Кудрявцев Л.Д. Курс математического анализа. В 3-х томах. Том 1 (2003), страница 20
Описание файла
PDF-файл из архива "Кудрявцев Л.Д. Курс математического анализа. В 3-х томах. Том 1 (2003)", который расположен в категории "". Всё это находится в предмете "математический анализ" из 1 семестр, которые можно найти в файловом архиве МГТУ им. Н.Э.Баумана. Не смотря на прямую связь этого архива с МГТУ им. Н.Э.Баумана, его также можно найти и в других разделах. Архив можно найти в разделе "книги и методические указания", в предмете "математический анализ" в общих файлах.
Просмотр PDF-файла онлайн
Текст 20 страницы из PDF
A&) D&) ∆ϕ&∆t) ∆ ' ( A&ϕ&t)) D&ϕ&t)) @ ( ϕ ∆t * &!wϕ)(ϕ((""t∈∆tNwϕ@(D&ϕ&t)) ∆t " ( (( "("t∈&∆tNwϕϕU<&wA))_()------ D&ϕ&t))I _D---------------_t_ ! ϕ(t)_ϕ ( t )--------------- IA&ϕ&t))ϕ$&t)_tU< wϕϕ &wA) U<"" ,wϕϕ &wA)(A&ϕ&t))ϕ$&t)"!" ( D&ϕ&t)) 5 (&<>F[) ) ' * ' ( ! /%< 6'9 : B$6?4 z&) y&)[ :(@ # '$&6[BB?$ %@5&6@[6 65@ '%&[>& # ('$&6%$8%&$&&5< ∫ y_z&& '# ('$&6%$8%&$&&5< ∫ z_y#∫ z_yIzyU ∫ y_z&<>F>) + ( z&) y&) ∆z&)(( wz∆y&)(( wy∆wIwzwy5w / " ∈ ∆Nw((!_&zy)Iy_zTz_y'z_yI_&zy)U y_z3 ' 4*< < ∫ _&zy)IzyT= ∫ y _z*+'4P < * ∫ z_y∫ z_yI ∫ _ &zy)U ∫ y_z+'zyT=∫ _&zy) = ∫ y_z(&<>F>) <)&###< 0 ! 6 #<6% %< JITXX /' 4?4 / ! : ""!E4%&&<;4%&;7 / 4%&;7JITX*!,<I|Y JIls J 5! T X " "<52%64B 40 J * ls J4!%$8%&6 #(<6% %< E F T F $< JITX!QJQ QJQI F T F <5hYij_` /_siq_bih_k` /0 J I T X " b& ) !1 " ϕ&)4JITX'& 7=>"!"! )JITX!!&)!& ( )0 & ) & !" ∈ ) T X 6 #<6%4 #<%6%&;7 ! "!4%&&<;4 / 48ϕ!JJ4 5$ &J!dhq J9ϕJUπVϕπ!! ihq J 5 dhq J J4Fπihq J J45 Jihq JIihcaq --- TVπVI4"VI<VIU<CI4π4ihq JI --F- `_qb II4ihq J+QJQIbdhq JIϕ1& =>)Ibcf` ϕIb`_b ϕ'JITXIb&cf` ϕTX`_b ϕ)+'&5 &(%64 B 4 6 #<6%5 %< J JITX!!(:!!("JI4,'bI4 ϕ ! / 0<T<XFTFX<IF<IF+ T4XI@4TXIX4T4XI4R$ ""J< I<TX<JFIFTT XF(XYZJ<TJF I &<TF)T&<TF)X&<=<)3 J< T JF " "J< JF& " ! JIJ<UJFJJFTJIJ<@JITXFTT&FT)XI<TX<5I<UFI<UF J<UJF""J<JFA ' &) &)'(&<=<) & ==<44):JITX*&) """ ! ""'!"""J<JF& ==<44)QJ<TJFQQJ<QTQJFQQQJ<QUQJFQQQJ<UJFQJFJJ F< QJFJ<447==J<J<FJF7<44 '" !" FPO*: " " J< I < T X< JF IFTXF(XYZJ<JF≡&<TX<)&FTXF) I &<FU<F)T&<FT<F)X &<=F)8 'XI4T<X ! + XX I U< + XX !FX -!FX IU<C'#(&<=F)!