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→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{ { } = = 4 < / M (C ) = c ∈ C f cn (0) 4 / / 4F / / / = /= = 4A / = / < 4 / > ;MN; O / = B / ∞ n =1 ≠∞ B / B = / = > B / / / L } >4 / B C4 L / 1 ' / A = = ? / /E 1 B 4 / Q A / / B / / @ E / = ED 2 / = G / / I (J I $J / / = / / L ( / 4D MD / 4 / ? /I 'J = B / /A / = /! B ( = / = /@A / / 2 = / =/ > A B (L 1 $ 6 3/ 4 512 , / + / A / // / / = /= / = = / Z n +1 = Z n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n +1 = Z n2 + C Z0 = 0 E > < <4 / A > ; / = B = B = 4/ /E /; ; = F = // = G /- . / = = / / > ? E Z0 = 0 Z1 = C Z2 = C 2 + C Z 3 = C 4 + 2C 3 + C 2 + C ... + B /E G > / 4/ /= /-/ > . D /- ./ 4 /A A / /= // /A = 3 = / / A < / @ / C 2 / / / G E/ 4 / A E A ; = / / 4/ / @24 = / / B = ? U ; ? = E / // / // C / = A / / = > = > = ? / + . L Z n = xn (C ) + jyn (C ) C = a + jb = /A xn (C ) = xn (C * ) yn (C ) = − yn (C * ) A V ; V // C 4? A Z n (C ) = xn (C ) + jyn (C ) Z n (C * ) = xn (C * ) + jyn (C * ) = xn (C ) − jyn (C ) 5 ?= L 2 Z n (C * ) = xn2 (C * ) + yn2 (C * ) = Z n (C ) /< 4 Z n +1 (C ) = y Z n +1 (C * ) = A / + + B // OL xn +1 (C * ) = xn (C * ) 2 − yn (C * ) 2 + a = xn (C ) 2 − yn (C ) 2 + a = xn +1 (C ) yn +1 (C * ) = 2 ⋅ xn (C * ) ⋅ yn (C * ) + b = −2 ⋅ xn (C ) ⋅ yn (C ) − b = − yn +1 (C ) /A 4/V ; V // C / A 4A ; xn +1 (C ) = xn (C ) 2 − yn (C ) 2 + a yn +1 (C ) = 2 ⋅ xn (C ) ⋅ yn (C ) + b / / A /A / 4A C 2 /E / / xn (C ) = xn (C * ) xn +1 (C ) = xn +1 (C * ) yn (C ) = − yn (C * ) yn +1 (C ) = − yn +1 (C * ) 4 /V ; OV C A = ; / = A A V ; V // C = A = // C / F- . 0 0F- U.? A = / = M (C ) = M (C * ) ?- . 0 0M? - U. 4 V ;V / 3-.5 != /> A = AE > ?/ > / > = B > / A = / / = A C= / = = > / /G // /+ = = @ D < / E G 4 A / / / / 4/ / / C 4A / A 24 G/ A A / G/ A / = = A A / / /A E / D / = > Z n +1 = Z n2 + C Z0 = 0 E E 4? = > / /= > /= > = / > / / E / F 4= = > E / = / = > B / / > C = / A /A / / / E / = < >4 Z n +1 = f c (Z n ), Z 0 = 0 / f c (Z ) = Z 2 + C A Z i = f ci (Z o ) ?A / + < B A A / F/ E E @2 /; 0 W; 4; 4; 4;(4 ; X / A = /= > > @2MC/ E > = > Z i = Z i+ N / A f c ( f c ( f c (... f c (Z i )...))) = f cN (Z i )= Z i #/4 / M/ = A > = > W; 4B -; . 4B -; . 4 4B M -; .X0 W ; 4; O 4; O 4 ; O M XB > / / A // = // = /= > /= = / 0 4 = @ = B 2 !