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a #$ % & / A )Lbc & (0 % ! > # " #$ % & ( $ ) , Q , >? @$1 $ 678 ( $ ) , " ) / Q ,: + "7FA )d ( $ ) , !$0; Q ( 1* >F ,0;( "0 (0; "5 3 * ( ? / A O$ ,:L " #$ % & :0 ) O$ ,:L " #$ % & ( $ ) , ( # , $ , , 0+ ) , > # "0; ,7F1 ) ( # " #$ % & gO$ , "0# ) 0# "0 ,0;( "0 " & , $ , , 0+ ) , > # ,0;( "0 Q hd ,$A* , , 0+ ) , , $ , "7F1( > A !$1( "?( " #$ % & ! A ( $ ) , (0 ( ( Q78 /* , ?( F19 gO$* ;, "5 , f ) * ) 8! ) hd ($0; ($A ) , , ( "0 ) > A0 "0; ,7F1 ) g, ( "0 ) > A0 , * ) h " & 1, "0 ) ($8 "0; ,7F1 ) , "$ ) * +$ ( #$ !0 ) !$0; &' ) F ( - > < * +$ 08 , ) ' F - @ ? ($P ) , 7FA ) ) K9 "0; >F > < 7P ) )7FA !F < / A! O$ >F /* , $* ;, " #$ % & / A a ( # " #$ % & bc +$ ,: /FA ,$A* , $0 ( > A0 ,7A ) ,:7FA ) F19 ($1 , &d ,$* + (0 /* @0 ( ? / A (0 )7FA % 0+ ) , 08 ! P >F " ) ($8 , 0; ) * !$0; , 0; ) 1, "0 ) , f ) "0 ( ? Q (d , f ) f ) 6$ ;,d , f ) $ O$ % , ; ? @$1 ,:0 ) /i >71( @ + @$1 )d ( $ ) , ( # " #$ ( ^ , "0 > A "0 &! ( ( ( ( f > A ( ( ( 0;( , 10 : 671 , ) ,:0 ) ($0 ( 60; ) :0 ) > , ( # " #$ % & ( ( Q * ! * R * ,7A F A* " ; F % ( !0 , ( ( ,0 A > A ( ? Q ( :0 ) (0+ ) ) 9d ( ( O$ ,:L Q$ ;, R )0#! >0+ 60; !$1( , +$ Q$ ;, , 08 ! P ( ( "0A 08 > # 671 ,0 A d "0 ( ? Q (> A $ O$ % , ; :0 ) 7P ) f ! ) # " + *d ( ( , 0; ) " #$ % & g h ( A ) (0 > ,:0A O$ ,:01 ) ,:0 ) > ( , ,: & > A 671 , ; R0 ($8 %*P , $ , (0+ ) ) > A> f ! " 71( , ; !0j % ? ( ($8 1, "0 ) Y ) ) A* " #$ R5 ( 0; RF8 !0 , > A /0 , 0; ) " #$ % & U j @ A ) ,L! , ;* , 0; ) " #$ % & ! * (0+ ) ($1d %*P , $ , % 0+ ) ) > A , 0; ) >$P % ?d " #$ % & ! * ,? d ( ( , 0; ) ) , 0+ )d , 0; ) f ) /7F1 )d :0R0,d ) * ( ( ( > ; " # % &! ,0 > A , 0; ) % , ; Q P ($P ) @$1 ) ,7A /* , $* ;, " #$ % & ,71 "0 ) ! " #$ % & , , 671 / A !0 , % ! : ;, :0 )d @$ ) O$* & ( A* ( ^ " # ( " ; /* , $* ;, " #$ % & ( ( , 0; ) %*P , $ , 56561 + ; < ! ! " +, = V # - - 91 ! & * =0 , , +$ ( $ & 0& "5 ,$* ; R ;, R ; , , FA @0 A ,0 01( )7FA V$! "7F1( )01 / A 0& "5 , ! ( R0 "0; >F 7P ) ,$* ; ( $ & , # 60; ($8 090> / A " ( ( 0# , ;9 >0A ) "F g +, 2G ; -; ; - * /* , $ > A : ;, ! "0; >F ( ( ) "7F1( ) F , $ > A0 f! = 090> "5 ,$* , "0; ($8 ,: ) , ( + R Y ) ,:0 ) ,0 A , $0 ( !0 , , & /0 Q ( "5 +$ #$ % "$8 " & Q , 0& "5 , ! ( ) 33 31 7F ) 9 A* "7F1( 090> , ,: & ,7A " #$d (0 , & @$1 ) ( ( ( 0# , ;9 >0A ) "F ( # ,78 ,$* ; ,? > A9 ,$* ; R ;, R ; , , FA ) &! 