(;( "(CJ<Ib<&cf` ϕ<TX`_b ϕ<)JFIJF&cf` ϕFTX`_b ϕF)J<JFIb<bFL&cf` ϕ<cf` ϕFU`_b ϕ<`_b ϕF)TTX&cf` ϕ<`_b ϕFT`_b ϕ<cf` ϕF)MIIb<bFLcf` &ϕ<TϕF)TX`_b &ϕ<TϕF)M!QJ<JFQIQJ<QQJFQdhq &J<JF)Idhq J<Tdhq JF&<=P) !* *dhq*" ' * " ' dhq J<dhq JF:QJ<JFJIQIQJ<QQJFQQJIQdhq &J<JFJI)Idhq J<Tdhq JFTTdhq JI " " I5J<IJFI I JIIJJ III < FPJQJIQIQJQIdhq JIIIdhq JTFVπVI4<F@!(! ,ϕ /!J "JIIϕTFπLLI4<F5II F dhq J Idhq J ! " I&ϕ T FπL) II Iϕ TFπIL Iϕ! IFπdhq J #FπI5*(* /%<ϕ∈dhq J&Iϕ∈dhq JIII+'JIb&cf` ϕ T X `_b ϕ)J Ib &cf` IϕTX `_b Iϕ)5 ! < &b I <) * JIcf` ϕTX `_b ϕI&cf` ϕTX`_b ϕ) Icf` IϕTX`_b Iϕ&<=R)<#B $<4S$ J< ----J<JFJF 4 ! <? :&<SS[/<[HR) /(J< JI ----%& &<9J<JFJF%<J<IJFJ+'QJ<QIQJFQ QJQdhq J<Idhq JFTdhq JJ<JJ<-----<QJQI ----I -------J dhq JIdhq J Idhq J<Udhq JFJFFF&<=H) ""J<.
&<=H) J I ---- JF" J< JF 4 7"" ! ( *"'" *" " +'!"!CI / 6 I(4 %" { I I J { I(I ,{ !J1F;X IU<' – < IX5'(F – < &UX) IU< UX – < – < IX – < IUXCIJIb&cf` αTX`_b ϕ){Iρ&cf` ϕTX`_b ϕ){ !J[Iρ &cf` IψTX`_b Iψ)Ib&cf` ϕTX`_b ϕ)1ρI I b 9 ( / ρ4{<{F{44{P{R7<4<4FJ7<4FJFQJ <J<J<4J< JFQJFJF7<4Pϕ T FVπ-IψIϕTFVπ&V /)ψI --------------------I+*"VI4<IU<,!'ψV{VIρ&cf` ψVT`_b ψV)ρ4 +" "V ψ!"ψVFπ '!"{VVI4<IU<-!IJJ4I{4{<{IU< {V V I 4 < I U < #" I( ρ {V {VU<"VI<FIU< {I U<{4 Fπ/I; <4<! IIH0 J I T X UX%#9' J! J J I U X A J ! J& <4F)-.&%&<4 QJQIQJQ4ihq JIUihq JFF JJIQJQ 4P JIJ4R J < T J F IJ<TJF4H J < F J F IJ<UJF4S J < J F IJ<JF4J<J< I ----- J 4[ ----FJFJF@<4& <4F) "FFFJJI&TX)&UX)I T IQJQ 4@P ,JITX J IUX J I F X ITXIJ R4 ! " J< JF"& <4P) J < J F '" ! !J<TJFJ < T J F@J <J F J <TJ F @H444@S [ *"""*"4 < Q J < J F QIQJ<JFQIQJ<QQJFQIQJ <QQJ FQIQJ < J FQdhq J < J F IUdhq J<JFIU&dhq J<Tdhq JF)IIUdhq J<Udhq JFIdhq J <Tdhq J FIdhq J < J F 4?[ 3 ("! (, !< T < X---------------------- FUFXF T F X( < T < X ) ( F F F X )< F F < F< F T < F< T < X- T -------------------------------- X---------------------- I ------------------------------------------------------ I --------------------------------FFF T F X( F T F X ) ( F F F X )F T F FF T FF< 332! <=<($ JITX % ": " "&)"∈∈ *,XYZ&)T&$$) I &T$T$)XYZ&)&$$) I &$U$$T$)&)∈&$$)∈;' " * llllll F<+! ( #< 6 #<6%@%<+ & 4) ! &" (")&4<)XYZ!X,X I &4<)@ XFI&4<)&4<)I&U<4)IU< XFIU<!&) &)ITX1JFζ nxJ&)I&4)T&4)IεI &4)T&4<)&4)ITX#" " <=<ζ47<4R)*+,-./.0/ ! – ! ( " & /)< 533942+ !!*".
