 +/Kids[333 0 R 339 0 R 345 0 R 351 0 R] +/MediaBox[0 0 595 842] +>> +endobj +17 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +19 0 obj +<< +/Length 1 +>> +stream + +endstream +endobj +4 0 obj +<< +/Length 33 +>> +stream +1.00028 0 0 1.00028 72 769.82 cm +endstream +endobj +358 0 obj +<< +>> +endobj +359 0 obj +null +endobj +360 0 obj +<< +>> +endobj +2 0 obj +<< +/Type/Catalog +/Pages 3 0 R +/Outlines 358 0 R +/Threads 359 0 R +/Names 360 0 R +>> +endobj +xref +0 361 +0000000000 65535 f +0000147972 00000 n +0000158284 00000 n +0000157929 00000 n +0000158134 00000 n +0000148136 00000 n +0000004048 00000 n +0000000009 00000 n +0000079121 00000 n +0000078937 00000 n +0000000913 00000 n +0000083937 00000 n +0000083751 00000 n +0000001906 00000 n +0000089176 00000 n +0000088988 00000 n +0000002823 00000 n +0000158034 00000 n +0000003740 00000 n +0000158084 00000 n +0000003993 00000 n +0000148239 00000 n +0000014634 00000 n +0000098988 00000 n +0000098799 00000 n +0000004109 00000 n +0000104259 00000 n +0000104069 00000 n +0000005055 00000 n +0000109563 00000 n +0000109374 00000 n +0000005991 00000 n +0000006967 00000 n +0000112907 00000 n +0000112713 00000 n +0000007921 00000 n +0000116290 00000 n +0000116104 00000 n +0000008867 00000 n +0000118638 00000 n +0000118447 00000 n +0000009831 00000 n +0000010825 00000 n +0000121306 00000 n +0000121112 00000 n +0000012441 00000 n +0000013451 00000 n +0000014523 00000 n +0000148344 00000 n +0000021645 00000 n +0000122722 00000 n +0000122528 00000 n +0000014696 00000 n +0000126621 00000 n +0000126426 00000 n +0000015667 00000 n +0000016619 00000 n +0000128600 00000 n +0000128405 00000 n +0000017526 00000 n +0000018508 00000 n +0000131257 00000 n +0000131071 00000 n +0000019485 00000 n +0000020230 00000 n +0000021497 00000 n +0000148449 00000 n +0000022278 00000 n +0000021707 00000 n +0000022233 00000 n +0000148648 00000 n +0000022975 00000 n +0000022340 00000 n +0000022930 00000 n +0000148753 00000 n +0000023665 00000 n +0000023037 00000 n +0000023620 00000 n +0000148858 00000 n +0000024384 00000 n +0000023727 00000 n +0000024339 00000 n +0000148963 00000 n +0000024965 00000 n +0000024446 00000 n +0000024920 00000 n +0000149163 00000 n +0000026199 00000 n +0000025027 00000 n +0000026063 00000 n +0000149268 00000 n +0000026906 00000 n +0000026261 00000 n +0000026861 00000 n +0000149373 00000 n +0000027636 00000 n +0000026968 00000 n +0000027591 00000 n +0000149478 00000 n +0000028259 00000 n +0000027698 00000 n +0000028213 00000 n +0000149679 00000 n +0000028946 00000 n +0000028322 00000 n +0000028900 00000 n +0000149787 00000 n +0000029280 00000 n +0000029010 00000 n +0000029234 00000 n +0000149895 00000 n +0000030545 00000 n +0000029344 00000 n +0000030408 00000 n +0000150003 00000 n +0000031294 00000 n +0000030609 00000 n +0000031248 00000 n +0000150111 00000 n +0000032007 00000 n +0000031358 00000 n +0000031961 00000 n +0000150499 00000 n +0000032717 00000 n +0000032071 00000 n +0000032671 00000 n +0000150607 00000 n +0000033928 00000 n +0000032781 00000 n +0000033768 00000 n +0000150715 00000 n +0000035161 00000 n +0000033992 00000 n +0000035024 00000 n +0000150823 00000 n +0000035891 00000 n +0000035225 00000 n +0000035845 00000 n +0000151030 00000 n +0000036620 00000 n +0000035955 00000 n +0000036574 00000 n +0000151138 00000 n +0000037303 00000 n +0000036684 00000 n +0000037257 00000 n +0000151246 00000 n +0000038008 00000 n +0000037367 00000 n +0000037962 00000 n +0000151354 00000 n +0000039339 00000 n +0000038072 00000 n +0000039202 00000 n +0000151561 00000 n +0000040108 00000 n +0000039403 00000 n +0000040062 00000 n +0000151669 00000 n +0000040842 00000 n +0000040172 00000 n +0000040796 00000 n +0000151777 00000 n +0000041523 00000 n +0000040906 00000 n +0000041477 00000 n +0000151885 00000 n +0000042253 00000 n +0000041587 00000 n +0000042207 00000 n +0000152092 00000 n +0000043545 00000 n +0000042317 00000 n +0000043385 00000 n +0000152200 00000 n +0000044847 00000 n +0000043609 00000 n +0000044710 00000 n +0000152308 00000 n +0000045614 00000 n +0000044911 00000 n +0000045568 00000 n +0000152416 00000 n +0000046392 00000 n +0000045678 00000 n +0000046346 00000 n +0000152524 00000 n +0000047110 00000 n +0000046456 00000 n +0000047064 00000 n +0000152912 00000 n +0000047691 00000 n +0000047174 00000 n +0000047645 00000 n +0000153020 00000 n +0000048981 00000 n +0000047755 00000 n +0000048844 00000 n +0000153128 00000 n +0000049766 00000 n +0000049045 00000 n +0000049720 00000 n +0000153236 00000 n +0000050525 00000 n +0000049830 00000 n +0000050479 00000 n +0000153443 00000 n +0000051167 00000 n +0000050589 00000 n +0000051121 00000 n +0000153551 00000 n +0000051874 00000 n +0000051231 00000 n +0000051828 00000 n +0000153659 00000 n +0000053223 00000 n +0000051938 00000 n +0000053086 00000 n +0000153767 00000 n +0000054020 00000 n +0000053287 00000 n +0000053974 00000 n +0000153974 00000 n +0000054804 00000 n +0000054084 00000 n +0000054758 00000 n +0000154082 00000 n +0000056183 00000 n +0000054868 00000 n +0000056023 00000 n +0000154190 00000 n +0000057426 00000 n +0000056247 00000 n +0000057266 00000 n +0000154298 00000 n +0000058744 00000 n +0000057490 00000 n +0000058607 00000 n +0000154505 00000 n +0000059567 00000 n +0000058808 00000 n +0000059521 00000 n +0000154613 00000 n +0000060377 00000 n +0000059631 00000 n +0000060331 00000 n +0000154721 00000 n +0000061125 00000 n +0000060441 00000 n +0000061079 00000 n +0000154829 00000 n +0000061919 00000 n +0000061189 00000 n +0000061873 00000 n +0000154937 00000 n +0000062754 00000 n +0000061983 00000 n +0000062708 00000 n +0000155325 00000 n +0000063621 00000 n +0000062818 00000 n +0000063575 00000 n +0000155433 00000 n +0000064453 00000 n +0000063685 00000 n +0000064407 00000 n +0000155541 00000 n +0000065168 00000 n +0000064517 00000 n +0000065122 00000 n +0000155649 00000 n +0000065925 00000 n +0000065232 00000 n +0000065879 00000 n +0000155856 00000 n +0000066242 00000 n +0000065989 00000 n +0000066196 00000 n +0000155964 00000 n +0000067599 00000 n +0000066306 00000 n +0000067462 00000 n +0000156072 00000 n +0000068394 00000 n +0000067663 00000 n +0000068348 00000 n +0000156180 00000 n +0000069270 00000 n +0000068458 00000 n +0000069224 00000 n +0000156288 00000 n +0000070165 00000 n +0000069334 00000 n +0000070119 00000 n +0000156578 00000 n +0000071038 00000 n +0000070229 00000 n +0000070992 00000 n +0000156686 00000 n +0000071897 00000 n +0000071102 00000 n +0000071851 00000 n +0000156794 00000 n +0000072712 00000 n +0000071961 00000 n +0000072666 00000 n +0000156902 00000 n +0000073609 00000 n +0000072776 00000 n +0000073563 00000 n +0000157109 00000 n +0000074506 00000 n +0000073673 00000 n +0000074460 00000 n +0000157217 00000 n +0000075291 00000 n +0000074570 00000 n +0000075245 00000 n +0000157325 00000 n +0000075938 00000 n +0000075355 00000 n +0000075892 00000 n +0000157433 00000 n +0000077490 00000 n +0000076002 00000 n +0000077330 00000 n +0000157541 00000 n +0000078873 00000 n +0000142265 00000 n +0000142070 00000 n +0000077554 00000 n +0000078477 00000 n +0000078815 00000 n +0000150401 00000 n +0000148554 00000 n +0000149068 00000 n +0000149584 00000 n +0000150302 00000 n +0000150219 00000 n +0000152814 00000 n +0000150931 00000 n +0000151462 00000 n +0000151993 00000 n +0000152715 00000 n +0000152632 00000 n +0000155227 00000 n +0000153344 00000 n +0000153875 00000 n +0000154406 00000 n +0000155128 00000 n +0000155045 00000 n +0000157831 00000 n +0000155757 00000 n +0000156479 00000 n +0000156396 00000 n +0000157010 00000 n +0000157732 00000 n +0000157649 00000 n +0000158216 00000 n +0000158239 00000 n +0000158261 00000 n +trailer +<< +/Size 361 +/Root 2 0 R +/Info 1 0 R +>> +startxref +158382 +%%EOF diff --git a/src/axiom-website/CATS/schaum13.input.pamphlet b/src/axiom-website/CATS/schaum13.input.pamphlet new file mode 100644 index 0000000..678e41c --- /dev/null +++ b/src/axiom-website/CATS/schaum13.input.pamphlet @@ -0,0 +1,5196 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/input schaum13.input} +\author{Timothy Daly} +\maketitle +\eject +\tableofcontents +\eject +\section{\cite{1}:14.280~~~~~$\displaystyle +\int{\frac{dx}{\sqrt{ax^2+bx+c}}}$} +$$\int{\frac{1}{\sqrt{ax^2+bx+c}}}= +\left\{ +\begin{array}{l} +\displaystyle +\frac{1}{\sqrt{a}}\ln\left(2\sqrt{a}\sqrt{ax^2+bx+c}+2ax+b\right)\\ +\\ +\displaystyle +-\frac{1}{\sqrt{-a}}\sin{-1}\left(\frac{2ax+b}{\sqrt{b^2-4ac}}\right)\\ +\\ +\displaystyle +\frac{1}{\sqrt{a}}\sinh^{-1}\left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right) +\end{array} +\right. +$$ +<<*>>= +)spool schaum13.output +)set message test on +)set message auto off +)clear all + +--S 1 +aa:=integrate(1/sqrt(a*x^2+b*x+c),x) +--R +--R (1) +--R [ +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R , +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R 2atan(------------------------------------) +--R a x +--R -------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E + +--S 2 +bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b) +--R +--R +--------------+ +--R +-+ | 2 +--R log(2\|a \|a x + b x + c + 2a x + b) +--R (2) -------------------------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 3 +bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c)) +--R +--R 2a x + b +--R asin(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R (3) - -------------------- +--R +---+ +--R \|- a +--R Type: Expression Integer +--E + +--S 4 +bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2)) +--R +--R 2a x + b +--R asinh(------------) +--R +---------+ +--R | 2 +--R \|4a c - b +--R (4) ------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 5 +cc1:=bb1-aa.1 +--R +--R (5) +--R +--------------+ +--R +-+ | 2 +--R log(2\|a \|a x + b x + c + 2a x + b) +--R + +--R - +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 6 +cc2:=bb1-aa.2 +--R +--R (6) +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a log(2\|a \|a x + b x + c + 2a x + b) +--R + +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- a \|a x + b x + c - \|- a \|c +--R - 2\|a atan(------------------------------------) +--R a x +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E + +--S 7 +cc3:=bb2-aa.1 +--R +--R (7) +--R - +--R +---+ +--R \|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +-+ 2a x + b +--R - \|a asin(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E + +--S 8 +cc4:=bb2-aa.2 +--R +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c 2a x + b +--R - 2atan(------------------------------------) - asin(--------------) +--R a x +-----------+ +--R | 2 +--R \|- 4a c + b +--R (8) -------------------------------------------------------------------- +--R +---+ +--R \|- a +--R Type: Expression Integer +--E + +--S 9 +cc5:=bb3-aa.1 +--R +--R (9) +--R - +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2a x + b +--R asinh(------------) +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 10 +cc6:=bb3-aa.2 +--R +--R (10) +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- a \|a x + b x + c - \|- a \|c +---+ 2a x + b +--R - 2\|a atan(------------------------------------) + \|- a asinh(------------) +--R a x +---------+ +--R | 2 +--R \|4a c - b +--R ----------------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E + +--S 11 +dd1:=simplifyLog cc1 +--R +--R (11) +--R log +--R +--------------+ +--R +-+ +-+ | 2 +--R ((4a x + 2b)\|c + (- 2b x - 4c)\|a )\|a x + b x + c +--R + +--R 2 +-+ +-+ 2 2 +--R (4a x + 4b x + 4c)\|a \|c - 2a b x + (- 4a c - b )x - 2b c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 12 14:280 Schaums and Axiom differ by a constant +ee1:=ratDenom dd1 +--R +--R +-+ +-+ +--R +-+ - 2a\|c + b\|a +--R \|a log(----------------) +--R a +--R (12) ------------------------- +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.281~~~~~$\displaystyle +\int{\frac{x~dx}{\sqrt{ax^2+bx+c}}}$} +$$\int{\frac{x}{\sqrt{ax^2+bx+c}}}= +\frac{\sqrt{ax^2+bx+c}}{a}-\frac{b}{2a}\int{\frac{1}{\sqrt{ax^2+bx+c}}} +$$ +<<*>>= +)clear all + +--S 11 +aa:=integrate(x/sqrt(a*x^2+b*x+c),x) +--R +--R +--R (1) +--R [ +--R +--------------+ +--R +-+ | 2 2 +--R (2b\|c \|a x + b x + c - b x - 2b c) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 2 +-+ +-+ +--R - 2b x\|a \|a x + b x + c + (4a x + 2b x)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R 4a\|a \|c \|a x + b x + c + (- 2a b x - 4a c)\|a +--R , +--R +--R +--------------+ +--R +-+ | 2 2 +--R (- 2b\|c \|a x + b x + c + b x + 2b c) +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R +---+ | 2 2 +---+ +-+ +--R - b x\|- a \|a x + b x + c + (2a x + b x)\|- a \|c +--R / +--R +--------------+ +--R +---+ +-+ | 2 +---+ +--R 2a\|- a \|c \|a x + b x + c + (- a b x - 2a c)\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 12 +t1:=integrate(1/sqrt(a*x^2+b*x+c),x) +--R +--R (2) +--R [ +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R , +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R 2atan(------------------------------------) +--R a x +--R -------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E + +--S 13 +bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1 +--R +--R (3) +--R - +--R b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|a x + b x + c +--R / +--R +-+ +--R 2a\|a +--R Type: Expression Integer +--E + +--S 14 +bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2 +--R +--R (4) +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--------------+ +--R \|- a \|a x + b x + c - \|- a \|c +---+ | 2 +--R - b atan(------------------------------------) + \|- a \|a x + b x + c +--R a x +--R ------------------------------------------------------------------------ +--R +---+ +--R a\|- a +--R Type: Expression Integer +--E + +--S 15 +cc1:=bb1-aa.1 +--R +--R (5) +--R +--------------+ +--R +-+ | 2 2 +--R (- 2b\|c \|a x + b x + c + b x + 2b c) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 2 +--R (- 2b\|c \|a x + b x + c + b x + 2b c) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 +-+ +-+ +--R - 4c\|a \|a x + b x + c + (2b x + 4c)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R 4a\|a \|c \|a x + b x + c + (- 2a b x - 4a c)\|a +--R Type: Expression Integer +--E + +--S 16 +cc2:=bb1-aa.2 +--R +--R (6) +--R +--------------+ +--R +---+ +-+ | 2 2 +---+ +--R (- 2b\|- a \|c \|a x + b x + c + (b x + 2b c)\|- a ) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (4b\|a \|c \|a x + b x + c + (- 2b x - 4b c)\|a ) +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +---+ +-+ +-+ +--R - 4c\|- a \|a \|a x + b x + c + (2b x + 4c)\|- a \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +---+ +-+ +--R 4a\|- a \|a \|c \|a x + b x + c + (- 2a b x - 4a c)\|- a \|a +--R Type: Expression Integer +--E + +--S 17 +cc3:=bb2-aa.1 +--R +--R (7) +--R +--------------+ +--R +---+ +-+ | 2 2 +---+ +--R (- 2b\|- a \|c \|a x + b x + c + (b x + 2b c)\|- a ) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (- 4b\|a \|c \|a x + b x + c + (2b x + 4b c)\|a ) +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R +---+ +-+ | 2 +---+ +-+ +-+ +--R - 4c\|- a \|a \|a x + b x + c + (2b x + 4c)\|- a \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +---+ +-+ +--R 4a\|- a \|a \|c \|a x + b x + c + (- 2a b x - 4a c)\|- a \|a +--R Type: Expression Integer +--E + +--S 18 +cc4:=bb2-aa.2 +--R +--R +--------------+ +--R | 2 +-+ +--R - 2c\|a x + b x + c + (b x + 2c)\|c +--R (8) -------------------------------------- +--R +--------------+ +--R +-+ | 2 +--R 2a\|c \|a x + b x + c - a b x - 2a c +--R Type: Expression Integer +--E + +--S 19 14:281 Schaums and Axiom differ by a constant +dd1:=ratDenom cc4 +--R +--R +-+ +--R \|c +--R (9) - ---- +--R a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.282~~~~~$\displaystyle +\int{\frac{x^2dx}{\sqrt{ax^2+bx+c}}}$} +$$\int{\frac{x^2}{\sqrt{ax^2+bx+c}}}= +\frac{2ax-3b}{4a^2}\sqrt{ax^2+bx+c}+\frac{3b^2-4ac}{8a^2} +\int{\frac{1}{\sqrt{ax^2+bx+c}}} +$$ +<<*>>= +)clear all + +--S 19 +aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x) +--R +--R (1) +--R [ +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 12b )x + 32a c - 24b c)\|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c + 8a b c + 3b )x + (- 32a b c + 24b c)x - 32a c + 24b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 3 2 2 2 +-+ +--R ((- 16a c - 4a b )x + (- 8a b c + 6b )x + (- 32a c + 24b c)x)\|a +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 4 2 2 3 3 2 +--R 16a b x + (32a c - 8a b )x + (24a b c - 18b )x +--R + +--R 2 2 +--R (32a c - 24b c)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 2 2 +-+ +-+ | 2 +--R (32a b x + 64a c)\|a \|c \|a x + b x + c +--R + +--R 3 2 2 2 2 2 2 +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|a +--R , +--R +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((- 16a b c + 12b )x - 32a c + 24b c)\|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (16a c - 8a b c - 3b )x + (32a b c - 24b c)x + 32a c - 24b c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 2 2 3 3 2 2 2 +---+ +--R ((- 8a c - 2a b )x + (- 4a b c + 3b )x + (- 16a c + 12b c)x)\|- a +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 4 2 2 3 3 2 2 2 +--R (8a b x + (16a c - 4a b )x + (12a b c - 9b )x + (16a c - 12b c)x) +--R * +--R +---+ +-+ +--R \|- a \|c +--R / +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (16a b x + 32a c)\|- a \|c \|a x + b x + c +--R + +--R 3 2 2 2 2 2 2 +---+ +--R ((- 16a c - 4a b )x - 32a b c x - 32a c )\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 20 +t1:=integrate(1/sqrt(a*x^2+b*x+c),x) +--R +--R (2) +--R [ +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R , +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R 2atan(------------------------------------) +--R a x +--R -------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E + +--S 21 +bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1 +--R +--R (3) +--R 2 +--R (- 4a c + 3b ) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 +--R (4a x - 6b)\|a \|a x + b x + c +--R / +--R 2 +-+ +--R 8a \|a +--R Type: Expression Integer +--E + +--S 22 +bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2 +--R +--R (4) +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R 2 \|- a \|a x + b x + c - \|- a \|c +--R (- 4a c + 3b )atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R +---+ | 2 +--R (2a x - 3b)\|- a \|a x + b x + c +--R / +--R 2 +---+ +--R 4a \|- a +--R Type: Expression Integer +--E + +--S 23 +cc1:=aa.1-bb1 +--R +--R (5) +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 12b )x + 32a c - 24b c)\|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c + 8a b c + 3b )x + (- 32a b c + 24b c)x - 32a c + 24b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 12b )x + 32a c - 24b c)\|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c + 8a b c + 3b )x + (- 32a b c + 24b c)x - 32a c + 24b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (- 24b c x - 48b c )\|a \|a x + b x + c +--R + +--R 3 2 2 2 +-+ +-+ +--R ((24a b c + 6b )x + 48b c x + 48b c )\|a \|c +--R / +--R +--------------+ +--R 2 2 +-+ +-+ | 2 +--R (32a b x + 64a c)\|a \|c \|a x + b x + c +--R + +--R 3 2 2 2 2 2 2 +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|a +--R Type: Expression Integer +--E + +--S 24 +cc2:=aa.2-bb1 +--R +--R (6) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((16a b c - 12b )x + 32a c - 24b c)\|- a \|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 +--R (- 16a c + 8a b c + 3b )x + (- 32a b c + 24b c)x - 32a c +--R + +--R 2 2 +--R 24b c +--R * +--R +---+ +--R \|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((- 32a b c + 24b )x - 64a c + 48b c)\|a \|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 +--R (32a c - 16a b c - 6b )x + (64a b c - 48b c)x + 64a c +--R + +--R 2 2 +--R - 48b c +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (- 24b c x - 48b c )\|- a \|a \|a x + b x + c +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((24a b c + 6b )x + 48b c x + 48b c )\|- a \|a \|c +--R / +--R +--------------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a b x + 64a c)\|- a \|a \|c \|a x + b x + c +--R + +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|- a \|a +--R Type: Expression Integer +--E + +--S 25 +cc3:=aa.2-bb1 +--R +--R (7) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((16a b c - 12b )x + 32a c - 24b c)\|- a \|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 +--R (- 16a c + 8a b c + 3b )x + (- 32a b c + 24b c)x - 32a c +--R + +--R 2 2 +--R 24b c +--R * +--R +---+ +--R \|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((- 32a b c + 24b )x - 64a c + 48b c)\|a \|c \|a x + b x + c +--R + +--R 2 2 2 4 2 2 3 3 +--R (32a c - 16a b c - 6b )x + (64a b c - 48b c)x + 64a c +--R + +--R 2 2 +--R - 48b c +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (- 24b c x - 48b c )\|- a \|a \|a x + b x + c +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((24a b c + 6b )x + 48b c x + 48b c )\|- a \|a \|c +--R / +--R +--------------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a b x + 64a c)\|- a \|a \|c \|a x + b x + c +--R + +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|- a \|a +--R Type: Expression Integer +--E + +--S 26 +cc4:=aa.2-bb2 +--R +--R (8) +--R +--------------+ +--R 2 2 | 2 +--R (- 12b c x - 24b c )\|a x + b x + c +--R + +--R 3 2 2 2 +-+ +--R ((12a b c + 3b )x + 24b c x + 24b c )\|c +--R / +--R +--------------+ +--R 2 2 +-+ | 2 3 2 2 2 2 +--R (16a b x + 32a c)\|c \|a x + b x + c + (- 16a c - 4a b )x - 32a b c x +--R + +--R 2 2 +--R - 32a c +--R Type: Expression Integer +--E + +--S 27 14:282 Schaums and Axiom differ by a constant +dd4:=ratDenom cc4 +--R +--R +-+ +--R 3b\|c +--R (9) - ------ +--R 2 +--R 4a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.283~~~~~$\displaystyle +\int{\frac{dx}{x\sqrt{ax^2+bx+c}}}$} +$$\int{\frac{1}{x\sqrt{ax^2+bx+c}}}= +\left\{ +\begin{array}{l} +\displaystyle +-\frac{1}{\sqrt{c}} +\ln\left(\frac{2\sqrt{c}{\sqrt{ax^2+bx+c}}+bx+2c}{x}\right)\\ +\\ +\displaystyle +\frac{1}{\sqrt{-c}}\sin^{-1}\left(\frac{bx+2c}{|x|\sqrt{b^2-4ac}}\right)\\ +\\ +\displaystyle +-\frac{1}{\sqrt{c}}\sinh^{-1}\left(\frac{bx+2c}{|x|\sqrt{4ac-b^2}}\right) +\end{array} +\right. +$$ +<<*>>= +)clear all + +--S 27 +aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) +--R +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R log(---------------------------------) +--R x +--R (1) -------------------------------------- +--R +-+ +--R \|c +--R Type: Union(Expression Integer,...) +--E + +--S 28 +bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x) +--R +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c + b x + 2c +--R log(---------------------------------) +--R x +--R (2) - -------------------------------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E + +--S 29 +bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c))) +--R +--R b x + 2c +--R asin(---------------) +--R +-----------+ +--R | 2 +--R x\|- 4a c + b +--R (3) --------------------- +--R +---+ +--R \|- c +--R Type: Expression Integer +--E + +--S 30 +bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2))) +--R +--R b x + 2c +--R asinh(-------------) +--R +---------+ +--R | 2 +--R x\|4a c - b +--R (4) - -------------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E + +--S 31 +cc1:=aa-bb1 +--R +--R (5) +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c + b x + 2c +--R log(---------------------------------) +--R x +--R + +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R log(---------------------------------) +--R x +--R / +--R +-+ +--R \|c +--R Type: Expression Integer +--E + +--S 32 +cc2:=aa-bb2 +--R +--R (6) +--R +--------------+ +--R +-+ | 2 +--R +---+ 2\|c \|a x + b x + c - b x - 2c +-+ b x + 2c +--R \|- c log(---------------------------------) - \|c asin(---------------) +--R x +-----------+ +--R | 2 +--R x\|- 4a c + b +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E + +--S 33 +cc3:=aa-bb3 +--R +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c b x + 2c +--R log(---------------------------------) + asinh(-------------) +--R x +---------+ +--R | 2 +--R x\|4a c - b +--R (7) ------------------------------------------------------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E + +--S 34 +dd1:=expandLog cc1 +--R +--R (8) +--R +--------------+ +--R +-+ | 2 +--R log(2\|c \|a x + b x + c + b x + 2c) +--R + +--R +--------------+ +--R +-+ | 2 +--R log(2\|c \|a x + b x + c - b x - 2c) - 2log(x) +--R / +--R +-+ +--R \|c +--R Type: Expression Integer +--E + +--S 35 +ee1:=ratDenom dd1 +--R +--R (9) +--R +--------------+ +--R +-+ +-+ | 2 +--R \|c log(2\|c \|a x + b x + c + b x + 2c) +--R + +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R \|c log(2\|c \|a x + b x + c - b x - 2c) - 2log(x)\|c +--R / +--R c +--R Type: Expression Integer +--E + +--S 36 14:283 Schaums and Axiom differ by a constant +ff1:=complexNormalize ee1 +--R +--R 2 +-+ +--R log(4a c - b )\|c +--R (10) ------------------ +--R c +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.284~~~~~$\displaystyle +\int{\frac{dx}{x^2\sqrt{ax^2+bx+c}}}$} +$$\int{\frac{1}{x^2\sqrt{ax^2+bx+c}}}= +-\frac{\sqrt{ax^2+bx+c}}{cx}-\frac{b}{2c}\int{\frac{1}{x\sqrt{ax^2+bx+c}}} +$$ +<<*>>= +)clear all + +--S 37 +aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x) +--R +--R (1) +--R +--------------+ +--R +-+ | 2 2 2 +--R (- 4b x\|c \|a x + b x + c + 2b x + 4b c x) +--R * +--R +--------------+ +--R | 2 +-+ +--R 2c\|a x + b x + c + (- b x - 2c)\|c +--R log(--------------------------------------) +--R 2c x +--R + +--R +--------------+ +--R +-+ | 2 2 2 2 +--R (2b x + 8c)\|c \|a x + b x + c + (- 8a c + b )x - 6b c x - 8c +--R / +--R +--------------+ +--R 2 | 2 2 2 +-+ +--R 8c x\|a x + b x + c + (- 4b c x - 8c x)\|c +--R Type: Union(Expression Integer,...) +--E + +--S 38 +t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) +--R +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R log(---------------------------------) +--R x +--R (2) -------------------------------------- +--R +-+ +--R \|c +--R Type: Union(Expression Integer,...) +--E + +--S 39 +bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1 +--R +--R +--------------+ +--R +-+ | 2 +--------------+ +--R 2\|c \|a x + b x + c - b x - 2c +-+ | 2 +--R - b x log(---------------------------------) - 2\|c \|a x + b x + c +--R x +--R (3) --------------------------------------------------------------------- +--R +-+ +--R 2c x\|c +--R Type: Expression Integer +--E + +--S 40 +cc:=aa-bb +--R +--R (4) +--R +--------------+ +--R | 2 2 +-+ +--R (4b c\|a x + b x + c + (- 2b x - 4b c)\|c ) +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R log(---------------------------------) +--R x +--R + +--R +--------------+ +--R | 2 2 +-+ +--R (- 4b c\|a x + b x + c + (2b x + 4b c)\|c ) +--R * +--R +--------------+ +--R | 2 +-+ +--R 2c\|a x + b x + c + (- b x - 2c)\|c +--R log(--------------------------------------) +--R 2c x +--R + +--R +--------------+ +--R | 2 2 +-+ +--R - 2b c\|a x + b x + c + (b x + 2b c)\|c +--R / +--R +--------------+ +--R 2 +-+ | 2 2 3 +--R 8c \|c \|a x + b x + c - 4b c x - 8c +--R Type: Expression Integer +--E + +--S 41 +dd:=expandLog cc +--R +--R (5) +--R +--------------+ +--R | 2 2 +-+ +--R (4b c\|a x + b x + c + (- 2b x - 4b c)\|c ) +--R * +--R +--------------+ +--R +-+ | 2 +--R log(2\|c \|a x + b x + c - b x - 2c) +--R + +--R +--------------+ +--R | 2 2 +-+ +--R (- 4b c\|a x + b x + c + (2b x + 4b c)\|c ) +--R * +--R +--------------+ +--R | 2 +-+ +--R log(2c\|a x + b x + c + (- b x - 2c)\|c ) +--R + +--R +--------------+ +--R | 2 +--R (4b c log(c) + 4b c log(2) - 2b c)\|a x + b x + c +--R + +--R 2 2 2 +-+ +--R ((- 2b x - 4b c)log(c) + (- 2b x - 4b c)log(2) + b x + 2b c)\|c +--R / +--R +--------------+ +--R 2 +-+ | 2 2 3 +--R 8c \|c \|a x + b x + c - 4b c x - 8c +--R Type: Expression Integer +--E + +--S 42 +ee:=ratDenom dd +--R +--R (6) +--R +--------------+ +--R +-+ +-+ | 2 +--R 2b\|c log(2\|c \|a x + b x + c - b x - 2c) +--R + +--R +--------------+ +--R +-+ | 2 +-+ +--R - 2b\|c log(2c\|a x + b x + c + (- b x - 2c)\|c ) +--R + +--R +-+ +--R (2b log(c) + 2b log(2) - b)\|c +--R / +--R 2 +--R 4c +--R Type: Expression Integer +--E + +--S 43 14:284 Schaums and Axiom differ by a constant +ff:=complexNormalize ee +--R +--R +-+ +--R (b log(c) + 2b log(2) - b)\|c +--R (7) ------------------------------ +--R 2 +--R 4c +--R Type: Expression Integer +--E + +@ + +\section{\cite{1}:14.285~~~~~$\displaystyle +\int{\sqrt{ax^2+bx+c}}~dx$} +$$\int{\sqrt{ax^2+bx+c}}= +\frac{(2ax+b)\sqrt{ax^2+bx+c}}{4a}+ +\frac{4ac-b^2}{8a}\int{\frac{1}{\sqrt{ax^2+bx+c}}} +$$ +<<*>>= +)clear all + +--S 44 +aa:=integrate(sqrt(a*x^2+b*x+c),x) +--R +--R +--R (1) +--R [ +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 3 2 2 2 +-+ +--R ((- 16a c - 4a b )x + (- 40a b c - 2b )x + (- 32a c - 8b c)x)\|a +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 4 2 2 3 3 2 +--R 16a b x + (32a c + 24a b )x + (56a b c + 6b )x +--R + +--R 2 2 +--R (32a c + 8b c)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32a b x + 64a c)\|a \|c \|a x + b x + c +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|a +--R , +--R +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 2 2 3 3 2 2 2 +---+ +--R ((- 8a c - 2a b )x + (- 20a b c - b )x + (- 16a c - 4b c)x)\|- a +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 4 2 2 3 3 2 2 2 +--R (8a b x + (16a c + 12a b )x + (28a b c + 3b )x + (16a c + 4b c)x) +--R * +--R +---+ +-+ +--R \|- a \|c +--R / +--R +--------------+ +--R +---+ +-+ | 2 +--R (16a b x + 32a c)\|- a \|c \|a x + b x + c +--R + +--R 2 2 2 2 +---+ +--R ((- 16a c - 4a b )x - 32a b c x - 32a c )\|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 45 +t1:=integrate(1/sqrt(a*x^2+b*x+c),x) +--R +--R (2) +--R [ +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R , +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R 2atan(------------------------------------) +--R a x +--R -------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E + +--S 46 +bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1 +--R +--R (3) +--R 2 +--R (4a c - b ) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R +-+ | 2 +--R (4a x + 2b)\|a \|a x + b x + c +--R / +--R +-+ +--R 8a\|a +--R Type: Expression Integer +--E + +--S 47 +bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2 +--R +--R (4) +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R 2 \|- a \|a x + b x + c - \|- a \|c +--R (4a c - b )atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R +---+ | 2 +--R (2a x + b)\|- a \|a x + b x + c +--R / +--R +---+ +--R 4a\|- a +--R Type: Expression Integer +--E + +--S 48 +cc1:=aa.1-bb1 +--R +--R (5) +--R +--------------+ +--R 2 2 | 2 +--R (4b c x + 8b c )\|a x + b x + c +--R + +--R 3 2 2 2 +-+ +--R ((- 4a b c - b )x - 8b c x - 8b c )\|c +--R / +--R +--------------+ +--R +-+ | 2 2 2 2 +--R (16a b x + 32a c)\|c \|a x + b x + c + (- 16a c - 4a b )x - 32a b c x +--R + +--R 2 +--R - 32a c +--R Type: Expression Integer +--E + +--S 49 +cc2:=aa.2-bb1 +--R +--R (6) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((- 16a b c + 4b )x - 32a c + 8b c)\|- a \|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((16a c - b )x + (32a b c - 8b c)x + 32a c - 8b c )\|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((32a b c - 8b )x + 64a c - 16b c)\|a \|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 32a c + 2b )x + (- 64a b c + 16b c)x - 64a c + 16b c )\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (8b c x + 16b c )\|- a \|a \|a x + b x + c +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((- 8a b c - 2b )x - 16b c x - 16b c )\|- a \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R (32a b x + 64a c)\|- a \|a \|c \|a x + b x + c +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|- a \|a +--R Type: Expression Integer +--E + +--S 50 +cc3:=aa.1-bb2 +--R +--R (7) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8b c)\|- a \|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c )\|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((- 32a b c + 8b )x - 64a c + 16b c)\|a \|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((32a c - 2b )x + (64a b c - 16b c)x + 64a c - 16b c )\|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (8b c x + 16b c )\|- a \|a \|a x + b x + c +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((- 8a b c - 2b )x - 16b c x - 16b c )\|- a \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R (32a b x + 64a c)\|- a \|a \|c \|a x + b x + c +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|- a \|a +--R Type: Expression Integer +--E + +--S 51 +cc4:=aa.2-bb2 +--R +--R (8) +--R +--------------+ +--R 2 2 | 2 +--R (4b c x + 8b c )\|a x + b x + c +--R + +--R 3 2 2 2 +-+ +--R ((- 4a b c - b )x - 8b c x - 8b c )\|c +--R / +--R +--------------+ +--R +-+ | 2 2 2 2 +--R (16a b x + 32a c)\|c \|a x + b x + c + (- 16a c - 4a b )x - 32a b c x +--R + +--R 2 +--R - 32a c +--R Type: Expression Integer +--E + +--S 52 14:285 Schaums and Axiom differ by a constant +dd4:=ratDenom cc4 +--R +--R +-+ +--R b\|c +--R (9) ----- +--R 4a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.286~~~~~$\displaystyle +\int{x\sqrt{ax^2+bx+c}}~dx$} +$$ +\begin{array}{rl} +\displaystyle +\int{x\sqrt{ax^2+bx+c}}=&\displaystyle\frac{(ax^2+bx+c)^{3/2}}{3a}\\ +&\\ +&\displaystyle-\frac{b(2ax+b)}{8a^2}\sqrt{ax^2+bx+c}\\ +&\\ +&\displaystyle-\frac{b(4ac-b^2)}{16a^2}\int{\frac{1}{\sqrt{ax^2+bx+c}}} +\end{array} +$$ +<<*>>= +)clear all + +--S 53 +aa:=integrate(x*sqrt(a*x^2+b*x+c),x) +--R +--R +--R (1) +--R [ +--R 2 2 3 5 2 2 2 4 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x +--R + +--R 3 3 2 +--R 384a b c - 96b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 2 3 3 2 5 2 2 3 4 2 +--R (- 288a b c - 144a b c + 54b c)x + (- 576a b c + 144b c )x +--R + +--R 4 3 3 +--R - 384a b c + 96b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 192a b c - 16a b )x + (- 384a c - 336a b c - 4a b )x +--R + +--R 2 2 3 5 3 +--R (- 1056a b c - 16a b c + 6b )x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (- 768a c - 288a b c + 72b c)x + (- 384a b c + 96b c )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|a x + b x + c +--R + +--R 4 3 2 6 3 2 3 5 +--R (128a c + 96a b )x + (672a b c + 120a b )x +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (768a c + 816a b c - 12a b )x + (1632a b c + 64a b c - 30b )x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (768a c + 480a b c - 120b c)x + (384a b c - 96b c )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 2 2 2 +-+ +-+ +--R ((384a c + 288a b )x + 1536a b c x + 1536a c )\|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 +--R (- 576a b c - 48a b )x + (- 1152a c - 864a b c)x - 2304a b c x +--R + +--R 2 3 +--R - 1536a c +--R * +--R +-+ +--R \|a +--R , +--R +--R 2 2 3 5 2 2 2 4 +--R (- 96a b c - 48a b c + 18b )x + (- 384a b c + 96b c)x +--R + +--R 3 3 2 +--R - 384a b c + 96b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 2 3 3 2 5 2 +--R (144a b c - 24a b c - 3b )x + (288a b c + 144a b c - 54b c)x +--R + +--R 2 3 4 2 4 3 3 +--R (576a b c - 144b c )x + 384a b c - 96b c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 3 2 3 5 3 2 2 2 4 4 +--R (- 96a b c - 8a b )x + (- 192a c - 168a b c - 2a b )x +--R + +--R 2 2 3 5 3 2 3 2 2 4 2 +--R (- 528a b c - 8a b c + 3b )x + (- 384a c - 144a b c + 36b c)x +--R + +--R 3 3 2 +--R (- 192a b c + 48b c )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- a \|a x + b x + c +--R + +--R 4 3 2 6 3 2 3 5 +--R (64a c + 48a b )x + (336a b c + 60a b )x +--R + +--R 3 2 2 2 4 4 2 2 3 5 3 +--R (384a c + 408a b c - 6a b )x + (816a b c + 32a b c - 15b )x +--R + +--R 2 3 2 2 4 2 3 3 2 +--R (384a c + 240a b c - 60b c)x + (192a b c - 48b c )x +--R * +--R +---+ +-+ +--R \|- a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((192a c + 144a b )x + 768a b c x + 768a c )\|- a \|c +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 +--R (- 288a b c - 24a b )x + (- 576a c - 432a b c)x - 1152a b c x +--R + +--R 2 3 +--R - 768a c +--R * +--R +---+ +--R \|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 54 +t1:=integrate(1/sqrt(a*x^2+b*x+c),x) +--R +--R (2) +--R [ +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R / +--R +-+ +--R \|a +--R , +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R 2atan(------------------------------------) +--R a x +--R -------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List Expression Integer,...) +--E + +--S 55 +bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1 +--R +--R (3) +--R 3 +--R (- 12a b c + 3b ) +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R (16a x + 4a b x + 16a c - 6b )\|a \|a x + b x + c +--R / +--R 2 +-+ +--R 48a \|a +--R Type: Expression Integer +--E + +--S 56 +bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2 +--R +--R (4) +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R 3 \|- a \|a x + b x + c - \|- a \|c +--R (- 12a b c + 3b )atan(------------------------------------) +--R a x +--R + +--R +--------------+ +--R 2 2 2 +---+ | 2 +--R (8a x + 2a b x + 8a c - 3b )\|- a \|a x + b x + c +--R / +--R 2 +---+ +--R 24a \|- a +--R Type: Expression Integer +--E + +--S 57 +cc1:=aa.1-bb1 +--R +--R (5) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x + 384a b c +--R + +--R 3 2 +--R - 96b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 2 3 3 2 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54b c)x +--R + +--R 2 3 4 2 4 3 3 +--R (- 576a b c + 144b c )x - 384a b c + 96b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x + 384a b c +--R + +--R 3 2 +--R - 96b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 2 3 3 2 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54b c)x +--R + +--R 2 3 4 2 4 3 3 +--R (- 576a b c + 144b c )x - 384a b c + 96b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R (128a c + 48a b c - 36b c)x + (512a b c - 192b c )x + 512a c +--R + +--R 2 3 +--R - 192b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|a x + b x + c +--R + +--R 2 2 3 5 3 2 3 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108b c)x +--R + +--R 3 3 2 4 2 3 +--R (- 768a b c + 288b c )x - 512a c + 192b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((384a c + 288a b )x + 1536a b c x + 1536a c )\|a \|c \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 +--R (- 576a b c - 48a b )x + (- 1152a c - 864a b c)x - 2304a b c x +--R + +--R 2 3 +--R - 1536a c +--R * +--R +-+ +--R \|a +--R Type: Expression Integer +--E + +--S 58 +cc2:=aa.2-bb1 +--R +--R (6) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x + 384a b c +--R + +--R 3 2 +--R - 96b c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 2 3 3 2 5 2 2 3 4 2 +--R (- 288a b c - 144a b c + 54b c)x + (- 576a b c + 144b c )x +--R + +--R 4 3 3 +--R - 384a b c + 96b c +--R * +--R +---+ +--R \|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 5 2 2 2 4 +--R (- 192a b c - 96a b c + 36b )x + (- 768a b c + 192b c)x +--R + +--R 3 3 2 +--R - 768a b c + 192b c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 +--R (288a b c - 48a b c - 6b )x +--R + +--R 2 3 3 2 5 2 2 3 4 2 +--R (576a b c + 288a b c - 108b c)x + (1152a b c - 288b c )x +--R + +--R 4 3 3 +--R 768a b c - 192b c +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R (128a c + 48a b c - 36b c)x + (512a b c - 192b c )x + 512a c +--R + +--R 2 3 +--R - 192b c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a \|a \|a x + b x + c +--R + +--R 2 2 3 5 3 2 3 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108b c)x +--R + +--R 3 3 2 4 2 3 +--R (- 768a b c + 288b c )x - 512a c + 192b c +--R * +--R +---+ +-+ +-+ +--R \|- a \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384a c + 288a b )x + 1536a b c x + 1536a c )\|- a \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 +--R (- 576a b c - 48a b )x + (- 1152a c - 864a b c)x - 2304a b c x +--R + +--R 2 3 +--R - 1536a c +--R * +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E + +--S 59 +cc3:=aa.1-bb2 +--R +--R (7) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96b c)x + 384a b c +--R + +--R 3 2 +--R - 96b c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 2 3 3 2 5 2 2 3 4 2 +--R (- 288a b c - 144a b c + 54b c)x + (- 576a b c + 144b c )x +--R + +--R 4 3 3 +--R - 384a b c + 96b c +--R * +--R +---+ +--R \|- a +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 5 2 2 2 4 +--R (192a b c + 96a b c - 36b )x + (768a b c - 192b c)x +--R + +--R 3 3 2 +--R 768a b c - 192b c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|a x + b x + c +--R + +--R 2 2 2 4 6 3 +--R (- 288a b c + 48a b c + 6b )x +--R + +--R 2 3 3 2 5 2 2 3 4 2 +--R (- 576a b c - 288a b c + 108b c)x + (- 1152a b c + 288b c )x +--R + +--R 4 3 3 +--R - 768a b c + 192b c +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 2 3 2 2 4 2 3 3 2 4 +--R (128a c + 48a b c - 36b c)x + (512a b c - 192b c )x + 512a c +--R + +--R 2 3 +--R - 192b c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a \|a \|a x + b x + c +--R + +--R 2 2 3 5 3 2 3 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108b c)x +--R + +--R 3 3 2 4 2 3 +--R (- 768a b c + 288b c )x - 512a c + 192b c +--R * +--R +---+ +-+ +-+ +--R \|- a \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384a c + 288a b )x + 1536a b c x + 1536a c )\|- a \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 +--R (- 576a b c - 48a b )x + (- 1152a c - 864a b c)x - 2304a b c x +--R + +--R 2 3 +--R - 1536a c +--R * +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression Integer +--E + +--S 60 +cc4:=aa.2-bb2 +--R +--R (8) +--R 2 3 2 2 4 2 3 3 2 4 +--R (64a c + 24a b c - 18b c)x + (256a b c - 96b c )x + 256a c +--R + +--R 2 3 +--R - 96b c +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 2 3 5 3 2 3 2 2 4 2 +--R (- 96a b c + 28a b c + 3b )x + (- 192a c - 72a b c + 54b c)x +--R + +--R 3 3 2 4 2 3 +--R (- 384a b c + 144b c )x - 256a c + 96b c +--R * +--R +-+ +--R \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ | 2 +--R ((192a c + 144a b )x + 768a b c x + 768a c )\|c \|a x + b x + c +--R + +--R 3 2 3 3 3 2 2 2 2 2 2 2 3 +--R (- 288a b c - 24a b )x + (- 576a c - 432a b c)x - 1152a b c x - 768a c +--R Type: Expression Integer +--E + +--S 61 14:286 Schaums and Axiom differ by a constant +dd4:=ratDenom cc4 +--R +--R 2 +-+ +--R (8a c - 3b )\|c +--R (9) ---------------- +--R 