Jadioe= 4 1 + p( nebn` 1 `z pba zehpjoúb way~ojphay jebejona D #s( / + B #s( / ¾ 4 7 @z `saj~a zo z` v`yofoja qp`
@saj~az
D #s ( / %
4
#s ( / %
s
Ha zehpjoúb n` ha `jpajoúb `z F #s( / 4 j~`( nebn` F #s( # s( / `z pba fpbjoúb ~ah qp` ∉ F #s ( / % ∉ s 4 D #s( / ∉ F #s ( / % ∉ 4 B #s( / Be `saj~az" Faj~ey ob~`lyab~`
Dph~owhojadez ha `jpajoúb D #s( / + B #s( / ¾ 4 7 wey ° #s( / n` feyda qp` ha `jpajoúb y`zph~ab~` z`a nof`y`bjoah `saj~a" Jpabne #∉ D % ∉ $ ∉ Δ % ∉ s / % B `z fpbjoúb n` s ° #s/ ° #s/ 4 `sw { ∫ [ # ∉ D % ∉ $ ∉ Δ % ∉ s / % B T ns t Jpabne #∉ Δ % ∉ s $ ∉ Θ % ∉ / % D `z fpbjoúb n` ° #/ ° #s/ 4 `sw { ∫ [ #∉ Δ % ∉ s $ ∉ Θ % ∉ / % D T n t
Jpabne #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #s D $ B/ `z fpbjoúb n` #s " / ° #s " / ° #s " / 4 `sw { ∫ [ #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #s D $ B/ T n #s "/ t Jpabne #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #D $ B/ `z fpbjoúb n` #s + / ° #s + / ° #s + / 4 `sw { ∫ [ #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #D $ B/ T n #s + / t Jpabne #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #b sd b$1 D $ d sd$1 b B/ `z fpbjoúb n` #sd " b/ ° #sd " b/ ° #sd " b/ 4 `sw { ∫ [ #∉ Δ % ∉ s $ ∉ Θ % ∉ / % #b s d b$1 D $ d sd$1 b B/ T n #sd " b/ t @jpajoeb`z nof`y`bjoah`z eynobayoaz n` wyod`y eyn`b n` lyane daey qp` 1
Hhadadez ¾ 4 w @jpajoeb`z y`zehpih`z `b Jpabne wen`dez n`zw`may ha `b fpbjoúb n` s n` ¾" 4 f #s( w/
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Z` n`yova ha `jpajoúb y`zw`j~e n` @jpajoeb`z y`zehpih`z `b w
Jpabne ~`b`dez pb wehobedoe n` lyane b `b w"
@jpajoúb n` Halyabl` $ N 4 s f #w/ + l #w/ ¾Ah`di`y~
Z` n`yova ha `jpajoúb y`zw`j~e n` s" Y`zph~a pba `jpajoúb hob`ah nebn` ha vayoaih` n`w`bno`b~` `z ha w s ha obn`w`bno`b~`" obn`w`bno`b~`" @jpaj jpajoe oeb` b`zz n` n` Jhao Jhaoya yap p~
4 s w + l #w/ #w/
Zehpjoúb l`b`yah= 4 s J + l #J/( # J/( nebn` J `z pba jebz~ab~`" Zehpjoúb zoblphay= s 4 $ l¾#w/ Awhojajoeb`z n` haz `jpajoeb`z nof`y`bjoah`z n` wyod`y eyn`b
^ya`j~eyoaz ey~elebah`z
Zeb haz jpyvaz qp` z` ob~`yz`jab feydabne pb áblphe y`j~e" Zo ha fadohoa n` jpyvaz ~o`b` wey `jpajoúb F #s( ,( / 4 7( ha `jpajoúb nof`y`bjoah n` haz ~ya`j~eyoaz ey~elebah`z a `hha `z e~ya fadohoa n` ha feyda F #s( $ 1% , ( / 4 7
