Solutii Navier Stokes
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Transcript of Solutii Navier Stokes
7/30/2019 Solutii Navier Stokes
http://slidepdf.com/reader/full/solutii-navier-stokes 1/12
UDHYV BB CHI IEYCV BIB NC]BI\'UVDOIU
Ndvi fi ey|u
Ed|nihby Lcːhcn
Ey{|bnu
3 Bnv|dfyei|i 3
< Udhyv(bb {i|gcninvi {i hbnbb fi ey|inv {c|chihi 5
<.3 Gbu(ec|ic ijnv|i {hcni {c|chihi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5<.< Gbu(ec|ic @cain'[dbuiybhhi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Udhyv(bb {i|gcninvi ijn gbu
(ecː|b fi |dvcv
(bi =
5.3 Gbu(ec|ic Edyivvi ijnv|i ebhbnf|b edcpbchb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
5.< Gbu(ec|ic ijn }cuyh fi |dvcv( bi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5.5 Gbu(ec|ic ijnv|i fdycː fbuey|b edcpbchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3;
5.6 Gbu(ec|ic ijnv|i fdycː edny|b edcpbchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Bnv|dfyei|i
Ieycv( bc Nc}bi|'Uvdoiu iuvi finygb|ic cudebcvcː {|bneb{byhyb ednui|}cː|bb bg{yhuyhyb (ieycv( bc fi gbu(ec|i"
c{hbecv ynyb ybf niqvdnbcn ccv ijn gbu(ec|i hcgbnc|cː3. C}cnf ijn }ifi|i ecː eihi gcb ijnvchnbvi ybfi fbn
c{hbecv( bbhi vi`nbei (c{c ci|yh yhiby|bhi ncvy|chi" uynv dgdaini hc nb}ih gce|dued{be u( b |iu{ievcː ey d lyncː
c{|dpbgcv( bi gdfihyh ednuvbvyvb} niqvdnbcn bc| nygi|dcui gbu(ecː|b chi ceiuvd| ybfi cy hde hc }bvizi ey
gyhv gcb gbeb fiecv }bvizc uynivyhyb u( b ijn ednfbv( bb c{|dc{i bzdvi|gi ued{yh einv|ch ch giecnbebb ybfihd|
}cuedcui iuvi |izdh}c|ic ieycv( bib Nc}bi|'Uvdoiu {inv|y d gbu(ec|i bzded|cː (ybf bnedg{|iublbh" ijn ec|i
ediffiebinvyh fi }buedzbvcvi iuvi ednubfi|cv ijnv|'d {|bgcː c{|dpbgcv( bi ednuvcnv α 7 α; bnfi{infinv fi
vig{i|cvy|cː. B{dvizihi ginv (bdncvi ui bcy ijn ednubfi|c|i ijn ceiuv ec{bvdh? gcb gyhv( udhyv
(bbhi {|izinvcvi
uynv dlv (bnyvi nygcb {inv|y gbu
(eː c|b {i|gcninvi .
Ieycv( bc Nc}bi|'Uvdoiu {inv|y yn ybf bnedg{|iublbh ui dlv( bni bnv|dfye|cnf |ihcv( bc ednuvbvyvb}cː {inv|yvinud|yh ipv|c'vinubyni
VI 7 < α; F (3"
ijn ieycv( bc fi gbu(ec|i Ecye`r
σ
∌ }
∌v/ a|cf} }
7 σ l ∜ a|cf { / fb}VI( (<"
3Ui {|iuy{yni ecː nygcː|yh \irndhfu ec|cevi|buvbe iuvi gcb gbe fiecv nygcː|yh \irndhfu e|bvbe \i 8 \ie| ynfi \i 7σ f ];$α; (]; u(b f ffibnf gcːuy|bhi fi |imi|bnv(cː {inv|y }bvizcː |iu{ievb} hynabgi σ finubvcvic ybfyhyb".
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F ffibnf vinud|yh ubgiv|be }bvizcː fi fimd|gcv( bi.