0& R , O$ ,:01 ) ($8 7F ) 9 090> / A (0 , & @$1 ) "7F1( ( ( ( , 0; ) R (( (0 , ( ? ) * % " P R ;, "7F1( " ) , # 60; ($8 # ,78 ,$* ; ,? & Q ( "5 671 0& "5 ($8 , 0; ) " #$ % & ,$* ; / A 671 !F8 :0 ) R &$ "0# *O$ 6, ) ,$* ; =$1( A* ,:L R A* , +$ ( $ & 0& "5 090> >F % ! > # 671 : A ) R$0 ( @7F @ ) R ;, " ` ) , 7( ( # ,$* ; d # ) - >F "0# , , # 60; R ; @ ) ($8 # ,78 ,$* ; ,? K( " &! 0& R , O$ ,:01 ) ;, > A ;9 @ j ;, ($8 , +$ ( $ & 090> / A ( , ;, ( ( ( " K( ,? , # 60; !0 ) !$0; ($8 7F ) 9 *O$ 6, & )F , $ 7F ) 9 090>d , Q , ,$* ; "7F1( ! 01 F8 L #$ > A0 % 80 , ] ^ "7F1( ) , ;, / A R Y ) % 0+ ) U0 "0 " ) ($8 , 0; ) A* (0 , & R &$ @ j $k ( )= ( )− ∫< ( − τ) ( τ) τ g NE h 2N ,:0 ) "0k ( )= − P( ') Z " ) %?( , ?( "F eo (t ) Z " ) " #$ % R >5 " #$ :0 ) 9 + ,?( A* # ,78 ,$* ; ! P " #$ % )F : + ) ) 678 !0; / + # ,78 ,$* ; "7F1( ) F Y! ,:0 ) >$A ) ! L '< +, #$ % )F ; < Y ( 09 # ,78 w ] ^x , 08 > A0 : ($8 01 ,: + ,$* ; k < ≤ C ( ) ≤ & > A g NERh ( ) = C ( ) ( ) !01 , FA " &! , ,0# , ) ( )≤ d F8 " +* , O$ , +! " ; " #$ % & , ! ( > A " #$ : , ! ( ;$ !0 , ) ,:5 , 71( (0 , % R " #$ $k ∞ ( ) − ∫ < ,L! , ' #$ % & & "7F1( ,L! , − ( ) ) i 0& ∫ < ( "5 , ! ( R ( ,0# , ;* ( !0j , ( ( " #$ g NNh A " #$ : ($8 # ,78 ,$* ; "7F1( ) F d , 08 7F ) ,:L g NGh > A , 0; ) 0# , ;9 / A " #$ % & , ! ( R ( d % "0 lim →∞ e − nt L > * "0; >F +, g ( )=< ;$ R0& " # u< F5 0# , ;9 ! 678 − A* / A , 08 d ] ^ ,$1 > # \ :0 ($8 090> "7F1( @71 ,: + 01 F8 L ; - F ( ) , 0; ) ,$* ; ,? / A 0& "5 , 0; ) " #$ % D F X , 0; ) 0# , ;9 / A 0& ≤ N [ e(t ) ] ≤ K "5 g h "$8 " & !0 , 60; , 71( O ,0# , ( "0; >F , ;, ( ω , 71( ≥ > A !0 , 60; 08 ,$A* * δ > " #$ % $ "7F1( , 08 k Re ( + dω>)P( dω) + / & ≥ δ > < , 7( g $A* , R -, R$0 (k h 'h > #O> A / A 'h / A , +$ ( $ & 090> 0@ )9 0; >F ,$* ; ,$* ; "F F @ d( ()F ,:5 R ;, R ; , , FA ) ;$ < < & < ∞ −∞ < > < ∞ Rh g ;$ & = ∞ ,$* ; (0 ,7A ,: j , $1 "0 ) g ''h −∞ < > ≤ < > A < < & < ∞ (h 0; >F ,$* ; (0 ,7A ,: j ,?