Pb da~`yoah yanoaj~ove z` n`zob~`lya a pba ya}úb wyeweyjoebah a ha jab~onan Da~`yoah yanoaj~ove wy`z`b~`" n B % n~ 4 $ k B 442 B #~/ 4 Be `sw #$ k ~/ Zo ha yawon`} n` dph~owhojajoúb `z wyeweyjoebah ah býd`ye n` iaj~`yoaz wy`z`b~`z `b Jph~ove n` iaj~`yoaz jana obz~ab~`" n B % n~ 4 k B 442 B #~/ 4 Be `sw #k ~/ Ha v`hejonan a ha qp` z` `bfyäa pba zpz~abjoa ah aoy` hoiy` `z wyeweyjoebah a ha H` n` `bfyoado`b~e nof`y`bjoa n` ~`dw`ya~pyaz n` ha zpz~abjoa n`h aoy`" n` B`|~eb n ^ % n~ 4 $ k #^ $ ^a/ 442 ^ #~/ 4 ^a + #^e $ ^a/ `sw #$ k ~/ nebn` ^e `z ha ~`dw`ya~pya obojoah ^a ha ~`dw`ya~pya n`h aoy` qp` h` yen`a"
@jpajoeb`z nof`y`bjoah`z eynobayoaz hob`ah`z n` z`lpbne eyn`b= a #s/ ¾¾ + i #s/ ¾ + j #s/ 4 y #s/ Ha zehpjoúb l`b`yah n` ha `jpajoúb jedwh`~a `z ha zpda n` ha zehpjoúb l`b`yah n` ha `jpajoúb cedelïb`a [ a #s/ ¾¾ + i #s/ ¾ + j #s/ 4 7 T dáz pba zehpjoúb way~ojphay n` ha `jpajoúb jedwh`~a [ a #s/ ¾¾ + i #s/ ¾ + j #s/ 4 y #s/ T 4 c + w
Ha zehpjoúb l`b`yah n` ha cedelïb`a `z ha qp` jeb~o`b` haz jebz~ab~`z ayio~yayoaz" @z pba jediobajoúb hob`ah n` zehpjoeb`z hob`ahd`b~` obn`w`bno`b~`z #
/ n`
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Zo haz zehpjoeb`z zeb hob`ahd`b~` obn`w`bno`b~`z n`i`yá z`y noz~ob~e n` j`ye" Zehpjoúb n` ha way~` cedelïb`a @jpajoeb`z nof`y`bjoah`z eynobayoaz hob`ah`z n` z`lpbne eyn`b n` je`fojo`b~`z jebz~ab~`z= a ¾¾ + i ¾ + j 4 7
Zpweb`dez ha zehpjoúb 4 `ds n` ha feyda= 9+id+j47 a d Hh`ladez a=
Zehpjoúb y`ah neih` #d/ Zehpjoúb= 4 J 1 `ds + J9 s `ds Zo cpio`ya zone ~yowh`= Zehpjoúb= 4 J 1 `ds + J9 s `ds + J: s9 `ds
Zehpjoeb`z jedwh`maz jebmplanaz= d 4 α ± ι o i9 + > a j 8 7 Zehpjoúb= 4 ` α s [ J1 jez #ι s/ + J9 z`b #ι s/ T @jpajoeb`z nof`y`bjoah`z eynobayoaz hob`ah`z n` z`lpbne eyn`b n` je`fojo`b~`z vayoaih`z" @jpajoeb`z n` @ph`y= 9 a s ¾¾ + i s ¾ + j 4 7
Zpweb`dez ha zehpjoúb 4 sd n` ha feyda= Zehpjoeb`z y`ah`z= d ≧ 4 J1 sd + J9 sd¾ d¾ Zehpjoúb neih`= d
4 J1 sd + J9 #hb s/ sd
Yaäj`z jedwh`maz 4 sα [ J1 jez #ι hb s/ + J9 z`b #ι hb s/ T jebmplanaz= jebmplanaz= d 4 α ± ι o Zehpjoúb n` ha way~` be cedelïb`a
A eme
Wen`dez ei~`b`y pba zehpjoúb way~ojphay n` ha way~` be cedelïb`a zob dáz qp` wyeiay a )eme) zehpjoeb`z zehpjoeb`z jedwyeiay jedwyeiay zo v`yofojab e be ha `jpajoúb nof`y`bjoah" nof`y`bjoah"