\ihcv( bc (3" iuvi edg{hivcvcː ey ieycv( bc fi ednvbnybvcvi
fb} } 7 ;( (5"
ynfi } iuvi ecg{yh fi }bvizcː { {|iubynic l md|v(c u{iebffiecː gcubecː u( b σ finubvcvic ybfyhyb.\izyhvcː md|gc }ievd|bchcː c ieycv( bib Nc}bi| ' Uvdoiu
σ
∌ }
∌v/ a|cf} }
7 σ l ∜ a|cf { / α;∍} (6"
ip{|iubi ie`b}chinvcː ey
σ
∌ }
∌v/ a|cf
}<
<
/ |dv} Ñ }
7 σ l ∜ a|cf { ∜ α; |dv(|dv}" ( (9c"
|iu{ievb} {|bn c{hbec|ic ‗|dvd|yhyb‗ |ihcv( bib (6"
σ
∌ ς
∌v/ |dv(ς Ñ }"
7 α;∍ς (9l"
ynfi u'c mdhdubv bfinvbvcvic fb}F ≣ ∍}$< / a|cf (fb}}" ey fb}} 7 ; |iu{ievb} ς 7 3$< |dv} (}ievd|yh
}c|vij" u( b bfinvbvcvic |dv(a|cfύ" ≣ ;. Bnv|'yn ubuvig ec|vizbcn |ihcv( bbhi (<" |iu{ievb} (6" u( b (5" ec{cːvcː
md|gihi
σ
∌ }b∌v
/ }3∌ }b∌p3
/ }<∌ }b∌p<
/ }5∌ }b∌p5
7 σ lb ∜
∌{
∌pb
/
/ α; ∌ <}b
∌p<3
/∌ <}b
∌p<<
/∌ <}b
∌p<5 ( (b 7 3( <( 5"( (=c"
∌ }3∌p3
/∌ }<∌p<
/∌ }5∌p5
7 ;. (=l"
[inv|y dlv( bni|ic ip{hbebvcː c ieycv( bib Nc}bi|'Uvdoiu ijn edd|fdncvihi ebhbnf|bei u( b umi|bei ijn |ihcv( bbhi (3"
― (5" ui bnv|dfye d{i|cvd|bb fbmi|inv( bchb u( b ip{|iubbhi ed|iu{ynzcːvdc|i edd|fdncvihd| |iu{ievb}i. Bn eczyh ijn
ec|i ybfyh fi hye|y iuvi edg{|iublbh u( b gbu(ec|ic nibzded|cː ui }c mdhdub {i hcnacː ieycv( bc fi ednvbnybvcvi
ijn md|gc edg{hivcː u( b |ihcv( bc ed|iu{ynzcːvdc|i c vinud|yhyb niqvdnbcn ipv|c'vinubyni d ieycv( bi fi uvc|i
ei ip{|bgcː {|iubynic mynev( bi fi finubvcvi.
Ubuvigyh fi ieycv( bb (=" iuvi yn ubuvig {c|cldhbe ey fi|b}cvi {c|v( bchi nihbnbc| (fcvd|bvcː ceeihi|cv( bib
edn}ievb}i" fi d|fbnyh fdb (d|fbnyh gcpbg fi fi|b}c|i iuvi fdb" ch ecː|yb nieyndueyvi uynv eihi v|ibedg{dninvi chi }bvizib (}3 }< }5" u( b {|iubynic {. [inv|y d |izdh}c|i edg{hivːc ubuvigyh fi ieycv( bb
(=" iuvi ijnudv( bv fi ednfbv( bb bnbv( bchi u( b hc hbgbvcː ed|iu{ynzcːvdc|i. Iuvi bg{d|vcnv fi |igc|ecv ecː ybfyh
niqvdnbcn cfi|ː c hc uy{|cmcv (c udhbfː c fieb }bvizc ybfyhyb hc ednvcevyh ey uy{|cmcv(c udhbfcː iuvi iachcː ey
}bvizc uy{|cmiv(ib |iu{ievb}i.
Fbn {ynev fi }ifi|i gcvigcvbe ipbuvinv(c u( b ynbebvcvic udhyv( bbhd| {inv|y ieycv( bc Nc}bi|'Uvdoiu uynv
cnchbzcvi ijn ecvi}c v|cvcvi fi u{iebchbvcvi < . Dlv( bni|ic udhyv( bbhd| cnchbvbei ipcevi u( b ip{yni|ic ijn fivchby
c {|deify|bhd| {inv|y |izdh}c|ic ynd| ey|ai|b {c|vbeyhc|i Nc}bi|'Uvdoiu mce dlbievyh v|cvcvihd| ehcubei fi
<Hcnfcy H. F. Hbmue`bz I. G. Mhybf Gie`cnbeu }dh. = Dpmd|f [i|acgdn [|iuu 3206Mdbcu E. Gcnhir D. \duc \. Vigcg \. Nc}bi| ' Uvdoiu isycvbdnu cnf vy|lyhinei Ecgl|bfai Ynb}. [|iuu Niq
Rd|o <;;3
<
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giecnbec ybfihd|.5.
Bn ceiuv ec{bvdh ui {|izbnvcː ecvi}c udhyv( bb ipcevi Nc}bi|'Uvdoiu {inv|y gbu(ec|ic {i|gcninvcː c ybfihd|
bnedg{|iublbhi (udhyv( bb bnfi{infinvi fi vbg{ {inv|y ybfi ey finubvcvi ednuvcnvcː". \izdh}cː|bhi cnchbvbei
Nc}bi|'Uvdoiu ffii u( b c{|dpbgcvb}i ednuvbvybi ifyecv( bc fi lczcː ijn fdginbyh giecnbebb ybfihd| ednv|blybnf
ijn gdf fiffinbvd|by hc md|gc|ic clbhbvcːv( bhd| uvyfinvyhyb fi c gdfihc ey|ai|b fi bnvi|iu {|cevbe chi ybfihd|
|ichi (}cuedcui ucy }buedihcuvbei gbu(ecː|b hcgbnc|i ucy vy|lyhinvi".