/ = = ; / A /@ /M= > = EDA / E = E / E A ? =/ > = = = <= C L / 2 = A > @2M / > = > / >4 / 4 EDA E = = / -; . 4 > / = > / /.A = / = 4 // -B -; . 4< =/ G B E = E/ D ? B 4@ ? 2 / -; O . = / / / -; O .= / /= / / > A / / = E / ; 0W 4B- . 4B - . 4B (- . 4B $- . 4B '- . 4B 6- .4B *- . X0 W; 4; 4 ; 4 ;(4 ;$4 ;'4 ;64 ;* X0 W; 4; 4 ; 4 ;(4 ;$4 ;'4 ;(4 ;$ X0 A B A / L 1 $ "4 2 06 ,. + / G/ A = E < /A B F0 -F . = 4= >. / > 4E @ F 24E = @ = / B =/ / / A E -F ./ B 2L > A G E / E g ′(x ) ≤ 1, ∀x ! /= /@ F 2A = > @24/ + = E = > = = / / D / /= > / < / > A / /= / / > /A G/ A / = / B /= / E >L > @ B 2L {..., Z , f (Z ), f (Z ),... f (Z ), f (Z ) = Z ,...} i c i 2 c i N −1 c i N c E = i i / A @ B2 / 4 / / A = / B / / = 0(L = = > ; / 4 / / / E /B 1 4 4< / E = / / / = /A B > / B > @ B 2 !B / / / $( > = > / / 4 / / E / 4A / 4= / / = 0 L 1 = A /4 / // / /= / / / A / / @ B2 = / > B @ B 2 / / E >4 E = > @ B 2 E 4= = 4 / /B $( = / > !B E /= / $ $ @ B2 A @ B2 B 4 / E 4 / @ B 2 > /= > / > = / = 4A / / ( 6 /. 4 127, 0 . 46189 / F = >4B L E / 4B / /= > @ B 2 ? / // > f c (Z ) = Z 2 + C 2 f c2 (Z ) = ( f c (Z )) + C ... ( ) f cN (Z ) = f cN −1 (Z ) + C + A 2; 0 B -;. 2 E / 2 = > = B 4 A ′ f cN (Z ) ≤ 1, ∀Z + / = / B E @ B 2L E = > !< / /E ′ ′ f cn ( Z )= 2 ⋅ f cn −1 ( Z ) ⋅ f cn −1 ( Z ) A ′ ′ f cN ( Z )= 2 ⋅ f cN −1 ( Z ) ⋅ f cN −1 ( Z )= ′ 2 ⋅ f cN −1 ( Z ) ⋅ 2 ⋅ f cN − 2 ( Z ) ⋅ f cN − 2 ( Z )= ... N N −1 N −2 2 ⋅ f c ( Z ) ⋅ f c ( Z ) ⋅ ... ⋅ f c1 ( Z ) ⋅ Z + E M = A > / = 4; < / = > 4/ 4< / /= / > = > @ B 2 #/4 24@ B -;. 2 ? / /E /E /< / @ B M -;. 2 / / // A /@ B -;. / > = > 4= / / / L / N df cN ( Z ) N = 2 ⋅ ∏ Z pi dZ i =1 / /;= /= A 4= / > = > / = = B 4 /A L N 2 N ⋅ ∏ Z pi ≤ 1 i =1 $ N 1 2N ∏ Z pi ≤ i =1 / = / > /@ ;=2 / = B 4 / / / E ? @ B2 = A / = E / > /= > /? = = > = / / @ B2 // = / / /= / 4 // = N ∏Z C ⊂ M (C ) i =1 ≤ pi / = / A / / / / 1 2N 6 /. 4 127, 0 . 4618 9 C / = D = B / / -// // / = = A = / /= > / / . / F = ! ? = E@ λ24 ? / / / / > /I 6J I *J / F = / L λ = lim n →∞ / /A F = > + / 4 n i =1 E xi / /A = /D / E = =>/ 4 / /λ n →∞ A df ( x) dx ln / 4 /@ K2 λ =lim ln /= 1 n / T4 n n ∏ i =1 df ( x) dx xi A @ B-F .0 B -;. 