Dï~ene n` hez je`fojo`b~`z obn`~`ydobanez
N`w`bn` n` ha feyda qp` ~`bla y #s/
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y #s/ 4 ` α s W
b #s/ jez
#ι s/ y #s/ 4 ` α s W
b #s/ z`b
#ι s/ Dï~ene n` vayoajoúb n` hez wayád`~yez
w #s/ 4 sz `α s [ #ae + a1 s + a9 s9 + """ + ab sb/ z`b #ι s/ + #ie + i1 s + i9 s9 + """ + ib sb/ jez #ι s/ T w #s/ 4 sz `α s [ #ae + a1 s + a9 s9 + """ + ab sb/ z`b #ι s/ + #ie + i1 s + i9 s9 + """ + ib sb/ jez #ι s/ T w 4 1 p + 9 v nebn` 1 ` 9 zeb nez zehpjoeb`z n` ha cedelïb`a hob`ahd`b~` obn`w`bno`b~`z #Ha zehpjoúb l`b`yah n` ha way~` cedelïb`a `z c #~/ 4 J1 1 #~/ + J9 9 #~/( wey `h dï~ene n` vayoajoúb n` hez wayád`~yez zpz~o~podez J 1 wey J1#~/ 4 p( J9 wey J9#~/ 4 v( azä qp` zpweb`dez ha zehpjoúb n` ha feyda #~/ 4 J 1 #~/ 1 #~/ + J9 #~/ 9 #~/" Wen`dez jahjphay hez je`fojo`b~`z J 1#~/( J9#~/( """ zpz~o~p`bne `b ha `jpajoúb eyolobah/ p 4 ∫ [ $ y #s/ 9 % \ #1( 9/ T ns v 4 ∫ [ y #s/ 1 % \ #1( 9/ T ns
4 p + p + p ; p 4 ∫ [ y#s/ \o #s/ % \ #s/ T ns ; \ o zpz~o~podez ha Eyn`b daey #e olpah/ w 1 1 9 9 : : o a ~y`z/ jehpdba o n` \ wey 7( 7 """ 1 Y`npjjoúb n` eyn`b n` pba `jpajoúb nof`y`bjoah n` z`lpbne eyn`b cedelïb`a
,, + w #s/ , + q #s/ 4 Y`npjodez `h eyn`b n` ha `jpajoúb ab~`yoey d`noab~` `h jadioe 4 1 p #s/ 7 nebn` 1 `z pba zehpjoúb way~ojphay qp` v`yofoja ha `jpajoúb"
Ew`yaney N Zo N y`wy`z`b~a `h ew`yaney n`yovana( N s 4 s , 4 n s % n ~ ( 1 % N z` n`fob` jede `h ew`yaney obv`yze n` N= #1 % N/ f #s/ 4 ∫ f #s/ n s 1" @sweb`bjoah" Pba zehpjoúb way~ojphay n` ha `jpajoúb f #N/ 4 A ` as `z~á nana wey w 4 [A % f #a/T ` as #zo f #a/ ≧ 7/ Zo f #a/ 4 7( ~`bny`dez `b jp`b~a qp` [1 % #N$a/ dT `as 4 [sd `as T % d! 9" Wehobedoe" Pba zehpjoúb way~ojphay n` ha `jpajoúb f #N/ 4 A s d `z~á nana wey 4 [A % a T [1 + l
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1 % #1 + s/ 4 1 $ s + s 9 $ s: + s> $ s0 + """ 1 % #1 $ s/ 4 1 + s + s 9 + s: + s> + s0 + """ :" Wehobedoe wey `sweb`bjoah= [1 % f #N/T f #s/ `as 4 `as [1 % f #N+a/T f #s/ >" Fpbjoúb ~yolebedï~yoja= Waya ipzjay pba zehpjoúb way~ojphay n` ha `jpajoúb f #N/ 4 A jez #a s/ ú A z`b #a s/; zo f #N/ `z pb wehobedoe( caj`dez `h jadioe N 9 4 $ a9 y`npjodez f #N/ a pb ew`yaney hob`ah `b N n` ha feyda α N + ι