Bn {|bneb{by ui {dv c{hbec fdycː {|deify|b {inv|y acːub|ic udhyv( bbhd| ieycv( bib Nc}bi|'Uvdoiu: (b" fbn
ieycv( bc fi ie`bhbl|y Ecye`r ui dlv( bn ip{|iubbhi edg{dninvihd| ipv|c'vinubynbb fy{cː ec|i ceiuvic ui bn'
v|dfye ijn (3" u( b ui acːuiue udhyv( bbhi {inv|y }bvizi u( b {|iubyni? (bb" ui |izdh}cː fb|iev ubuvigyh (=" c}cnf ec
nieyndueyvi edg{dninvihi }bvizib u( b {|iubynic. [|bgc {|deify|cː ui c{hbecː fi |iayhcː nygcb gbu(ecː|bhd|
ynbfb|iev( bdnchi ijn ec|i ceeihi|cv( bc ybfyhyb ui {dcvi niahbjc ucy iuvi bfinvbe nyhcː (}. gbu(ecː|bhi }buedgiv'
|bei ucy ipvinubdnchi".
< Udhyv(bb {i|gcninvi {i hbnbb fi ey|inv {c|chihi
<.3 Gbu(ec|ic ijnv|i {hcni {c|chihi
Gbu(ec|ic }buedgiv|becː ijnv|i {hcni {c|chihi iuvi d gbu(ec|i {hcncː (gbu(ec|ic c|i hde nygcb ijn {hcnyh (p3
p<" ffibnf bnfi{infinvcː fi cpc Dp5" ynbfb|iev( bdnchcː ey }bvizc }(p<" 7 }3(p<". Ieycv( bbhi (=" fi}bn
; 7 ∜∌{
∌p3
/ α;f<}
fp<<(1c"
; 7 ∜ σ a ∜∌{
∌p<
(1l"
; 7 ∜ ∌{∌p5
(1e"
ynfi ∌ }∌p3
7 ; (fbn ieycv( bc fi ednvbnybvcvi" ∌ }∌v
7 ; (gbu(ec|i {i|gcninvcː" bc| imd|vyh vcnainv( bch
ed|iu{ynzcːvd| |ihcv( bib ednuvbvyvb}i (3" iuvi fcv fi ip{|iubc
φ 7 α; ε˒ 7 α;f}
fp<. (0"
Fbn cnchbzc ubuvigyhyb (1" ui dlui|}cː ecː {|iubynic iuvi d mynev( bi fi md|gc
{ (p3( p<" 7 {3 (p3" / {< (p<" (2"
ey
{3 7 o3p3 / o< (3;"
u( b
{< 7 ∜ σ a p<. (33"
Bn (3;" ednuvcnvihi o3(< cy y|gcːvdc|ihi uignbffiecv( bb: o3 7 o |i{|izbnvcː a|cfbinvyh fi {|iubyni ijn hynayh
5 Li|oi| \. Bnv¶ia|cvbdn fiu isycvbdnu fy gd}iginv f‒yn ybfi }busyiyp bnedg{|iuublhi bn @cnflye` fi| [`rubo }dh.]BBB$< If. Mhyaai Li|hbn U{|bnai| ]i|hca 32=5
Bcedl E. Bnv|dfyevbdn gcv`¶igcvbsyi kc hc g¶iecnbsyi fiu ybfu If. Cecfigbib Lyey|iuvb 3292Ui||bn J. Gcv`igcvbech {|bneb{hiu dm ehcuubech ybf gie`cnbeu bn @cnflye fi| [`rubo }dh. ]BBB$3 If. Mhyaai
Li|hbn U{|bnai| ]i|hca 3292
5
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Mbay|c 3: Fbuv|blyv( bc fi }bvizi ijn gbu(ec|ic {hcn'{c|chihcː. Cbeb o 7 ∜∍ {$h ∍ { ffibnf fbmi|inv(c fi {|iubyni|c{d|vcvcː hc hynabgic h.
fb|iev( bib fi gbu(ec|i {D p3w (o iuvi d ednuvcnvcː niacvb}cː fidc|iei gbu(ec|ic c|i hde fi hc {|iubyni gcb
gc|i hc {|iubyni gcb gbecː" bc| o< |i{|izbnvcː }chdc|ic {|iubynbb hc p3 7 ;. Fbn (33" ynfi u'c ednubfi|cv
p< 7 ;( {< 7 ; |izyhvcː ecː {|iubynic c|i d }c|bcv( bi fi vb{ `bf|duvcvbe {i fb|iev( bc nd|gchcː gbu(ecː|bb ei c|ihde {i hbnbb fi ey|inv {c|chihi.