24 /A d (Z 2 + C ) ′ f ′( x )= f c (Z ) = =2 Z dZ A λ =lim ln n →∞ n n ∏ 2Z i =1 i ' λ =lim ln 2 ⋅ n n→∞ A /= B /; n ∏Z i =1 / i > ; O 4 / ; < / ;∞ = /< A /; = / A - / //= A @ B2 / A / / / / > 4= > E = = > MC/ A / ? <? E /; / = /+ / A / F </ / = @ C 24= // A E /= /E / / 4A E/ /4 / / C / / / L ∏Z n →∞ < / /@ ;2 / > / i =1 / = / / / 4@ ;=2 > i 4A / 4 = /A ∏Z n→∞ i =1 λ = ln 2 ⋅ > λ4? / G pi 1/ N N ∏Z i =1 B 1/ N N λ =lim ln 2 A 4= = > . / A > = > 4 B 4? / λ /E B = / </ n/ N N λ = lim ln 2 ⋅ n > / 4= pi / ≤ /= / > < < 4< 1/ N N ∏Z 2⋅ i =1 ∏Z i =1 N ≤1 pi 1/ N N pi ∏ Z pi ≤ i =1 A4 ≤ 1 2 1 2N 6 / / A 4= / = > 4 /= /;= / / / E / E /A / / > / = A / /A @ B2 < = / 4 A / 4 = / F 4 / / // < E ; !/ A > /C / = /4= / A / Za ⋅ Zb = Za ⋅ Zb + /E /= 4/ D $ / / = / / / B > E 4/ 4 // B > = 4= / // 0 4 ? ( $ 1/ = D = 4 A / > 4/ A = 0 / / < A < / D = / A / / E L /D / = / < /D / / / 1 2 / // A Y / > ? ; = E /@ / ; < / 2 + /< / ;L /A ; O < Z n +1 = Z n + / /A E > = = / / /E /= ) > / A > Z ≤ A /A E : 2127, 0 . 461 /A + / /A E /> G /= B / > A < / > Z n = Z n2 + C > = / / / 4 4/ 4 Z = Z2 +C / = /A C =Z − Z 2 > ; > E E = YL 1 Z = e jΦ 2 * 1 jΦ 1 j 2 Φ e − e 2 4 Cl1 = = / // /A E= C < E / φ + = B > = > / Π + B > F = // / / A Φ ⊂ [0,2Π ) + / / / / E /= 0 B D A 1 !B E / / /= A = . /< ! > E = < < = 0 . = / / = / / /A / = / ? > > = / / A = = Z = Z2 +C / φ $$ > 4/ / / /A / > ? E E $$ = = = E/ /= / L B / /4 / B < < B 4A / / > E / 4A > B-F 4 ?.A / < B > $$ < B > / Z2 −Z +C = 0 S 1 ± 1 − 4C Z= 2 / = //= / -F 4 ?. 4? < Z ≤ F = /> 1 2 4/ > B f ( x, y ) ≤ 0 / ( f ( x, y )=256 x 2 + y 2 ) ( 2 ) − 96 x 2 + y 2 + 32 x − 3 A f ( x, y ) < 0 f ( x, y ) = 0 f ( x, y ) > 0 ! / > / / 0 0 F 0 L 2 Z ≤ 1 4 1 ± 1 − 4C ≤ 1 C = x + jy ?< / 1 − 4C = a + jb / ( 1 − 4 x ± 1 − 8 x + 16 x 2 + y 2 a = 2 2 2 b = a − 1 + 4x 2 / ) A (1 ± a )2 + b 2 ≤ 1 ( ) ± 1 − 8 x + 16 x 2 + y 2 ≤ 2a ( ) ( − 1 + 16 x 2 + y 2 ≤ ±2 1 − 8 x + 16 x 2 + y 2 ) 5 ( ) 1 − 32 x 2 + y 2 + 256 x 4 + 256 y 4 + 512 x 2 y ≤ 4 + 64( x 2 + y 2 ) − 32 x ? / ( 256 x 2 + y 2 $ !/ = / E / /A L 1/ ) ( 2 ) − 96 x 2 + y 2 + 32 x − 3 ≤ 0 ) A = > A D / 0 / /A = E /E / 4;= ? ;= + Z p1 ⋅ Z p 2 = Z p1 ⋅ Z p 2 ≤ + /< ;= ? ;= /E / / / 1 4 > Z = f c ( f c (Z )) Z n+2 = Z n A / = / L Z =Z 4 + 2C ⋅ Z 2 + C 2 + C ( ) ( ) C 2 + C ⋅ 1 + 2Z 2 + Z 4 − Z = 0 ? // // L C l1 = Z − Z 2 C l 2 = −1 − Z − Z 2 / ; A / /= / /E /;= ) /A = // / 0 / < < / > 4= / A = > C = 4(4$ ? A / < / / > A / ? / > + /< = / = ; / / / / #/4 / = / / = C/ / / / = > / = G A ? E /= / 4 4 =/ E + /= 0 ? / / > / /A Z 2 + Z + (C + 1) = 0 !