Zoz~`daz n` `jpajoeb`z nof`y`bjoah`z nof `y`bjoah`z Jebzon`y`dez `h zoz~`da hob`ah n` `jpajoeb`z nof`y`bjoah`z be cedelïb`e= s , #~/ 4 W #~/ s #~/ + i #~/"( nebn` s , #~/( s #~/ i #~/ zeb v`j~ey`z jehpdba W #~/ `z pba da~yo}" Zo i #~/ 4 7( `h zoz~`da `z cedelïb`e" cedelïb`e" Zo an`dáz W #~/ 4 A #da~yo} n` je`fojo`b~`z jebz~ab~`z/ `h zoz~`da qp`na( qp`na( s , #~/ 4 A s #~/" Ei~`b`dez hez vahey`z λo v`j~ey`z wyewoez o n` ha da~yo} A" Zehpjoúb n` ha way~` cedelïb`a= s , #~/ 4 A s #~/
A `z ha da~yo} n` hez je`fojo`b~`z n`h zoz~`da hob`ah ab~`yoey; ~y A 4 a + n( ha ~ya}a n` ha da~yo} A; n`~ A 4 a n $ i j( `h n`~`ydobab~` n` A ∆ 4 #~y A/9 $ > n`~ A n`~ A 2 7" ~y A 2 7 42 Bene odwyewoe ob`z~aih`
∆27
n`~ A 2 7" ~y A 8 7 42 Bene odwyewoe azob~ú~ojad`b~` `z~aih` n`~ A 8 7 42 Wpb~e n` `bzohhanpya ob`z~aih` ~y A 2 7 42 dabab~oah #bene wyewoe ob`z~aih`/
∆47 ~y A 8 7 42 zpdon`ye #bene wyewoe azob~ú~ojad`b~` `z~aih`/ ~y A 4 7 42 wpb~e j`b~ye #`z~aih`/
∆87
~y A ≧ 7 ( ~y A 2 7 42 Feje #wpb~e `zwoyah/ ob`z~aih` ~y A ≧ 7 ( ~y A 8 7 42 Feje #wpb~e `zwoyah/ azob~ú~ojad`b~` `z~aih` @z~aiohonan
$ Zo ah d`bez pba yaä} ~o`b` ha way~` y`ah wezo~ova( `h wpb~e n` y`weze `z ob`z~aih`" $ Zo haz yaäj`z zeb jedwh`maz jeb way~` y`ah bpha( `z `z~aih`"
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7 L #s( / 4 7
Awyesodajoúb hob`ah
s,4as+i ,4js+n nebn` a 4 ∉ F % ∉ s ; i 4 ∉ F % ∉ ; j 4 ∉ L % ∉ s ; n 4 ∉ L % ∉ #zpz~o~ponez `b hez wpb~ez n` `qpohoiyoe/ @z~aiohonan z`lýb Hoawpbev
Z`a `h zoz~`da zoz~`da s , 4 F #s( / / ; , 4 L #s( / #1/ Pba fpbjoúb @ #s( / n`fobona wezo~ova ~ah qp` n @ % n~ 4 # ∉ @ % ∉s / F + # ∉ @ % ∉ / L `z z`don`fobona b`la~ova y`joi` `h bediy` n` fpbjoúb n` Hawpbev n`h zoz~`da #1/" Wey `m`dwhe( pba fpbjoúb n` Hawpbev dp `dwh`ana `dwh`ana `z @ #s( / 4 a s 9 + j 9 jeb a( j 2 7" $ Zo `soz~` pba fpbjoúb n` Hawpbes @ #s( / waya `h zoz~`da #1/ `b~ebj`z `h W j #7(7/ `z `z~aih`" $ _ zo n @ % n~ 4 # ∉ @ % ∉s / F + # ∉ @ % ∉ / L `z n`fobona b`la~ova( `b~ebj`z `b~ebj`z `h W j #7(7/ `z azob~ú~ojad`b~` `z~aih`" $ Zo waya `h zoz~`da #1/ @ #s( / 2 7 n @ % n~ 2 7( `h W j #7(7/ `z ob`z~aih`" Jáhjphe vayoajoebah
qp`y`dez caj`y `s~y`dah ha ob~`lyah #`b~y` s 1 s9/