Fbuv|blyv( bc fi }bvizi ui dlv( bni bnvia|cnf fi fdycː d|b |ihcv( bc (1c":
f}
fp<7
3
α;o p< / E3 (3<c"
} 73
<α;o p<
< / E3p< / E< (3<l"
ynfi ednuvcnvihi fi bnvia|c|i E3 u( b E< ui dlv( bn fbn ednfbv( bbhi hc hbgbvcː? }. Mbay|c 3:
} 7 ∜ ]<( {inv|y p< 7 ; (35c"
} 7 ]3( {inv|y p< 7 ` (35l"
Bn ffinch |izyhvcː ip{|iubc
} (p<" 7o
<α;p< (p< ∜ `" /
]3 / ]<
`p< ∜ ]<. (36"
Ui dlui|}cː ecː fbuv|blyv( bc fi }bvizi (36" ui edg{yni cfbvb} fbnv|'d {c|cldhcː u( b d f|ic{vcː.
Fbuv|blyv( bc {c|cldhbecː fi }bvizcː iuvi aini|cvcː fi gbu(ec|ic [dbuiybhhi (fcvd|bvcː {|izinv(ib a|cfbinvyhyb
fi {|iubyni" bc| fbuv|blyv( bc hbnbc|cː iuvi ec|cevi|buvbecː gbu(ecː|bb fi cnv|inc|i Edyivvi ei c|i hde ijnv|i {hcni
{c|chihi.
Fbn (0" u( b (36" |izyhvcː fbuv|blyv( bc imd|vyhyb vcnainv( bch |iu{ievb} d fbuv|blyv( bi hbnbc|cː {inv|y gbu(ec|ic
[dbuiybhhi u( b d }chdc|i ednuvcnvcː ijn eczyh gbu(ecː|bb Edyivvi ijnv|i {hcni {c|chihi.
Vdv d gbu(ec|i {hcn'{c|chihcː iuvi ey|ai|ic {i|gcninvcː ey uy{|cmcv( cː hbli|cː {i yn {hcn ijnehbncv ey
yna`byh γ c ynib {ihbeyhi (ffihg‘" fi ybf }cuedu fi a|dubgi ednuvcnvcː ` (}. Mbay|c <". Gbu(ec|ic iuvi
ijn ceiuv ecz aini|cvcː fi md|v(c gcubecː fi a|iyvcvi? ieycv( bc (1c" ynfi a|cfbinvyh fi {|iubyni iuvi ijnhdeybv
fi edg{dninvc md|v(ib u{iebffiei fi a|iyvcvi {|dbievcvcː {i fb|iev( bc {hcnyhyb fi}bni
; 7 σ a ubn γ / α;f<}
fp<<(39"
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Mbay|c <: Gbu(ec|ic {hcn'{c|chihcː {i {hcnyh ijnehbncv.
ey udhyv( bc
} 7
σ a ubnγ
α; p<
` ∜
p<<
(3="
ynfi u'cy ednubfi|cv ednfbv( bbhi hc hbgbvcː
p< 7 ;( } 7 ;? (31"
p< 7 `(f}
fp<7 ;. (30"
Ednfbv( bc (31" |i{|izbnvcː ednfbv( bc fi cfi|inv( cː c ybfyhyb hc {hcn bc| (30" ednfbv( bc fi imd|v vcnainv( bch
nyh {i uy{|cmcv(c hbli|cː ie`b}chinvcː ey }bvizc gcpbgcː {i uy{|cmcv(c hbli|cː }. |ihcv( bc (0".
<.< Gbu(ec|ic @cain'[dbuiybhhi
Gbu(ec|ic @cain'[dbuiybhhi iuvi ey|ai|ic ei c|i hde ijnv|'d ednfyevcː eb|eyhc|cː {i hbnbb fi ey|inv {c|chihi
(uy{|cmiv(ihi fi ey|inv ffibnf ebhbnf|b edneinv|beb chyniecːvd|b {i fb|iev( bc cpib edgyni" fcvd|bvcː ynyb a|cfbinv
ednuvcnv fi {|iubyni o. Bn {|izinvyh ipig{hy ednfyevc ui ednubfi|cː d|bzdnvchcː fieb md|v(ihi gcubei ny
ui {|dbieviczcː {i fb|iev( bc ey|ai|bb. C}cnf ijn }ifi|i ip{|iubc imd|vyhyb vcnainv( bch φ 7 α; ε˒ u( b c }bvizib
fimd|gcv( bib u{iebffiei ε˒ 7 f}$f| fbuv|blyv( bc fi }bvizi c ybfyhyb niqvdnbcn {i fb|iev( bc cpib Dz (bfinvbecː
ey cpc ednfyevib" iuvi fcvcː fi ieycv( bc fbmi|inv( bchcː
f}
f|
73
< α;o | (32"
ynfi }z 7 } (|".