/ // ? = / ;= Z= − 1 ± − 3 − 4C 2 / /= / /E L ; -;= − 1 + − 3 − 4C − 1 − − 3 − 4C 1 ⋅ ≤ 2 2 4 ;= . 4 A (− 1 + )( ) − 3 − 4C ⋅ − 1 − − 3 − 4C ≤ 1 1 + − 3 − 4C − − 3 − 4C + 3 + 4C ≤ 1 4 + 4C ≤ 1 4⋅ 1+ C ≤ 1 1+ C ≤ 1 4 AE 2 f ( x, y ) = (x + 1) + y 2 − 1 16 ) 0M # /A A > / 4 0 / > / 4= = B Z L / C l 2 = −1 + 1 jΦ e 4 B / 1 > C/ L $' E4 = /= D A /< E= C 4 /A /= = B 4/= = /= = 4/ / B ED / E D 0 B < /< < / / > B-F4 ?. #= < /= / > / 4 / / / 0 ? 0 / > >L / = / /? G + = / A B // C l1 = Z − Z 2 C l 2 = −1 − Z − Z 2 4 ? L Z − Z 2 = −1 − Z − Z 2 A // ? A / / = / = / 3 4 / 0 ? 0 4? A / = C l1 (Φ ) φ0±Π 1 A = 1 2 / / C t12 = − A Z =− E / 4 E / 4/ / C / = = = A = /E 0 4 $6 E > = 0 /[ \ -A 0 . 4A / ED / E A E / / > @ / 24 ;0M Y4 A / = > $ / 1/ /4? ) ED / 4= 4/ Z p1 ⋅ Z p 2 ⋅ Z p 3 = Z + /< ;= 4 ;= ? ;=( /E / / ⋅ Z p 2 ⋅ Z p3 ≤ 1 8 > Z n +3 = Z n A p1 /A Z = f c ( f c ( f c (Z ))) = L Z =Z 8 + (4C ) Z 6 + (6C 2 + 2C ) Z 4 + (4C 3 + 4C 2 ) Z 2 + (C 4 + 2C 3 + C 2 + C ) C 4 + C 3 (4 Z 2 + 2) + C 2 (6 Z 4 + 4 Z 2 + 1) + C (4 Z 6 + 2 Z 4 + 1) + ( Z 8 − 1) = 0 / ; = ( = / A = / A 0 / 4 = 4 A /;= 4? A ? / > 4A B / /A 4 0( / A E / / = > / < / / 0 4 E/ C= C l1 =Z − Z 2 B E 4 = /A = / E/ = C/ 4 / L C 4 + C 3 (4Z 2 + 2) + C 2 (6Z 4 + 4 Z 2 + 1) + C (4 Z 6 + 2 Z 4 + 1) + ( Z 8 − 1) = C − (Z − Z 2 ) = C 3 + C 2 (3Z 2 + Z + 2) + C (3Z 4 + 2 Z 3 + 3Z 2 + 2 Z + 1) + ( Z 6 + Z 5 + Z 4 + Z 3 + Z 2 + Z + 1) = 0 B # / = / 4 / 4 /A F/ ( / / 4A D / /< / C/ / C / / / = + / A / =/ 4// / 4 A A / / E // C AC / 4/ / /A C = Z −Z2 - / / 4 < ? / 0( + / A / / 4 / = / / // 4 ? / / /< / B / C / 0( 0 4= / A = / 0 / E/ / ( + 0 . C 3 + C 2 (3Z 2 + Z + 2) + C (3Z 4 + 2Z 3 + 3Z 2 + 2 Z + 1) + ( Z 6 + Z 5 + Z 4 + Z 3 + Z 2 + Z + 1) = 0 4Z 2 + 2Z + 1 = 0 ( Z= A / = A 4 / = 4 Ct13 = = + / A / /? 0 ? B < / / =/ > G A Y C l1 (Φ ) = / B /= / A F/ φ0± Π⁄( / C / / = / 0(4 /@ / / A /= = / 4 / /= / 0( / / /= / D A 4 2 / < < / / 4 ( 1 = − 1 ± j3 3 8 / = B $* / = / / 0 ? 