( (71( g Q ! L ' h A F ,$* ; R ; , + , , FA ) kOp − 76 $ & g + ω> Im P( dω) , 7( g h , R &$ : Y ) >F !0j ω "0# , Y! R + ($8 "7FA ) , ` ) h *O$ 6, ($8 G ( jω ) Re P( dω) = − 7FA ) , ` ) ' 0( α > A β A / A & g + ω> Im P( dω) A* )01 / A "7FA ) 090> "7F1( ! 01 F8 3h L E α = t a n − ω> β = tan − +, ; F ( ) g 2h ω> +, ; D ) > V0P : A ) "0 @0;( ($8 "7FA ) , ` ) ? 3 4- A* $1 , $0 ( > A0 ω H71 0& "5 $1 , $0 ( > A0 > ( ( 01 ) ,:5 O ( "0; >F g~ ω h Y! R + ($8 "7FA ) 090> (0 "0 @0;( !0j , # 60; ω d $1 , $0 ( > A0 , # 60; g 2h & ,L! "7FA ) 090> % 0+ ) R ; "0& k 1* ( ! , , # 60;d 678 @$1 ) g P* ( dω) = Re P( dω) + dω Im P( dω) ,:0 ) "0 P* ( dω) / A " K( ,? P( dω) "7F1( + , , # 60; " P "7F1( 678 "0& g9 +! ω ($8 " #$ P( dω) U0 "0 7F ) ,:L Re P* ( dω) > − & g # ,$* ; 'h (0 , + > Im P* ( dω) ,? )$* + # Eh 80 ($8 , $8* R & > ;, / g Gh E' +, ; F ( q≥0 k P * ( dω ) :0 ) ! K, ` ) P* ( dω) "7FA ) 090> "7F1( Q ( "5 Re P* ( dω) = − > A % 0+ ) 1* ( 8! , P ( dω) "7F1( ! L & F8 g Nh 7FA ) 090> ,:0 ) ! K, ` ) + > Im P* ( dω) , # 01 * ) i E 60; L '3 > A '2 0( γ "7F1( "5 γ = tan − > $k g h $ * ,7A ( ( '3 > A '2 O$*P ,?( P * ( dω ) " O$ R + ($8 , ;9 ,$* ; " ; O$*P ,?( F8 " & ! ! A P * ( dω ) ) >F ,:$1( , 71( +! &! A* (0 ) ,:5 Z e U0 "0 R &$ , "0 /F1 ( 9 (71( +, ; F " "0; >F , 0; ) 0; >F ,:7FA ) F19 ! A > p p F # ,78 ,$* ; ,? d " ) " #$ % " #$ ( ) "7F1( ( RF8 k ( )= ,:0 ) "0 < , '< +, < − + '< −' + < $1 , $0 ( > A0 " #$ % ; Y) − g " #$ - h E3 ) Q$ ) "F >5 ] ^ "7F1( ( RF8 ( ) = A ;$ O p A # ,$* ; ,? / A 0& "5 T ;, " ` ) , 7( g 'h "0; >F , A # G ( jω ) > A !0 , Y ) 60; , 71( O / A * ;$ ,0; , ( 0;, ($8 %*P , $ , A* 7F ) 9 090> ( , ;, ( " K( ,? , # 60; ($8 7F ) 9 *O$ 6, > A @ j @ A ) @$1 ) > A0 ( ( , 0; ) R ( ( +, ; F ( ) ' Pj]d ω ^ 4) < $0 , E2 +$ ( $ & "7FA ) ,:0A ,0& ) O$ , Z 7F ) 9 090> !F8 :0 ) ) ( ( @ ) , 0; ) % (d ! A % 0+ ) ;, , ;, R5 )F F8 ( ( (0 # ,$* ; ,? 0& "5 > A ,$* ; R ;, R ; , , FA ) 94 H $ % " P ) + (7$ ( + ,?( ( ( ,$* ; d ( 9 A0 + @$A ) ( !0 , /0+) ( ( 01 /71 7F ) 9 ,$* ; "7F1( ,:L R A* F8 L :0 ) ( 09 ,?( 7R ) ! 60; ( 7F ) 9 % ( $ @$A ) " & # Q ( "5 !0 , ( ( F19 /* 7F ) , 0; ) " #$ % & ($1 , & 47$ "0# + ,?( , 0; ) " #$ % & 'N ( ( ) # ,$* ; ,? d 7F ) 9 Q ;9 Q^ ,$* ; ,? 