2 +--R 24a +--R Type: Expression Integer +--E +@ + +\section{\cite{1}:14.287~~~~~$\displaystyle +\int{x^2\sqrt{ax^2+bx+c}}~dx$} +$$\int{x^2\sqrt{ax^2+bx+c}}= +\frac{6ax-5b}{24a^2}(ax^2+bx+c)^{3/2}+ +\frac{5b^2-4ac}{16a^2}\int{\sqrt{ax^2+bx+c}} +$$ +<<*>>= +)clear all + +--S 62 +aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x) +--R +--R +--R (1) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200b c)x +--R + +--R 2 4 3 3 5 2 2 5 2 4 +--R (9216a b c - 13824a b c + 2880b c )x + 6144a c - 9216a b c +--R + +--R 4 3 +--R 1920b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 3 4 2 3 3 5 2 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480b c)x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400b c )x +--R + +--R 2 5 3 4 5 3 2 6 2 5 +--R (- 12288a b c + 18432a b c - 3840b c )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c + 2a x)\|a x + b x + c - 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 5 2 4 2 3 4 7 +--R (- 1536a c - 2304a b c - 96a b )x +--R + +--R 4 2 3 3 2 5 6 +--R (- 12544a b c - 3456a b c - 16a b )x +--R + +--R 4 3 3 2 2 2 4 6 5 +--R (- 13056a c - 18240a b c - 80a b c + 20a b )x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 31104a b c + 480a b c + 24a b c - 30b )x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 18432a c + 768a b c + 2816a b c - 720b c)x +--R + +--R 2 4 3 3 5 2 2 +--R (- 7680a b c + 11520a b c - 2400b c )x +--R + +--R 2 5 2 4 4 3 +--R (- 6144a c + 9216a b c - 1920b c )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|a x + b x + c +--R + +--R 5 4 3 8 5 2 4 2 3 4 7 +--R (3072a b c + 768a b )x + (6144a c + 11264a b c + 896a b )x +--R + +--R 4 2 3 3 2 5 6 +--R (30208a b c + 9984a b c - 32a b )x +--R + +--R 4 3 3 2 2 2 4 6 5 +--R (21504a c + 31488a b c - 320a b c + 80a b )x +--R + +--R 3 3 2 3 2 5 7 4 +--R (42624a b c - 4896a b c + 152a b c + 210b )x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (21504a c - 2304a b c - 6464a b c + 1680b c)x +--R + +--R 2 4 3 3 5 2 2 +--R (10752a b c - 16128a b c + 3360b c )x +--R + +--R 2 5 2 4 4 3 +--R (6144a c - 9216a b c + 1920b c )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 3 3 3 4 2 3 2 2 +--R (12288a b c + 3072a b )x + (24576a c + 30720a b c)x +--R + +--R 3 2 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|a x + b x + c +--R + +--R 5 2 4 2 3 4 4 +--R (- 6144a c - 9216a b c - 384a b )x +--R + +--R 4 2 3 3 3 4 3 3 2 2 2 +--R (- 49152a b c - 12288a b c)x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 3 4 +--R - 98304a b c x - 49152a c +--R * +--R +-+ +--R \|a +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (- 1536a b c + 1920a b c + 96a b c - 120b )x +--R + +--R 3 4 2 2 3 4 2 6 2 +--R (- 3072a c + 768a b c + 4800a b c - 1200b c)x +--R + +--R 2 4 3 3 5 2 2 5 +--R (- 9216a b c + 13824a b c - 2880b c )x - 6144a c +--R + +--R 2 4 4 3 +--R 9216a b c - 1920b c +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|a x + b x + c +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c + 288a b c + 15b )x +--R + +--R 3 4 2 3 3 5 2 7 3 +--R (6144a b c - 7680a b c - 384a b c + 480b c)x +--R + +--R 3 5 2 2 4 4 3 6 2 2 +--R (6144a c - 1536a b c - 9600a b c + 2400b c )x +--R + +--R 2 5 3 4 5 3 2 6 2 5 +--R (12288a b c - 18432a b c + 3840b c )x + 6144a c - 9216a b c +--R + +--R 4 4 +--R 1920b c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 5 2 4 2 3 4 7 +--R (- 768a c - 1152a b c - 48a b )x +--R + +--R 4 2 3 3 2 5 6 +--R (- 6272a b c - 1728a b c - 8a b )x +--R + +--R 4 3 3 2 2 2 4 6 5 +--R (- 6528a c - 9120a b c - 40a b c + 10a b )x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 15552a b c + 240a b c + 12a b c - 15b )x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (- 9216a c + 384a b c + 1408a b c - 360b c)x +--R + +--R 2 4 3 3 5 2 2 +--R (- 3840a b c + 5760a b c - 1200b c )x +--R + +--R 2 5 2 4 4 3 +--R (- 3072a c + 4608a b c - 960b c )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- a \|a x + b x + c +--R + +--R 5 4 3 8 5 2 4 2 3 4 7 +--R (1536a b c + 384a b )x + (3072a c + 5632a b c + 448a b )x +--R + +--R 4 2 3 3 2 5 6 +--R (15104a b c + 4992a b c - 16a b )x +--R + +--R 4 3 3 2 2 2 4 6 5 +--R (10752a c + 15744a b c - 160a b c + 40a b )x +--R + +--R 3 3 2 3 2 5 7 4 +--R (21312a b c - 2448a b c + 76a b c + 105b )x +--R + +--R 3 4 2 2 3 4 2 6 3 +--R (10752a c - 1152a b c - 3232a b c + 840b c)x +--R + +--R 2 4 3 3 5 2 2 +--R (5376a b c - 8064a b c + 1680b c )x +--R + +--R 2 5 2 4 4 3 +--R (3072a c - 4608a b c + 960b c )x +--R * +--R +---+ +-+ +--R \|- a \|c +--R / +--R 4 3 3 3 4 2 3 2 2 +--R (6144a b c + 1536a b )x + (12288a c + 15360a b c)x +--R + +--R 3 2 3 3 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- a \|c \|a x + b x + c +--R + +--R 5 2 4 2 3 4 4 +--R (- 3072a c - 4608a b c - 192a b )x +--R + +--R 4 2 3 3 3 4 3 3 2 2 2 +--R (- 24576a b c - 6144a b c)x + (- 24576a c - 30720a b c )x +--R + +--R 3 3 3 4 +--R - 49152a b c x - 24576a c +--R * +--R +---+ +--R \|- a +--R ] +--R Type: Union(List Expression Integer,...) +--E + +--S 63 +t1:=integrate(sqrt(a*x^2+b*x+c),x) +--R +--R (2) +--R [ +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a x)\|a x + b x + c + 2a x\|c +--R + +--R 2 +-+ +--R (- 2a x - b x - 2c)\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|a x + b x + c - b x - 2c +--R + +--R 2 2 3 3 2 2 2 +-+ +--R ((- 16a c - 4a b )x + (- 40a b c - 2b )x + (- 32a c - 8b c)x)\|a +--R * +--R +--------------+ +--R | 2 +--R \|a x + b x + c +--R + +--R 2 4 2 2 3 3 2 +--R 16a b x + (32a c + 24a b )x + (56a b c + 6b )x +--R + +--R 2 2 +--R (32a c + 8b c)x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32a b x + 64a c)\|a \|c \|a x + b x + c +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8a b )x - 64a b c x - 64a c )\|a +--R , +--R +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8b c)\|c \|a x + b x + c +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8b c)x - 32a c + 8b c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b x + c - \|- a \|c +--R atan(------------------------------------) +--R a x +--R + +--R 2 2 3 3 2 2 2