0 ? A /< 4 = / C / = 4 / /= E / > 4/ / ? A / −1± j 3 4 $* /B ( = / / /A / = ? A / / / 0 $ $ / / & B " E / = 4 > /D / E / E E = = ? /A ( /= / = / / = > / /D / = E / E C / // D4 / A B /A / / /E 4 A / / / B > / / / /A / / 4 / = C/ 4B / = / = /> B ? / > / / 0 ? 0 4? A E /E / > / / / 0( B > A / / / G / F/ / / > = / 4 = / / = / > 4/ @ 2 B 4= / A / // $ / = / / < = ;, 27, 0 <2 ,. 4 <0 / / B // A / = / A /= / > 3 = C A @ @ = C / B ! / = B > / // @ // < / A / < => //-/= 2A E / B @ 2 / E / N ∏Z i =1 A E B pi / 4 /B ≤ 1 2N / / 4 / = = ? / / > = = A = D ? A A C/ = @ 2 = / = /3 3 / 2 / / 2 F = = A / = / /= 0 4 B @ / / / = / 0 =4 A > ? = 2 /= < / . 4/ = AC / / B > / N ∏Z E i =1 pi ≤ A ? / L 1 2N / N N 2 N ⋅ ∏ Z pi ≤ 1 2 N ⋅ ∏ Z pi ≤ 1 E i =1 /A E / + /= i =1 / / / / // / 4A / = / + /@ B / / 2 = g (C ) ≤ 1 / N N i =1 i =1 g (C ) = 2 N ⋅ ∏ Z pi = 2 N ⋅ ∏ Z pi A & G / B /A / E > 4 =/ A F = /> ; 4? = > B = = / = / B > B E B /> /;=4 / = ' + = / = 4/ /A - . F A - . / /D / E / 0 ? 0 B-F 4 ?.A > / 4 /4 ! - . ] E D / . = / / 4/ B > = f ( x, y ) = g (C ) − 1=g ( x, y ) −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f cN (0 ) = 0 & D / F = = = = + ? / /< ? A L PN (C ) = f cN (0)= 0 /= /+ - .= /= / / L P1 (C ) = C P2 (C ) = C 2 + C P3 (C ) = C 4 + 2C 3 + C 2 + C P4 (C ) = C 8 + 4C 7 + 6C 6 + 6C 5 + 4C 4 + 2C 3 + C 2 + C ... C / + ? L PN +1 (C ) = (PN (C )) + C 2 P1 (C ) = C / = = / D / / / / /? = = = * + - ./ M + 4+ / 4A / / / / /= < = M F/ / = @2 / / / / 0 4 ?( / / E /A = 0 4 = 0 ? ( = 0(4A G / = E/ / / A 4 ? / = 4 E = A C / = 4( 4$ 4 = / 4@ 2 G /@ E / 2 = A 4E M < <4 /B = = = / / A / E/ / F/ E 4 = / M = / U N = 2 N −1 − F / A 4 F/ / 4 = ! 4/ / ? / 4 M / UK K N / @ ^V 2 / = 4= B @ ^ /= E 2 4 A /E / / / / 4@ ^ / E/ 2 L U 1 = 21−1 = 1 U 2 = 2 2−1 − U 1 = 2 − 1 = 1 U 3 = 2 3−1 − U 1 = 4 − 1 = 3 U 4 = 2 4−1 − U 2 − U 1 = 8 − 1 − 1 =6 ... ) /A E / /E /= 0 4 / ? ( < / / ! /= /E 0 W4 4(464 '4 *46(4 A G / 4 / M B / M + G = / / / = /A / < ! /3 - . = / E/ / 4? A / = @ E B /E = B C = B < / // / A / 4A E /+ - . ! = > A B ? /= / / / - A /A = / . 4 = + - . / E/ M 4A / + - . 4 / > AC = [ 4? A / / = = /E E /= = = = C + - .+ / A / > / M / / @ E 2= / /+^- . A @ ^ E 2 / / / / = = M 0 B / / 4 X U N < 2 N −1 − 1 /= 4= 4 ' 4$5' /A U N = 2 N −1 − 1 /= A = / / / /L / / / > / E + - .