" * #%<(&<;%&;76 #<6%@%<0"J*I! I,JIII<F *$%&;:#%<&<;%&;6 #<6%(@%<JIIITIXII<F^%<ζIξTηX:(&%9#< [%<<9<7254%&&<;5%<εW4%$8%&$&&64 IεIWIε#<9(&%9%&QJIUζQVε'# j_s JIIζI→JJIK"ζ& <4R)-!('# "5 < * j_s JIIζJJIK"I→* j_s QJIUξQI4I→"+ζIξTηXJIIITIXII<F+QIUξQQJIUζQQIUηQQJIUζQ&,# )QJIUζQQIUξQTQIUηQ&,# " " ) JJI IITIXKζIξTηX ""JIKJIK"ξη3 j_s JIIζI→ j_s IIξ j_s IIηI→I→+ " * 2%6 <4; " !""!*0# o > ! ! (#! !" k$ 5&;[%<&<;%&;JJIK5 &%&<; #%<&<;%& J{IK #(<%&;JII&{I) %<%$8%&$%&99"W4&69[&QJIQ"Q{IQII<F<3'!,I{I4II<F'*,""JJIKJ{IK*"$W4I4QJIQ"$Q{IQIII4I4T<' J {<J{FJI4 F <"Isi^ ------<- ------F- ----------------- "$ {I4F<QJIQ"Q{IQII<F /%<JII&{I){II&JI)& 2$ 5(&;[%<&<;%&JJIKJ{IK5#96#%&;JI {I ! k$ 5&;[ & #%<&<;%&;JJIK 9<9&%9 2%6 <4 # %7 % #%<(&<;%&;7J{IK#%&;JII&{I)%<%$8%&$&2%(69 <9 #%<&<;%&; JαIK &69[ & JI IIαI{III<F%*%<&<;%&JJIKJ{IK:7&%9>6<& < % #&&%6 [ %< %$(8%&$&&69#%<&<;%&;JεIK&j_s εII< JIIεI{I II<FI→'#JI∼{III<F)*+,-./.0p1 1 !JI{{I!"!JII{IT&{I)II<F1 ,JII"{IT&{I)II<FJII&{I): (F;A&J)IQJQA&J)IJ 5!'( " " " *C({IA&J) J∈{∈(A! K{; ( { I QJQ ! F ( { I J / ! /F' ! { I J ! ! * " "( " "(&(()! #"("#"(0(A&J)J∈54 '%&' (QA&J)Q- ! (A(QAQ + *$%&; 6 #<6%:9 B$6?9 A #(< '%$%&;J4∈|$6?9A:(&%9 #4 &6 J4 %< <9 <725 ε W 4 %$(8%&$&δW4&6[&<9%@&6J∈$<&(978@ $%<7 QJ U J4Q V δ #<9&%9 %&QA&J)UA&J4)QVε:(' "(& HH)0 ( ' 3(QA&J)QUQA&J4)QQA&J)UA&J4)Q( A&J) J4' ,J4∈(QA&J)Q'; ( (AC J4∈(A TCACC&J4)4AjC'3 ' ! IΣ V J V '(( V V IYI&J) I V!4I 4 < I!J4∈& [<)<! *9$+IYI&J)IIJ TIU<JIU<TT<JT4J∈&<=S)/ !*'((ddI4<I0'(( & HP) I 4 I %&(#;7 5< U3 ! L aL&J)#IYI&J)*HV&J)Vo`&J)`IILTV4`VLYI&J)YI&J)IHV&J)aL&J)TY`&J)+'5" HV&J)Y`&J)YI&J)aL&J)< 5(<YI&J)aL&J)YL&J) /< aL&J) /<&< HV / %& o`&J) / %&&6 YI&J)aL&J)5LI<`I4 '0 J4 YI&J4) I 4 6 &<=S)CYI&J)I<JUζζ /!YI&J)I&JUζ)aIU<&J)TbaIU<&J) /IU<b / 5 J4 YI&J) YI&J) ! J U J4 &<6 )C YI&J) &J U J4)V &V / VT<)&JUJ4)V6&%&;769J45 #%& V(VW< /6& 6 -!J4VYI&J)VYI&J)I&JUJ4) aIUV&J)aIUV&J) /IUVaIUV&J4)4 ! %964 5<YI&J)%I< ʄ 6;J<CV YI&J)I&JU J < )V<a I F V &J) a I F V &J<)4<< a I F V &J) # I :<a I F V &J) !# < " !<JFC'VFV<YI&J)I&JU J < ) &JU J F )aI F V< F VFVF&J<)4 a I F VaI F V< F VF< F VF&J)&JF)4+ '#L# Y I F V F F V &J)II<LYI&J)* ,V<VFYI&J)II&JU J < ) &JU J F ) &JU J L )VL&<=[)V<TVFTTVLII6'4 5(<%I< &&I64[%<6'46(;%&&;%&<;6:[6656&%&;< 6&<[P4/<[>P) /(&<=S)!YI&J)'(( '((YI&J),YI&J)IIJITIU<JIU<TT<JT4: YI&J) %#9'YI&J) ""Y I ( J ) IYI& J )IY I ( J ) I I J T I F < JIII J TIU< JIU<IF<T … T I J T 4 ITT< J T4IYI& J )5 OI&J)IY&J)+ J4YI&J) V J4 YI&J) "("YI&J)I&JUJ4)VaIUV&J)aIUV&J4)4 VYI&J)I& JU J4) aIUV& J)aIUV& J4)4+ ζ I J & J J / )#(VYI&ζ)I&ζU J4) aIUV&ζ)aIUV& J4)4 J4 VYI&J)+ '(( YI&J) ' YI&J)YI&J)+'J4VYI&J)'(( J4 V'5&JUJ4)&JU J4)&J)'(( J4 I T X - J4IUX'FF&JUJ4)&JU J4)I&JUUX)&JUTX)I&JU) T IFFFF!J UFJT T IJ TOJT\F&<=>)F OIUF\I T O\FF5O gRU\IU '4 J4 * FO------ U\V4R&<==)5! ! , &<==) F"J TOJT\&O\) /*3 I '(( ααFβYI&)II&U<) <&Uh) b& TO<T\<) <βF& TOsT\s) sbsΣ α TF X!4Σ β d IIX!4 XOF-----d- U\dV4R&<=<4)dI<Fs'((I<bO<\<Os[\s+'<b / YI&) * J4 J4 F TOT\I&UJ4)&U J4)!J!