Fidc|iei }bvizc iuvi nyhcː hc {i|ivihi ednfyevib
} 7 ;( {inv|y | 7 \ (<;"
udhyv( bc ieycv( bib (32" fi}bni
} (|" 7o
6 α;
|< ∜ \<
(<3"
(u'c |iacːubv ceiicu( b fbuv|blyv( bi {c|cldhbecː ec ijn eczyh gbu(ecː|bb uyl {|iubyni fbnv|i {hcni {c|chihi". Ui
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Mbay|c 5: Fbuv|blyv( bc fi }bvizi u( b c imd|vy|bhd| vcnainv( bchi ijn gbu(ec|ic @cain ' [dbuiybhhi (gbu(ec|iynbfb|iev( bdnchcː cpbch ubgiv|becː".
dlv( bni ip{|iubc filbvyhyb v|cnu{d|vcv
S 7ϋ o
< α;
\;
|
|< ∜ \<
f| 7∍ { ϋ \6
0 α; h(<<"
ynfi u'c ednubfi|cv o 7 ∜∍ {$h ∍ { ffibnf ecːfi|ic fi {|iubyni (ijn hynayh ey|ai|bb" {i hynabgic h fi
ednfyevcː.
Mdhdubnf |izyhvcvyh (<<" ui dlv( bni ip{|iubc }bvizib fi fimd|gcv( bi hc {i|ivihi ednfyevib ε˒ q 7 6]g
\ ey
]g 7 ∍ {\<
0 α; h}bvizc gifbi. [inv|y ceicuvcː gbu(ec|i ui {dcvi echeyhc ipcev ediffiebinvyh fi {bi|fi|b hbnbc|i
fi {|iubyni (Fc|er" {i hynabgic h c ednfyevib? fbn iachbvcvic `|ο :7 ∍ {σa
7 0ϋ< f9
ο h S< |izyhvcnf
}chdc|ic
ο 7
=6
\i (<5"
ynfi \i 7 σ f]g$α; \i 8 \i e| ∸7 <5;; f 7 <\ ffibnf fbcgiv|yh ednfyevib.
Bn Mbay|c 5 uynv |i{|izinvcvi fbuv|blyv( bbhi fi }bvizcː u( b fi imd|vy|b vcnainv( bchi ijnv|'d ednfyevcː d|b'
zdnvchcː. D aini|chbzc|i c ceiuvib gbu(ecː|b ui {dcvi ednubfi|c gbu(ec|ic [dbuiybhhi ijnv|i ebhbnf|b edneinv|beb
ccv( b ijn |i{cyu ucy ijn gbu(ec|i fi v|cnuhcv( bi.
5 Udhyv(bb {i|gcninvi ijn gbu
(ecː|b fi |dvcv
(bi
Gbu(ecː|bhi fi |dvcv( bi chi ybfihd| }cuedcui niqvdnbini iju( b acːuiue nygi|dcui c{hbecv( bb vi`nbei ijn u{iebch
ijn fdginbyh hyl|bffiecv( bib u( b ch |idgiv|bib. Iuvi ncvy|ch ec gbu(ecː|bhi fi |dvcv( bi ucː ui |i{|izbnvi ijnv|'ynubuvig fi edd|fdncvi ebhbnf|bei ucy umi|bei |dvcv( bc c}cnf hde ijn ceiuv ecz fy{cː cpc Dύ. Bn eczyh ijn ec|i
ebnigcvbec gbu(ecː|bb iuvi bnfi{infinvcː fi cpc fi |dvcv( bi gbu(ec|ic {dc|vcː finygb|ic fi cpbch ubgiv|becː
ffibnf ijnfi{hbnbvcː ednfbv( bc
∌ •
∌ύ≣ ; (<6"
(fi |igc|ecv ecː u( b gbu(ec|ic @cain'[dbuiybhhi uvyfbcvcː ijn ¡<.< iuvi ijn edd|fdncvi ebhbnf|bei d gbu(ec|i
cpbch ubgiv|becː mcː|cː ijnucː c ffi d gbu(ec|i fi |dvcv( bi".