= / = / / = / /// / 2L Q N (C ) = PN (C ) ∏ QK (C ) K |N S / /= / / /L Q1 (C ) = C Q2 (C ) = C + 1 Q3 (C ) = C 3 + 2C 2 + C + 1 Q4 (C ) = C 6 + 3C 5 + 3C 4 + 3C 3 + 2C 2 + 1 ... B / /= /- / + / A 3 - ./ = / / / / = / = = / 4/ / = / / / / // C / = : 2127, 0 %/ A / / / /> L B / /A / - / / / / .< 4 ED / 4 < < / A $ /+ - .. /: , 6 / =:14 1 ,1 0101 / EDB C /= / 3 + 3 - .0 0 4< / Q1 (C ) = 0 C=0 A / A @ 2 = 0 / = = + 3 - .0 0 4< / Q2 (C ) = 0 C +1 = 0 C = −1 A = + / B A 0(43(- . 0 0 / 0M 4 A ? / /> / Q3 = 0 C + 2C 2 + C + 1 = 0 3 A / / / /E = /+ =4 C = −3 1 + C + C 2 / C = −1.7548775 5 A F ? A < F/ 4 ? - O *'$S**'. = / 4 4 0( / C 3 + 2C 2 + C + 1 = C 2 + 0.2451224C + 0.5698401 C + 1.7548775 C = −0.1225612 ± j 0.7448616 A = / / // C / / = 4 AC / 1 = @ / 2 / /G D = = + /A / /< = 4/ L '( / / /= / A A 0(4A =/ >4 0$43$- . 0 / // // ( A = /A ? / E 4E / > = = = = = / E C 6 + 3C 5 + 3C 4 + 3C 3 + 2C 2 + 1 = 0 A / E/ / A // / / / / L C = −1.940799 C = −1.310702 E = - O 5$ *55. _ - O ( * . 4 /A C 4 − 0.251501C 3 + 1.27394662C 2 − 0.5024681C + 0.393097 = 0 A #/4 / / / = // /A / = / / / (C − Z a )(C − Z a* )(C − Z b )(C − Z b* ) = 0 ( B B / 4 / C / C / 4/ A C = 0.28226546 ± j 0.5300536 C = −0.15651495 ± j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xn +1 = xn2 + a x0 = 0 / 4 / = 4 Z n = xn + jyn C = a + jb ! B > / 4= -/ / /4= / =? @2 A E / /A / = B B . #/4 / E / @0 2 - .# / /= / = > / / 4 A / = / // / / A > / ! = = / A // /E / /A // G / A > / / / = = / / / / > / B A B = . /A /E / - ? E / I M 4Z J 4A / / > / = / / / < = /= > / > < /= /= > / /< > A = < 1 I SJ I 5J C /* / / . 4? /> / / $ 665 = C / E = 0 4? E = (4 HE/ HI J 4= = / B 0( / / = ! / B = / + E? / (( + = A / / / / < / D // / > / ? /> / E = > / 0 ! D G = / 4/ = /3 + / A / /E / > @ F =2 B F / > / B / 4/ 6 L 1 6 /A / =/ = = / = / ! 4 / /= / ! > D / = /= / / /= /A < // / // /B / 0 E / = = 4/ = @2 ? < 1 6 B /< A B = / 6 L > ($ + /= D > > / B 6 B / = / / > 4 / 0 6 ( / < /= = / /E / = = > B E 4= / D / = 0 4 D / > + / / / B / C 1 < < </ / < D ? 