##! ! ! "!.&<=<4)(&<=[)&<=>), &<=[) &JUJ4)&JU J4)(&<=>)- "J4 J4(&<=<4)7 &<=<4)'")*+,-./.0/ *IT<"J<JFJIT<"Y&J)"*I[!*'((8 < < … <J< JF … JI T < J <I J FI … J II T <<% 54714;1$+Y&)o&)Y&) Y&)Io&)b&)&<=<<) b&) / <&< Y&)6Y&) Y&)I&U<)α<&Ub)αb&FTO<T\<)β<βF& TOsT\s) s&<=<F) < b / FTOdT\d*'FOd------ U\dV4dI<Fs1R'((Od\d&dI<Fs)5o&)Y&)!λ<λbFµ<o&)I&U < ) &U b ) & TO<T \ < ) µsF& TOsT \ s ) &<=<P)λXαX XI<Fb µXβd dI<Fs&<=<R)"" FU TOT\&<=<H)FO\O gRU\V4 o&) ! ! o&) ! &<=<H) (&<=<<) o&) F U TOTFT\ I" TOT\Y&)1' " &<=<F) ; &<=<R) , ( &<=<<) o&) # Y&)+ Y&) a&) * Y&) a&) " 28 <&< 5!*"! !* '" " (2<;M 28 <&< CY&)a&)&<=<F),α b′α′Fβ <′Fβ′Y&)I$&U <′ ) < &Uα b′) & T O <′ T\ <′ ) & T O s′ T\′s′) s′&<=<S)α <″α b″″Fβ <″Fβ s″″a&) I %& U <″) & U b″″) & T O <″ T \ <″) & T O″s″ T \″s″ ) &<=<[) " !* o&) &<=<P) UV &VI<Fb)F TO`T\` &`I<Fs)" &<=<S) &<=<[)&<=<>)+ '(( &<=<>) "&<=<S)&<=<[) X V′ d ′̀ X ″V d `″&<=<R)λVα′X′ λVα″X ″ VI<FbVV&<=<=)µ`β″d″µ`β″d″`I<FsVt ! &<=<P) ! !# !* Y&) a&) !" !λVVI<Fbµ``II < Fs! " !λVIs_b Jα′X′ α″X″ KVI<Fb&<=F4)VVµ`Is_b Jβ′X′̀ β′d″̀K`I<Fs '" o&)!!*Y&)a&) ! ! &<=<P)&<=<=) o&)!!!*Y&)a&) 3!*!# !* " !#"1!#"!*"""# & ( &<=<P) ! )1 " !# !* " !n#!"!**!#!*#!# !* Y&) Y$&)+ α Y&) Y&)I&U)αY<&)Y<&)4&<=F<)αU<Y $&)((&<=F<)Y$&)Iα&U )αF<Y<&)T&U)α Y <′ &)I&U)αU<YF&)YF&)IαY<&)T&U) Y <′ &)YF&)IαY<&)4+!!βFY&)I& TOT\) YP&)&<=FF)FO gRU\V4J<JF&JFI J<)"F TOT\*YP&J<)4YP&JF)4Y$&)I& TOT\)βU<YR&)FYR&J<)4YR&JF)4 YR&J)FTOT\((&<=FF)FFY$&)Iβ& TOT\)βU<&FTO)YP&)T& TOT\)βY′P &)II&FTOT\)βU<YR&)FYR&)Iβ&FTO)YP&)T& TOT\) Y P′ &)YR&J<)Iβ&FJ<TO)YP&J<)4YR&JF)Iβ&FJFTO)YP&JF)4! J< UOgF JF UOgF * 3Y&)&<=<F)Y$&) Y$&)I=&U < )α< F <&U b )Fαb F <& TOsT \ s )βs F <&FTO<T \ < )β< F <YH&)YH&)UXXI<FbF TOdT\ddI<Fs !*"Y&)3 ( &<=<P) &<=F4) !#!* o&) Y&) Y$&)o&)I&U < )α< F <&U b )Fαb F <& TOsT \ s )&FTO<T \ < )βs F <β< F <&<=FP)3 #!#!* " Y&) a&) # * !#!*+ ! , ' &<=<S) &<=<[) " Y&) a&) @* ! !# !* " Y&) a&) <!<5& /6< 5#+Y&)!# a&) 7 Y&) a&) a<&) o<&) ! ! # a&) & a&) !! #),Y&)Ia&)a<&)To<&)3'(,<) Y&)a&) o&) o<&)'1F) a&)o<&) o&) Y&)'o&)5 !* Y&) a&) "!#!*!*!#!*a&)o<&)7a&)o<&),a&)Io<&)aF&)ToF&)1 !o<&)IoF&)aP&)ToP&)oVUF&)IoVU<&)aV&)ToV&)<C & PSH / P44 ') / @ oX&) X I < F !'*&!LT<)oLT<&)I4oLU<&) I oL&)aLT<&)+ Y&) a&) a&) o<&) o<&) oF&)oLU<&)oL&)!*!#!*;oLU<&)oL&)'oL&)!#!*oLU<&)oL&)!#!*Y&) a&)<+ *92241#+Y&)a&) /!*'((a&) /Y()- :&%9 #<;4[ %<+?<;9 2; -----------a()% 5<Y&) ;M% 5<a&) #<;4[ %< % 5< Y&) ;M% 5<a&) ! ! !Y( )- C ! -----------a() Y< ( )Y()-------------- Io&)T --------------a< ( )a()&<=FR)Y< ( )- /o&)Y<&)a<&) / --------------a ()<!Y()& ' ( *$%&; ------------a()/ #<;9 ?<;9 2;[Y&)a&) / 5<%4%&&<; 6>BB?(& 1 /%< %< 9<9&%9 4%&&<; 66&%&α< 5<a&)&1 1a&)I&U)αa<&)a<&)4& %$8%&$7& 4%&&<; %< 5<Y<&)%4%&&<; 6>BB?