678 @$1 ) %*P , $ , ,$* ; ,? O$* 7F( ($8 9 + &$ "0# *O$ 6,d ) "0# T0@ * 7F ) 9 S$*P " 10 q 0; >F /0 , 0; ) " #$ % & A*d (0 , & @$A ) /* , $* ;, " #$ % & ,71 "0 ) ,$* ; ,? " & + ,?( > A , ;, % ; ($P ) / A /* @0 , , 0; ) ,$* ; ,? "7F1( + ,?( %*P > A +$ ,:0 ) # " #$ ($8 O$* & ( A* ;$ !0 , , 0; ) % 0+ ) , & Q ;9 Q^ ,$* ; ,? "7F1(d % "0 @$A ) !0 , * #$ ( ( 7F ) 9 % 80 , ,$* ; " P ,:L R A* ,:0 ) ( 7F ) A* ;$ , 0; ) ,$* ; / A R ;, R ; , , FA ) > A (0 # ,$* ; ,? / A 0& "5 K( F8 R + ) F 0& "5 g% 0+ ) (0 ) ! Y! R + ! K, ` ) Hhd % "0 + > @$1 ) 7F ) 9 A! !0+ , +* / A !0 , 7F ) 9 ) # "$ )d Q ;9 Q^ A! ,:$* # " 1, 7( 60; ($8 % +$ ,$* ; R Y ) ( ( ( ^ Q , ( ( , A # (F R " #$ : :0 ) , 71( , ; 7F ) 9 A! !0+ , * (0A )01 / A 7F ) 9 ( + R Y ) " #$ 0A / A !0 , 7F ) 9 : ;, " -( /71( " & % 80 , ( ( R ( ( > A ,L! " #$ % ,0# , ( ; "0 ,71 @ "0 ) ,:0 ) $* + ,:0 ) !0 , 60; ,:7FA ) F19 " K( R , 7F ) 9 A* % 0+ ) ( ( +$ ,: /FA "$ )d ( ? Q ( > # ( ; "0 ,71 @ "0 ) ( % -( $1( / A ( # Q , EE 7F8 ) ($8 ( ( 01 , # R ( ( / + A! !0+ , ($8 # ,78 ,$* ; > A % ;, O$ / A A! !0+ , P / A !0 , 01 "7FA ) (0 ) $1 , $0 ( > A0 R + "0 > A , # 60; ,? $ > A0 7F ) ,:L ( + R Y ) " #$ 0A P (0 @ )k + C( ;, O$ 08 ) , 0; ) ;$ , ω)P( dω) = < "7F1( ( # % &! ,: * @$A ) 7F ) 9 % ( / R Y ) ( ( " #$ % & ,$* ; / A R ( d % "0 7F ) ! K, ` ) > A 4* 9$ 0> / A ( ( 7F ) 9 , ?( F19 "7F1( 678 @$1 ) R 678 / A 0& >$A !0+ ;, 7F ) 9 4* 9$ 0> ($P ) (0 , & @$A ) % &! ,: ;$ R ( ;$ / AR (R * ( F d /$( "0 7F ) 9 090> "7F1( @$1 ) " & Q , 0& "5 ,$* , "0; ( ;$ # ,78 ,$* ; A! R ; , + , , FA ) > A # ,78 ,$* ; ,? / A % 0+ ) "5 d % "0 @$A ) , +$ ( $ & "7FA ) ,:0A ,0& ) O$ , Q ( "5 ) ) ,:5 ( ( "0 /F1 " & , 0; ) 0& "5 7F ) 9 !0+ 08 ) , 0; ) "7F1( @$A ) " & % &! ,: / # ($0; 671 0& "5 ($8 , 0; ) P ,:F1 ) $9 ,:0 ) > ( % &! ,: ( ( * ;$ ,0; R ; , + ,7A 671 R ;, "5 (0 / + O$ ,F ,? $ /71( ($8 ) , ;, > A "0; >F ( ( % % f , $0 ( > # + ,?( @0 7( , 19 ) +* : =0+ 08 ) , 0; ) ($P ) ( # , ;, RF8 >L %*P , $ , " #$ % & ,71 "0 ) g h * > j (0A R ;, /71( ,:0 ) > ( ( ) ! 671 0& "5 ($8 ,$* ; !0 , ( ( , $* ;, $1( =0 , >? @$1 > # " #$ A* / A 7F ) 9 , ($8 4* 9$ 0> / A " #$ % "$8d ) % 0+ ) / A " #$ % ( # ( 671 0& "5 U0 "0d ;$ % 0+ ) ,L! : !0 , A! 4* 9$ 0>d % 0+ ) (0 ) i / A " #$ % & ,$* ; / A % 0+ ) 0& "5 ! 