1 /= = 1 C/ = @2 / E4 / A / = = / = /G / B ? G / ED 6( > A / / 1 /= / / /E F = / B (' % / " , 6 /" ED= / / D /= /+ / /A / / > ? > / / ! /= //A / / / / /? E / 4 /+ ? / / 4 4 / / / = ^ E/ + C / C / 4 / / A 4 B 4/ = = / /= 0 + - . / A B /= / < 4 / /= / 4 /E = A > / / // B / / / / = ? </ /< A < E = F D / B A /E / / /= 1 4? / / > / / = Q B 4= / / = / > = / /E / L 6$ 4 P1 (C ) = C P2 (C ) = C 2 + C P3 (C ) = C 4 + 2C 3 + C 2 + C ... + / = /= /= +( = / = G E/ /+ B A E / / 4 /= ( ? / = /= / = / 4 /= + 0 0 . =/ A /C = / > 4/ A ? /+ F/ / 4 (6 E 4 = 4A = /= / /= > / A /= / = < = + /E/ 6 '4 /< / = +6 ? A A < / +6 = / = /= / /A 4= / > / / E/ E = B B < 1 % # < / / B / = E/> /+ / 66 / / / B = / 4 / ED / / > = B 6' " , 6 /"? 1 2 127, = A E /= / / / > /= + 4+ ? +( C = 6 @ /.21 F/ /= /3 ? D / / 4 ? 4G A = = / /= /+ #/4 = /= // = = / / E/ / = /= = / > < /= /+ < /= / 4= E B @ 2 // 4= / > /= / D= / / / / ? E/ < < 4/ " = / F = = / / ED / 4? A = /= B 6* = / /A D L (* 1 66 1 6* (S ! B = > / > / = / /E / /> @2 7 / /= / = / M C/ E / / E > = > / = / / 4 / = + - .E = / @2 - 0 ./ =/ = / = / > / / / / @2 / F A =/ > / / 4 / > / E = / / / = + / / A / F E > = > B = /= /F / = / > / =4 > / 4/ /= = / = /4 / 4A / > E 4 // = @ / 2 > / ? / / 4 / 4 ? E E 4/ = / / => A / / / // / B F / = C/ E B 1 B / L 6S D A / < / = = / +(- . > / 4? < +S- . / / / A C 4/ / / F /@ / / 2 / / / / 4A / 4 / 4 /= / / 4/ 4 /= / /A > / / B ) / A /= + / = = E A % 4/ A ? / > / / /= / 4 / ? 4+ / = / // = C/ / > = > = / / B E = / 4/ /A /216 , /0 "/ 34 1 2 127, / / B // / / / / / = ? / 4 @ /.21 /A /+ E D @ = 2 > / 4/ = /` + > < a+ / A + / = 4 / > = = -@2. 4 /A B > = /= / / // 4/ G C/ / = B = + 4 = / > = =/ 4 < 4/ > = @ 2 =/ = / E/ #/4 / / /= / B >4 / 4 /= / / / 4 = @= 2 = < = E (5 + F = / / D A 4/ 4 > @ B > @ = / 4F = +4 = 4= / A B C / E [ 4 /E / 24 /A +S > 2 / B D = / F B 6 S #E D = = B 24= / = C/ 4 @ / F/ E /< / @24 < > +( / @20M / / /4 B PN (−2) = f −N2 (0) = 2 P1 (−2) = f −12 (0) = −2 ! B = = B + /= = // B A /= & D = // E / ? > A =4 B /A / B / = >4 // / 4= B / ? / A 4 E E / 4A = / / / / A / B /= / = > / /= / / = // B // / // E E / = / / / 4? /A / 1 / / / / / B /A /= / / / 4 / B = / # / ED 4 @ B E E /= / 2 / 65 > = / = /A G / /= / B / F/ = A = /= // / B / ? 4= / A 0(4 = / $ %$ 6A// 34 ED/ / = + A </ < < = 4 G = + + O C / /E / / / / / /: , 6 /" = C 4 < / = / = / A B PN (C ) = / 2 M −1 i =1 = = A A = C / /G /= / #/4/ F = / /+ /= / / C B / // ain C i A ∞ 0W4 4 4'4 $4$ 4 ( 4$ 54 $( 4$S6 46*5'4'S*S64 X $ ( ) 0 < / A 4 / 0 / = B / 4/ < B // B > A / C/ = > 1 / / > 0 F B / = D / / < A / = E ? / / 4/ / E / > E/ /B = > / A = D ?