Ieycv( bc Nc}bi|'Uvdoiu (6" {inv|y gbu(ecː|b {i|gcninvi chi ynyb ybf bnedg{|iublbh c|i ijn edd|fdncvi
ebhbnf|bei {| ( ύ ( zw ip{|iubc:
=
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σ
}|
∌ }|∌|
/3
|}ύ
∌ }|∌ύ
/ }z∌ }|∌z
∜}<ύ|
7 σl| ∜
∌{
∌|/
/ α;∌ <}|
∌|< /
3
|
∌ }|
∌| /
3
|<
∌ <}|
∌ύ< /
∌ <}|
∌z< ∜
}|
|< ∜
<
|<
∌ }ύ
∌ύ
(<9c"
σ
}|
∌ }ύ∌|
/3
|}ύ
∌ }ύ∌ύ
/ }z∌ }ύ∌z
/}|}ύ
|
7 σlύ ∜
3
|
∌{
∌ύ/
/ α;
∌ <}ύ∌|<
/3
|
∌ }ύ∌|
/3
|<∌ <}ύ∌ύ<
/∌ <}ύ∌z<
/<
|<∌ }|∌ύ
∜}ύ|<
(<9l"
σ
}|
∌ }z∌|
/3
|}ύ
∌ }z∌ύ
/ }z∌ }z∌z
7 σlz ∜
∌{
∌z/ α;
∌ <}z∌|<
/3
|<∌ <}z∌ύ<
/∌ <}z∌z<
/3
|
∌ }z∌|
(<9e"
|ihcv( bc fi ednvbnybvcvi ffibnf fcvcː fi
∌ }|∌|
/}||
/3
|
∌ }ύ∌ύ
/∌ }z∌z
7 ; (<="
Ubuvigyh fi ieycv( bb (<9"― (<=" c|i ecvi}c udhyv( bb cnchbvbei c{|dpbgcvb}i {inv|y gbu(ecː|b cpbch'ubgiv|bei
fi bnvi|iu {|cevbe fbnv|i ec|i ginv( bdncːg: gbu(ec|ic ijn }iebncːvcvic ynyb fbue ijn |dvcv( bi6 gbu(ec|ic fi
|dvcv( bi {i ei|ey|b edneinv|bei ijnv|i {hcni {c|chihi9 gbu(ec|ic ijn }iebncːvcvic ynyb {ynev fi bg{cev= u( b
yn nygcː| fi udhyv( bb cnchbvbei ipcevi fbnv|i ec|i ui }d| v|cvc ijn ednvbnyc|i: gbu(ecː|bhi }buedgiv|bei fi vb{
Edyivvi ijnv|i ebhbnf|bb edneinv|beb u( b fbuey|b edneinv|bei |iu{ievb} gbu(ec|ic fi |dvcv( bi |babfcː‘ c ynyb
ybf }cuedu ijnv|'yn }cu ijn |dvcv( bi.
5.3 Gbu(ec|ic Edyivvi ijnv|i ebhbnf|b edcpbchb
Bn eczyh gbu(ecː|bb fi |dvcv( bi ynbfb|iev( bdnchi ijnv|i ebhbnf|b edcpbchb ednubfi|cv( b fi hynabgi bnffinbvcː u( b
ccv( b ijn gbu(ec|i fi |dvcv( bi |ihcvb}cː |ihcv( bbhi (<9" uynv ie`b}chinvi ey ubuvigyh
∜σ}<
|7 ∜
∌{
∌|(<1c"
; 7∌φ
∌|/
< φ
|(<1l"
; 7 ∜ σ a ∜ ∌{∌z
(<1e"
\ihcv( bbhi (<1" ui dlv( bn fbn (<9" ey }ύ 7 } (|" }| 7 }z 7 ; ∌ }$∌z 7 ; u( b |iuv|bev( bc (<6"? (<9l"
ffibnf ie`b}chinvcː ey (<1l" ynfi imd|vyh vcnainv( bch c|i ip{|iubc
φ 7 α; ε˒ 7 α;
f}
f|∜
}
|
( (<0"
6Ue`hbe`vbna @. Ldynfc|r hcri| v`id|r =v` Ifbvbdn Ge'A|cq @bhh Niq Rd|o {. <35 32=09Li|oi| \. Cn ipcev udhyvbdn dm v`i Nc}bi 'Uvdoiu isycvbdn Bnv. J. Ina.Ueb. <;(<" <31 ― <5; 320<=E`y|e`bhh U. Q. ]buedyu dqu? v`i {|cevbech yui dm v`id|r Lyvvi|qd|v`u {. <9; 3209
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(<1l" c}cnf udhyv( bc
φ 7E
|<. (<2"
Gbu(ec|ic fiue|bucː fi ubuvigyh (<1" iuvi d gbu(ec|i cpbch ubgiv|becː ijn ec|i fbuv|blyv( bc fi }bvizi iuvi
bnfi{infinvcː fi cpc Dz.
Fbn (<0" u( b (<2" ui dlv( bni fbuv|blyv( bc fi }bvizi ijnv|i eib fdb ebhbnf|b
f}
f|∜
}
|7
E3
|<. (5;"
Udhyv( bc aini|chcː c ieycv( bib (5;" ui dlv( bni ec uygc fbnv|i udhyv( bc ieycv( bib dgdaini }; 7 E<| u( b d
udhyv( bi {c|vbeyhc|cː } { 7 ∜ E3
<| |iu{ievb}
} 7 }; / } { 7 E< | ∜E3
< |(53"
Ednuvcnvihi fbn (53" ui fivi|gbncː fbn ednfbv( bbhi hc hbgbvcː fi ipig{hy
| 7 \3 ( } 7 ς \3 (5<"
| 7 \< ( } 7 ; (55"
ynfi ς iuvi vy|cv( bc ednuvcnvcː c ebhbnf|yhyb bnvi|bd| ebhbnf|yh ipvi|bd| ffibnf ednubfi|cv ijn |i{cyu (}. Mbay|c
6". [|bnv|'yn echeyh ubg{hy ui dlv( bni fbuv|blyv( bc fi }bvizi ijnv|i eib fdb ebhbnf|b ijn ednfbv( bbhi inynv(cvi
} 7 ς |
\<<
|<∜ 3
\<<
\<3
∜ 3(56"
ynfi u'cy mdhdubv }chd|bhi ednuvcnvihd| fbn (53"
E3 7 < ς\<3\<
<
\<3 ∜ \<
<
( E< 7 ς\<3
\<3 ∜ \<
<
. (59"
Bn eczyh ynib fbmi|inv(i |ihcvb} gbeb fbnv|i eib fdb ebhbnf|b ζ $\ 88 3 (ζ 7 \< ∜ \3( \3 7 \"
fbuv|blyv( bc fi }bvizi iuvi mdc|vi c{|dc{i fi eic hbnbc|cː bc| }bvizc fi fimd|gcv( bi u{iebffiecː iuvi ednuvcnvcː
ε˒ ∸7 ς\ζ
(}. Mbay|c 6".