& &6[&Y< ( )Y()-------------- I ---------------------- T ---------------------------------------------ααF<a()a ()( F )( F )<Y< ( )- &6'9<9&%9#<;452; ---------------------------------------------αF<a< ( )( F ) 0 ! ! !Y< ( )Y()------------- I ---------------------------------------------αF<a()( F )a ()< ---------------------α- !( F )Y< ( )Y()- U ---------------------------------- I ---------------------- T ---------------------------------------------ααF<αa()a< ( )( F )( F )( F )Y ( ) F a < ( )( F )( F ) a< ( )-I ---------------------α- T ---------------------------------------αI&<=FH)+ Y&) # α a&) I & U ) a<&) 5 a<&)#a&)&α <) ' ! ! Y ( ) F a < ( )Y ( ) F a < ( )- I ----------------------------------------- ! ---------------------------------------αa()( F ) a< ( )! ! ! ! Y&) U a<&) !'U3 Y&) U a<&) I 41 Y()---------------- a<&)4I a()<+ ! !Y ( ) F a < ( )----------------------------------------( F )α a< ( ) U ' ' * !Y< ( )- !! ---------------------------------------------αF<( F )a< ( )* ! '(( U ' !'(( '(( 9 < C Y&J) a&J) '((JI /α<a&) &<=FH)'!* @' " <Y()& ' ( *$%&; ------------a()/ #<;9 ?<;9 2;[Y&) a&) / 5< % 4%&&<; 6>BB(?& 1/%<6 #<6%%<J<ITX&4%&(&<; 4)9<9&%96 6&%&β< 5(<a&)&1 1βFa&)I& TOT\) a<&)F5a<&J<)4 TOT\I&UJ<)&UJ <)&%$8%&$7&4%&&<; %<xn 5<Y<&)% 4%&(&<; 6>BB?& &6[&Y< ( )Y()x T n-------------- I ---------------------------------------- T ---------------------------------------------------------------ββF<a()FFa< ( )( T O T \ )( T O T \ )Y< ( )- &6'9<9&%9#<;452; ---------------------------------------------------------------βF<F( T O T \ )a< ( ) !""xnY< ( )Y()- I------------- I -------------------------------------------------------Fa()( T O T \ ) β a < ( )Y()x T nx T n- T --------------------------------------------------------- U ---------------------------------------- II --------------------------------------βββFFF( T O T \ )( T O T \ ) a < ( )x T n( T O T \ )( T O T \ )Y ( ) F ( x T n )a < ( )- T ----------------------------------------------------------------- I --------------------------------------ββF<FF( T O T \ )a< ( )&<=FS)&<=FS)!+ ! x n ! F'! TOT\I&UJ<)&U J <)'!"!xn!J<!Y&)U&xTn)a<&) <=P J < J< !5'*F &<=<4) TOT\3&<=F[)Y&J<)U&xJ<Tn)a<&J<)I4Y ( J< )------------------ C'xJ<TnI a(J )<<a<&J<)4+J<ITXY&J<)ga<&J<)ITX1xJ<TnII TXx&TX)TnITX5 xTnIxI'((xn(xI ---- nIU --- &<=F>)+'""xnY&)U&xTn)a<&)F TOT\@*&<=FS)FTOT\!Y< ( )----------------------------------------------------------------βF<F( T O T \ )a< ( )!* ! '(( '(( ' !'(( @('*$%&; Y&)ga&) / #<;9 ?<;9<2; Y&)a&) / 5<%4%&&<; 6>B(B?& 1/%<) ' * ' ( α<αbβ<FβsFa&)I&U < ) &U b ) & TO<T\ < ) & TOsT\ s ) &<=F=)X /## :< 4%&&<; 6 5<(a&)6&%&αXXI<FbF TOdT\dI&UJd)&UJd)JdJd/##:<#:@d%$8%&6 #<6%( 6 5< a&) 6&%& βd d I < F s(α)& %$8%&$7&4%&&<;%< X XI<Fb(β)αI<FαX x d nddI<FsβI<Fβd&6[&(<)( α< )(F)<<<Y( )------------- I --------------------------- T ------------------------------------ TT ----------------- TF<αα F <a()<<( F < )( F < )(<)( αb )(F)bbb(<)(<)x< T n<- T ----------------------------------- TT ---------------- T ------------------------------------------------ T T ------------------------αα F<βF( F b )bbb(F)( β< )( F b )(F)F( T O< T \< )<( β< )x< T n<x< T n<- TT -------------------------------------------------------TT --------------------------------------Fβ< F <F T O< T \<( T O< T \< )(<)(<)(F)(F)( βs )( βs )xs T nsxs T nsxs T ns- TT --------------------------------------- T ---------------------------------------------β- T -----------------------------------------------------F<FβssFF T Os T \s( T Os T \s )( T Os T \s )&<=P4)<6 !* '((# a&) &) Y()- ' ! -----------a()#'((# 3 &<=F=)a&)I&U < )9αFαbα<a<&)β<FFβsa<&)I&U F ) &U b ) & TO<T\ < ) & TOsT\ s )a<&<)4' <(<)Y< ( )<Y()- T ---------------------------------------------------------------- I -------------------------αα< F <a()<( F < )( F < )a< ( )+α<W<!!' Y< ( )- ! --------------------------------------------------α F<( F < )(<)<a< ( )(F)<YF ( )<Y()- T ----------------------------------- T ---------------------------------------------------------------- I -------------------------α<α< F <α< F Fa()( F < )( F < )( F < )aF ( )+ ' U < ! ! UXXIFb!(<)( α< )(F)<<<Y()-T -------------------------------- TT ---------------- T------------- I -------------------------F<αα F <a()<<( F < )( F )(<)(F)( αb )bbbYO ( )- T ---------------------------------- TT ---------------T ------------------------T ---------------αbαb F < F baO ( )( F b )( F b )YO ( ) ---------------/ ! aO ( )YO&) aO&) / '((aO&)"YO ( )+ F! ---------------aO ( )* ' (&<=P4) 7!x T n---------------------- 4 ---------------------------------------- xFTnFW4αβF( F )( T O T \ )FO\xn /O gRU\V4F&" TOT\*)>< & ?<; 29 - ! %9(69$<9#<;9?<;92; '&2&;:<'%$ $>< &@?<;@24+ &<=P4) ! ! ! " ' ( ( 5Y()- *! -----------a()(α) &<=P4)'(( X(β)(β) x d n d &XI<FbαI<FαXd I<FsβI<Fβd)+'!!*#" '(( +'a&)I!*&<=P4)!*I U < I '(( (α)(β)(β)" X x d n d I&&<=<4)),bsΣ α TF d!4Σ β d IIX!4 X-!II @* # 5 &<=P4)!*!a&) ! ! # '1 # '(( " ( F <)( F F)- ' 7 ! ----------------------------------------F!@&<=P4) =------------------------------------------ I -------------- T -------------- T -------------- F<T<FF( F F < )( F F )+ ! !* ! I&T<)&UF)T&U<)&UF)T =&U<)&T<)&<=P<)9 + &<=P<) #I<IU<IF"< IUFU<ISFIP=IU<gFIU<gS=IFgP-! <<F------------------------------------------ IU ----------------------- U ----------------------- T ----------------------- F( F <)S( T <)P( F F)( F F < )( F F )&<=PF) ; ' ! F F <----------------------------- 5!*( F T < )F',F T =l T w F<----------------------------- I ---- T ------------------------- T --------------------- FFFFF T<( T <)( T <)+ ! !* ! FU<I&FT<)FT&T=)T&lTw)&FT<)+'(("",U<I4I=Tw<IFTTl4Iw[4ITl",IU<IF=I4lI<wI4' F<F F<----------------------------- IU --- T ------------------------- T -----------------FFFFF T<( T <)( T <)&<=PP)@"" '! !*!"'((! ; !F F<-------------------------------- '"!