01 ,: + L 'Nd 7F ) 9 !0+ 08 ) / A % 0+ ) R -, R$0 ( ,:0 ) > A ,:7FA ) F19 > A "7F1( %* $ R Y ) "7FA ) ) 1( "7, , +, ; EG EN & 3 ; # 0H! 0H!3 0H!; '# & ( !+ H3 S −01 S S− − D B DS − D !+ > !+ ! !+ K 0< ; − ! !+ ,− B S 0− − D B S −0 S − − D S −03 S − − D 0; ! !+ ,− ! !+ !+, 01 !3 + 0= ! !3 + 02 0> B, , !+ S S D − DS − − S −0 S − − D S− − D B +, S− !+, 04 + , + 3< E S −3 − D ! ,D S + − D S S− − D S ! ,D ! ,D S + − D −3 − D :S + A S S − − D S − − ,D S − − , ,(, − ) := , 0− − D − 0− −,D , ,− − D 0− −,D − , −,D 0− − D , ,− δ ( ) = 0( ) = lim ! D ! D S+0 S − D ! ,D A= 0K +∞ ∑ δ( D→< = < D S S− !, − ,) −,D − ,D ! D S +0 S3 − ! , − ( S− S! ! !+ − D S3 − B + ,3 − , − D− S/S , − B ! !+ !+ B S− − D −3 ! , S/S − − D 0+ D B 0B 0@ − D − −,D S S − − D S − ,− ,D B, 03 S/ D − 0+ − D S + 0− − D − D − D − B 0B !+ − B !+, D3 − D S S + − D S− − D ; − 0B 00 S − − D B !+ ; D;S S3 + 1S + 0 ) 68 SH S DSH S 3 D S S @ H3 S 0 ; ;X !; = ! − D) 0− − DE = S S −0 E & * ( # " ! : ; - #- @ ,# " ZS V #Y S @ ,#Z S - B ' @ \− # Y S ) \ ; B5 @ Q [S[ D /V-@ V @5 V-B Q [S[ Q V-@ D \ T ( ' #YS S Y #- Q [S[ Q V % -/V-B &( ' , V-B Q [S[Q V-@ B + YS Q% ( '# ) # /! ! [ [#V-B Q [S[ D Q [ [ V-@ ^ " ' ] ) N ( % $ , " % N YS −S S #- V-B Q [S[ Q V-@ _ M % S = > -I YI SI V-B Q [S[ Q V-@ C N -B Y S 0 Q [S[ Q V- − V- + _ $ ^ - < ( - -< % YS _T S→ ∞ I - (M M & ( ' ' T" Q< YS#ZS % -/V-B V B5 Q [S[ Q% K ) 3πW # ∫ Y(U) ⋅ D $ N /V-@ V @5 V-BV B Q [S[ Q V-@ V B D $ N S Z × U−0 U 0< - ∞ ∑ -(%) (% − ) 0 V- S Y S # Z S V-B Q [S[ Q V-@ 0 Q [S[ Q V + V − %=−∞ 00 +∞ ∑ -( ) =−∞ 03 D ' 0 − S −0 YS % 0− S S −0 −0 ' $ $ V- [S[ + Y∞ T- D D&( ' * _T YS ' T G< !& ! ! 56 +$ (0 >$A ) ( # , ;, 1= C - < ' ω `- >_ +$ R P0 0A C= >6 'α + sin 'α π +$ % E6 VF/ - 1= C C F8 `- α sin 'α cos' α + −d π ' π 'π ' sin α = − e ! = ! _ C= − < C >5 ,:? (0 ,: j `P^ '& C (cos α + cos α ' ) π!( _ + ) &C (sin α − sin α ' ) \d π!]_ + ^ _ sin α = e ' α = e != ! _+ +$ 60 - 1= C C= 36 - `- 'α + sin 'α C= − π _ @ ?] ^ = sin α = 16 # ' C C < C C@ P^ (0 ,: j U `- % - : )) : H( ! , % 0+ ) " 80 Ua 3Y< max C= (cos α + d sin α) π!Y; sin α = ! @ != _ = Y; < U `- Z -3 ' T6 = ? N ⇒ C = ' π = − ? 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