Fbn cnchbzc ieycv( bbhd| (<1c" u( b (<1e" ui dlv( bni md|gc fbuv|blyv( bib fi {|iubyni
{ (| ( z" 7 {; / a (z" / m (|" (5="
ynfi {; iuvi d ednuvcnvcː (}chdc|ic {|iubynbb hc z 7 ` 7 ednuvcnv " bc| mynev( bbhi a(z" u( b m (|" ui dlv( bn {|bn
bnvia|c|ic ieycv( bbhd| ginv( bdncvi ynfi ui v( bni ednv fi (56". \izyhvcː
{ (| ( z" 7 {; / σ a (` ∜ z" / σ
E<< |<
<∜ <E3E< hn | ∜
E<3
<|<
(51"
ednuvcvihi fi bnvia|c|i ffibnf fcvi fi (59".
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Mbay|c 6: Fbuv|blyv( bc fi }bvizi ijn gbu(ec|ic Edyivvi ijnv|i ebhbnf|b edcpbchb ({|iuy{yu( b fi hynabgi bnffinbvcː".
Mbay|c 9: Uy{|cmcv(c hbli|cː c ybfyhyb ccv ijnv|'yn }cu ijn |dvcv( bi.
5.< Gbu(ec|ic ijn }cuyh fi |dvcv
(bi
Gbu(ec|ic ynyb ybf }cuedu ijnv|'yn }cu ccv ijn |dvcv( bi (}. Mbay|c 9" iuvi fiue|bucː fi ceihicu( b ieycv( bb
(<1" ednfbv( bbhi hc hbgbvcː ffibnf fi ceicuvcː fcvcː
| 7 ; ( } 7 ; (50"
| 7 \ ( } 7 ς \ (52"
Fbn (53" |izyhvcː
} 7 ς | (6;"
ynfi E3 7 ; u( b E< 7 ς.
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Mbay|c =: Gbu(ec|ic fi |dvcv( bi ijnv|i fdycː fbuey|b edneinv|bei ijn hb{uc ceeihi|cv( bib.
Bn ceiuv ecz fbuv|blyv( bc fi }bvizcː fbn ybf iuvi bfinvbecː ey eic c ynyb udhbf |babf ccv ijn gbu(ec|i fi
|dvcv( bi. Fbuv|blyv( bc fi {|iubynb (51" ijn ybf fi}bni
{ (| ( z" 7 {; / σ a (@gbn ∜ z" / σς< |<
<(63"
Ieycv( bc uy{|cmiv(ib hbli|i ui dlv( bni {yncnf ednfbv( bc ec { (| ( z" 7 {; ijn (63" |iu{ievb}
z 7 @gbn /ς< |<
<a. (6<"
Fbn ednfbv( bc fi ednui|}c|i c }dhygyhyb fi ybf fbn }cu ui {dv dlv( bni ip{|iubbhi ijncːhv( bgbhd| @gbn u( b
@gcp ijn mynev( bi fi ijncːhv( bgic ybfyhyb ijn uvc|i fi |i{cyu @; (}. Mbay|c 9"
] dh 7 < ϋ
\;
z | f| 7 ϋ \< @; (65"
Fbn (6<" u( b (65" |izyhvcː
@gbn 7 @; ∜ς<\<
6a(66"
|iu{ievb}
@gcp 7 @; / ς<
\<
6a. (69"
5.5 Gbu(ec|ic ijnv|i fdycː fbuey|b edcpbchi
Fbuv|blyv( bc fi }bvizi ijn gbu(ec|ic cpbch'ubgiv|becː fi |dvcv( bi fbnv|i fdycː fbuey|b edneinv|bei (}. Mbay|c
=" iuvi udhyv( bc ieycv( bib
; 7∌ <}
∌|</
3
|
∌ }
∌|/
∌ <}
∌z<∜
}
|<(6="
dlv( bnyvcː fbn (<9l" ijn b{dvizc }| 7 }z 7 ; u( b }ύ 7 } (| ( z".
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Ednfbv( bbhi hc hbgbvcː {inv|y (6=" uynv
z 7 ; ( } 7 ; (61"
z 7 `( } 7 | ς (60"
Fbuv|blyv( bc fi }bvizi ec|i }i|bffiecː (6=" ― (60" iuvi
} 7| ς
`z. (62"
\izyhvcː ε˒ 7 |ς`
(}bvizc fi fimd|gcv( bi u{iebffiecː" u( b φ 7 α;|ς`
(imd|v vcnainv( bch".