*FF F (< T )!F' ,FFFF<F F ( T < ) T F<----------------------------- I --------------------------------------------------- I ------------------------- U -------------------------- IFFFFFFF( T <)( T <)( T <)( T <)FF( T < ) F F( T <)( T <)<F( T <) T<- U ------------------------------------ IU --- T ------------------------- T ----------------- I -----------------------FFFFFF+ &<=PP)!'"!)*+,-./.0/ &<=P4)!Y()- / 9 F C -----------a()!'(( < &<=FH) ' ! <&<) !! ---------------------α !*(J F )(d)αdVXY(J)------------ I Σ Σ ----------------------------------------X!< d!<αX F d T <a(J)( J F X )9 < V / a&J)αX /XXI<FV'α<TT αFTαVa&J) =3#"= 0$#2241'*(""'"(+' ! "" ' ( & ( * ( & HP)) * ( !'""!&&<=FR)&<=P4))3 & <>F)7!'""!@ ! ---------------------I- II<F( F )CII<&( F <>F)- _Ijb QUQT=∫ ------------F&F4<)I<&( < <>F)T=∫ ---------------------I- _IU -------------------------------------------------IF<( F )(I F <)( F )&F4F)x T n- 7! --------------------------------------IF( T O T \ )FO------ U\V4II<F@II<9ROFOF- FTOT\I T --F- T \U ----ROOFF- W4 W4tIT --F- I\U ----ROx t F --- T nFx T n- _I ∫ ------------------------------------- _t!∫ ------------------------------FFF T O T \t TxOt_t_t- T nU --------- ∫ ------------------- I!x ∫ -----------------FFFF Ft Txt TFn F xO- jb &t T )T -------------------------- ihcaq --t- T=II ----FFx- jbI ----FFF&FF T OFn F xO- ihcaq ------------------ T=TOT\)T ------------------------FFOF&F4P)OF-IW<#tIT --F- I\U ----R! !Fn F Oxx T nt_t( T O T \ )(t T )_t- _Ix ∫ --------------------------- T -------------------------- ∫ ---------------------------&F4R)∫ --------------------------------------IFFFF IFF I(t T )7 #"'E",FF< _(t T )t_t<- I --- ∫ ---------------------------- IU ----------------------------------------------------------- T=∫ -------------------------FFF IFF IFF IF<(t T )(t T )F(I F <)(t T )&F4H) &F4R) +_t- II<FPuII ∫ -------------------------FF I(t T )+ uI z I<FIt_t- _y I _t _z I U ------------------------------------ I -------------------------FF IFF IT<(t T )(t T )Fy I t! # ( ' _tt(t T )(t T )tF- I --------------------------- TFI ∫ ------------------------------------ _tIuII ∫ -------------------------FF IFF IFF IT<(t T )FF(t T ) F tF- TFI ∫ -------------------------------------- _t!I -------------------------FF IFF IT<(t T )(t T )t_t_t- TFI ∫ -------------------------- ! -------------------------- U ∫ ----------------------------------FF IFF IT<FF I F(t T )(t T )t(t T )F- TFIuIUFI uIT<uII -------------------------FF I(t T )<tFI F <- T ------------------ uIII<FuIT<I -------------F- -------------------------FFF IFI ( t T )FI&F4S)3u<& <>P(<F)1( &F4S) uF1 uF ( uP '# !uI&II<F)= 4;113 <=S * F4< *) ' * ' ( .#<4&5<&<724?<;(42%96 # '$&6[6& : &<;228&%9$<;[%$8%&$&'&%9(:>< &B$6?[ 9<9&%9<52(%64 %$ 4 %$##:?4 ?<;@ 24[ 6&(5%&$<;@<5B 1- <(&<=FR)&<=P4)&<>[) &<>>) &<>=) &F4<)/&F4S) ( !(, $ % ! ! &<=FR) C # !'"!