= / A = = //= = / 4 C / = / / = > A B T // / /= / / / B D/ = / ED D = // / D/ / / / B ? / > D A /4 A / 0 ! /= / /= / / / 4/ / =/ > = ( A // > // / / 4//= / = E/ = / / ? // > 4 / / / / T/ 6 /. 4 127, 0 14 127, ,. 4 B? / A 0 ? = / E F/ > A E 4/ = E / = E B B < A E E > 4= / A Z = Z2 +C Z2 −Z +C = 0 Z= / 4 / 1 ± 1 − 4C 2 / 4 C= Z= Z= 1 jΦ 1 j 2 Φ e − e 2 4 1 ± 1 − 2e j Φ + e j Φ 2 (1 − e ) jΦ 2 1± 2 1 ± 1 − e jΦ Z= 2 2 − e jΦ Z = jΦ2 e 2 ( / / // // / // > + / ) > 4/ = Y4A = 0 / φ / E $ A B = D / =/ > Y_ φ 4 / / C = C l 1 (Φ ) ( 3/ 4 5127, 0 / E Z= 1 jΦ e 2 /: ,./0 . 1, /= / / 0 ? 0( 4 / = = E E $ ,21 / . /A /= / L 3 4 − 1 ± j3 3 = 8 C t12 = − C t13 A = /= / = -φ. 4? A 4 C E Φ 2 = 2Π ⋅ / 4 / = /= / 1 2 1 2 Φ 3 = 2 Π ⋅ , 2Π ⋅ 3 3 < < /= / A / 0 E / = E/ A = /= / E -φ.= E Φ N = 2Π ⋅ / 0( / E / 0' G E/ A / / / 0( / + 0 4 G / 4/ = = A F /= / B / 4 Y F/ N =4 N =5 > > 4/ A A /E > = n N \ / / =B + = 4= / < E/ 4 \ (? \ ( 4 ? < / / / / 0$ / 0 ? 1 C l 1 ( 2Π ) 4 3 C l 1 ( 2Π ) 4 1 C l 1 ( 2Π ) 5 2 C l 1 ( 2Π ) 5 3 C l 1 ( 2Π ) 5 4 C l 1 ( 2Π ) 5 $( + A < = 4 = /= // /E / > !B * / A /= / / = > / &= / < /= / @ / / 2 L 1 * $$ * / / < 4= • • • • • • • • • • / / D A / 6 /. 4 127, < A @ E/ > F= ? G/ A = / ? # D // / / E/ / • • 6 /. 4 127, /2 346 ,. @ /@ @ B > @ > @ > / + / 2 / ;, 27, @ 2 ;, 27, @ = /+ ? 32 6 /. 4 127, @C = < / = /32 /2 346 ,. ? 0 6 /. 4 127, @ B> / = 2 : 2127, C /= /3 = / 0 4 4( ? $ ;, 27, @C = < /2 346 ,. /2 346 ,. /2 346 ,. >L /= 2 ;, 27, / / /2 346 ,. ?0 6 /. 4 127, @ : 2127, = / • • • > /= /= / / / G / / / / /+ ? +/ E / / = / > > B = /= / 0 4 ?( / 2 / 2 / 2 2 ? = 2 2 $' # IJ + /8 H 4@ /M 24"% L S$M( > IJ ! 4b &/ / c/ c = / d D 4 b= (5M ' ?4# 4 =? / = F/" " 4 b+ < /? 5S' I (J I $J c/ 4 4b /< </ <H 4b< Q / BB / B < /B < / $* - 55S. 4 'M 6* // 4 b# /< H? </ <H 4@< % "/ ?L( I 'J+ B '4 55 Q D M I 6J8% / < + " L < I *J Q M5'S'MK4 5SS + I SJ < % + Q& < 4@< % H4 @ & ?/ d < B < B \ f= / ? 4@ ! ? = / ?/ / e # / H\ B / \? = 1 4@ E / % < E / / /B ? B1 / 2 d 24 + = E < < B / / < /Q / BB ?4 4!8 4# 8 / ?/ / B Q ?2 '4 5S < =L\ \/ ? B < ? B < < E/ A ? ? M) / = / ! ? = ?/ / 2 ! /# 'S1 (e 4 5S6 F = E /B B < F = / 2 E\ 4 / 4 5S I 5J B I J# / 2 4@ 3 / HE/ H4@ H E E/ ? B / / B / B / 2 +<?/// 4 5*5 < F/ / / / / 64 56$ $6