Udhyv( bc (62" iuvi ijnucː }chclbhcː nygcb ijn eczyh ijn ec|i edg{dninvc ceeihi|cv( bib einv|bmyai fbn (<1c"
ui niahbjiczcː edg{hiv (ijn hb{uc ceiuvib b{dvizi ny iuvi {dublbhcː fivi|gbnc|ic fbuv|blyv( bib fi {|iubynb fbn
(<1c" u( b (<1e" ec ijn eczyh gbu(ecː|bhd| fi |dvcv( bi {|ieifinvi". Bg{dublbhbvcvic dlv( bni|bb ynib fbuv|blyv( bb fi
{|iubynb { 7 { (| ( z" ijn ednmd|gbvcvi ey fbuv|blyv( bc fi }bvizi (62" figdnuv|iczcː mc{vyh ecː {inv|y \i
> ; ebnigcvbec gbu(ecː|bb fi |dvcv( bi ijnv|i fbuey|b edneinv|bei v|ilybi ucː ednv( bncː eih {yv( bn u( b edg{dninvc
}bvizib {i fb|iev( bi |cfbchcː.
5.6 Gbu(ec|ic ijnv|i fdycː edny|b edcpbchi
Ubgbhc| ey gbu(ec|ic ijnv|i fdycː fbuey|b edcpbchi gbu(ec|ic ijnv|i fdycː edny|b edcpbchi c|i udhyv( bi ipcevcː
ijn hb{uc md|v(ihd| fi bni|v( bi (gbu(ec|ic ffibnf uvyfbcvcː ijn edd|fdncvi umi|bei". Bn ceicuvcː b{dvizcː imdvyh
vcnainv( bch (φ 7 vύΰ" ui dlv( bni ec udhyv( bi c ieycv( bib fi gbuec|i ; 7 ∌φ ∌ΰ
/ < edv ΰφ |iu{ievb}
φ 7E
ubn<ΰ(9;"
fbuv|blyv( bc fi }bvizi {i fb|iev( bc fi |dvcv( bi c edny|bhd| }ύ 7 } (| ( ΰ" (}| 7 }ΰ 7 ;" u( b }bvizc ed|i'
u{ynzcːvdc|i fi fimd|gcv( bi c}cnf ip{|iubbhi:
} 7 | ubn ΰ m (ΰ" (93"
ε˒ 7 ubn ΰfm
fΰ(9<"
Cnchda ey fbuv|blyv( bc (62" }bvizc ybfyhyb fbnv|i eihi fdycː edny|b (93" ui ednubfi|cː c}cnf d fbuv|blyv( bi
hbnbc|cː ijn |c{d|v ey fbuvcnv(c mcv( cː fi cpyh fi |dvcv( bi ijn ceiuv ecz (| ubn ΰ". Bn ceiuv ecz {inv|y μ 7 γ<∜γ3
gbe u( b γ< 7 ϋ$< }bvizc fi fimd|gcv( bi u{iebffieːc fi}bni ε˒ ςμ
.
Ednfbv( bbhi hc hbgbvcː {inv|y gbu(ec|ic uvyfbcvcː uynv:
ΰ 7 γ3 ( } 7 | ubn γ3 ς (95"
ΰ 7 γ< ( } 7 ; (96"
ynfi u'c ednubfi|cv ecː yna`by|bhi hc }c|m chi edny|bhd| uynv < γ3 |iu{ievb} < γ< (}. Mbay|c 1".
Fidc|iei φ 7 α; ε˒ |izyhvcːfm
fΰ7
E3
ubn5ΰ(99"
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Mbay|c 1: Aidgiv|bc gbu(ecː|bb fi |dvcv( bi ijnv|i fdycː edny|b edneinv|bei.
{|bn bnvia|c|i dlv( bncnfy'ui
m (ΰ" 7 E< / E5
hnva
ΰ
<∜
edu ΰ
ubn<ΰ
(9="
Mdhdubnf (95" u( b (96" ui fivi|gbncː ednuvcnvihi E< u( b E5 fbn (9=" fbuv|blyv( bc fi }bvizi (93" ecː{cːvcnf
ip{|iubc
} 7 | ς ubn ΰ
hn
vaγ<<
va ΰ<
∜eduγ<ubn<γ<
/ edu ΰubn<ΰ
hnva
γ<<
vaγ3<
∜eduγ
<
ubn<γ</ eduγ3
ubn<γ3
. (91"
Bnv|'yn gdf ubgbhc| ui {dcvi uvyfbc u( b gbu(ec|ic fi |dvcv( bi c ynyb ybf niqvdnbcn ijnv|i fdycː umi|i
edneinv|bei (}. ec{bvdhyh 6 fbn Hcnahdbu1".
1Hcnahdbu Q. I. Uhdq }buedyu dq Gcegbhhcn Edg{. Niq Rd|o 32=6
3<