&<=P4)&<>[)&<>>) (&<>=)&F4<)/&F4S)_ 8 ∫ ----------------------------------------F( F <)( F F)&&<=PF))'<<F----------------------------------------- IU ----------------------- U ----------------------- T ----------------------- FF(<)S(T<)P(FF F)( F <)( F F)<__<_F_- U --- ∫ -------------- T --- ∫ -------------- IIU --F- ∫ ------------∫ ----------------------------------------FS T<P FFF<( F <)( F F)F<<IU --F- jb QU<QU --S- jb QT<QT --P- jb QUFQT=SRF T F T F F <_@!* ∫ ----------------------------------------------------FF( T <)1SRFF T F T F F < F<----------------------------------------------------- IT ----------------------------- FFFF( T <)( T <) # ! '!&(&<=PP)),FF< F<----------------------------- IU --- T ------------------------- T ----------------- FFFFF T<( T <)( T <)'SRFF_ T F T F F <_- T ∫ ------------------------- T ∫ ----------------- _I_I ∫ _U ∫ -----∫ ----------------------------------------------------FFFFF T<( T <)( T <)FF_( T <)F< _( T <)- Ujb QQT ∫ -------------------------- T --- ∫ -------------------------- II ----FFFFF T<( T <)F<<F- Ujb QQU ----------------- T --- jb & T<)T=I ----FFF T<@ ! !*, * ! ! &<=<4) 5 """!! * F _- ; u I ∫ -----------------------F P(< F )*('!_- _zI_+ zI_yI -----------------------F P(< F )<- yI ---------------------------F FR(< F )<F_(< F )(< F )R(< F )<<- I ----------------------------- U --- ∫ ------------------------- _uIU --F- ∫ ------------------------RF PF FF F(< F )+!#F ( "!,< ( < F F ) T FR(< F )(< F )R(< F )<_<F F _<- U --- ------------------------------------ _ ! ----------------------------- U --- ∫ ----------------- U --- ∫ ------------------------- Iu I ---------------------------F F R∫F FF F RF RF F<<(< F )F_(< F )T- U --- jb <- -------------------------- II ----------------------------------------- T ->>∫F FF FR(< F )<F(< F )<<_T- T --- ∫ ----------------- I- U --- jb <I ----------------------------------------- U ------------------------FF>>F F<F>(< F )<FR(< F )<T- T=- U ------ jb <I ----------------------------------------- U ------------------------F FF<S<FR(< F )>(< F )= $$ <=S ! ! !'"!; F4<!<x T n O T O T \F- -------------------------------- ------ U\V4 '"! ------------FRF(ihcaq &<TF)TT jb &<TF)T=&F4<)&F4P))1!'< ! ---------------------α- α I F P ( F ) !1 ! ' !( x T n )---------------------------------------- βIFP(&F4R)&F4H)&F4S)( F T O T \ ) β( <F <>P !!*!(ihcaq &<TF)T=*OF T O T \- ------ U\V4 +'!! ------------------------------FR ! ! ! !* ! &! ) (-* ! ! ------------Fx T nOF-------------------------------- ------ U\V4F T O T \ RY()- / - ! -----------a()!α<bβ<FFa&)I&U < ) &U b ) & TO<T \ < ) & TOsT \ s )βs/ &<=<4) *Y<&)a<&),X[XI<Fbxdnd[dI<FsY()- _I∫ -----------a()Y ()b F XsxTn<Xdd--------------- T ∫ Σ --------------- T Σ ----------------------------------- _1I aX!<X!< F()< T Od T \d&F4[) !Y ()Y ()Y()<F- _I --------------- T ∫ --------------- _∫ -----------a()a ()a ()<&F4>)FaF&)I&U<)&Ub)&FTO<T\<)&FTOsT\s)3(&F4F)&F4S)a<&)a<&)Iα < F<I&U <)αb F <&U b)β<F <F& TO<T\ <)Fβs F <& TOsT\ s ) !# !* a&)a$&)&&<=FP))<.