УДК 622.692.4.058 Кутуков С.Е., Бахтизин Р.Н. Уфимский

Реклама
M>D
Dmlmdh\K?;ZolbabgJG
Mnbfkdbc]hkm^Zjkl\_ggucg_nlyghcl_ogbq_kdbc
mgb\_jkbl_l
=B>JH>BG:FBQ?KDB?MKEH<BYKMS?KL<H<:GBY
=:AH<UOKDHIE?GBC<LJM;HIJH<H>:O
:GGHL:PBY
JZkkfhlj_gu ]b^jh^bgZfbq_kdb_ mkeh\by kms_kl\h\Zgby b fb]jZpbb
]Zah\uo kdhie_gbc Ij_^eh`_gZ ]b^jh^bgZfbq_kdZy fh^_ev jZkkeh_ggh]h
l_q_gby ijh^mdlZ \ ljm[hijh\h^Zo iha\heyxsZy gZ bg`_g_jghf mjh\g_
ij_^kdZau\Zlv
\hafh`gh_
iheh`_gb_
]Zah\h]h
kdhie_gby
\
ihehklb
ljm[hijh\h^ZIhdZaZgh^bgbanbabq_kdboZki_dlh\\ebygbyj_ev_nZljZkkugZ
ijhimkdgmxkihkh[ghklvljm[hijh\h^Z
<<?>?GB?
Hiul wdkiemZlZpbb fZ]bkljZevguo ljm[hijh\h^h\ ihdZau\Z_l kgb`_gb_
ijhimkdghc kihkh[ghklb ih kjZ\g_gbx k ijh_dlghc Ijbq_f q_f [he__
g_^h]jm`_gmqZklhdl_f[hevrbf]b^jZ\ebq_kdbfkhijhlb\e_gb_fhgh[eZ^Z_l
H^ghc ba ijbqbg kgb`Zxsbo ijhimkdgmx kihkh[ghklv ebg_cghc qZklb
FGI y\ey_lky ]Zah\ha^mrgu_ kdhie_gby \ ih\ur_gguo mqZkldZo ljZkku
kh^_j`Zsb_dZd]Zaug_hj]Zgbq_kdh]hijhbkoh`^_gby1&2+6b^jlZdb
e_]db_ njZdpbb m]e_\h^hjh^h\ KG KG Kms_kl\m_l ^\_ lhqdb aj_gby gZ
ijbqbgmh[jZah\Zgby]Zah\uokdhie_gbch^gZbagbok_iZjZpbyjZkl\hj_ggh]h
]ZaZgZ\hkoh^ys_fmqZkld_ljm[hijh\h^Zkihke_^mxs_cdhZ]meypb_cimaujvdh\
\ kdhie_gb_ ]ZaZ D=>hg_p >@ ^jm]Zy aZs_fe_gb_ agZqbl_evguo h[t_fh\
Zlfhkn_jgh]h \ha^moZ \ ih\ur_gguo mqZkldZo ijb aZiheg_gbb mqZkldZ
ljm[hijh\h^Zihke_j_fhglZbebj_dhgkljmdpbbdhlhjucg_\ughkblkybaljm[u
baaZfZeuokdhjhkl_c^\b`_gbyg_nlb$:.DOLQVNH>@EKFZkeh\>@
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
H[hkgh\Zgb_ \hafh`ghklb ijbf_g_gby l_hjbb l_q_gby `b^dhklb \
hldjuluo jmkeZo ^ey hij_^_e_gby nhjfu b jZaf_jh\ ]Zah\h]h kdhie_gby
gZoh^ys_]hky\gZdehgghfljm[hijh\h^_aZi_j_\Zevghclhqdhcfh`ghgZclbm`_
\jZ[hlZo;:;Zof_lv_\Z^Zlbjh\Zgguo]>@
Nbabq_kdZy dZjlbgZ ihlhdZ ijh^mdlZ ih^ ©g_ih^\b`gufª ]Zah\uf
kdhie_gb_f \_kvfZ [ebadZ d fh^_eb [_agZihjgh]h ^\b`_gby `b^dhklb \
pbebg^jbq_kdhf dZgZe_ ih^jh[gh hibkZgghc \ deZkkbq_kdbo dmjkZo
]b^jhf_oZgbdb>@
<hijhkhf kms_kl\h\Zgby mklhcqb\h]h jZkkeh_ggh]h l_q_gby ^\monZagh]h
ihlhdZ aZgbfZebkv fgh]b_ hl_q_kl\_ggu_ b aZjm[_`gu_ mq_gu_ GZb[he__
ba\_klgu^bZ]jZffuij_^eh`_ggu_:B=m`h\uf>@ZaZjm[_`hf±L_cl_e_fb
>Zde_jhf>@
Ih^Zggufhlq_lZaZ
]>@ih
ijh]jZff_78))3
m]hegZdehgZ
gZgbkoh^ys_fmqZkld_
ϑ] fk
ϑ` Jbk>bZ]jZffZkljmdlmjguonhjf^\b`_gby]Zah`b^dhklgh]hihlhdZ
=jZ^Zpby kljmdlmjguo nhjf ^\b`_gby ]Zahg_nlygh]h ihlhdZ m jZaguo
bkke_^h\Zl_e_cdhe_[e_lkyhl^hFh^_evL_cl_ey>Zde_jZij_^eZ]Z_l>@
JZkkeh_ggZyVWUDWLILHG
JZkkeh_ggZyk\hegh\hcih\_joghklvxjZa^_eZnZaVUWDWLILHGZDY\
Ijh[dh\ZyLQWHUPLWWHG
Dhevp_\ZyDQQXODU
WfmevkbhggZyGLVSHUVHG
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
:B=m`h\jZaebqZ_lkljmdlmjguonhjfl_q_gby<NF_^\_^_\>@
Gh g_baf_ggh \h \k_o bkke_^h\Zgbyo ihdZaZgh qlh ijb fZeuo kdhjhklyo ]ZaZ
©g_ih^\b`gh_ª kdhie_gb_ b kdhjhklyo ^\b`_gby `b^dhklb « fk j_`bf
^\b`_gby±jZkkeh_gguc
FH>?EVJ:KKEH?GGH=HL?Q?GBY<LJM;HIJH<H>?
JZkq_lgmx
ko_fm
we_f_glZjgh]h
mqZkldZ
ljm[hijh\h^Z
Ziijhdkbfbjm_fh]h ijyfhc k m]ehf gZdehgZ ℜ gZ ijhnbe_ ljZkku fh`gh
hibkZlv
fh^_evx
klZpbhgZjgh]h
jZkkeh_ggh]h
ihlhdZ
\
gZdehgghf
pbebg^jbq_kdhfdZgZe_jbk
::
:
=Za
4
+
@b^dhklv
∞]
ϑ
:
*
'
7Z
7L
ℜ
∞[
JbkJZkq_lgZyko_fZihlhdZih^©g_ih^\b`gufª]Zah\ufkdhie_gb_f
KhklZ\bf^eybah[jZ`_ggh]hgZjbkmgd_we_f_glZjgh]hmqZkldZmjZ\g_gb_
;_jgmeebihgZijZ\e_gbx^\b`_gby
(ϑ + Gϑ )
S
SR
ϑ
+α
= G+ + R + α + G K lj WJα ⋅ G[ +
J
J
ρJ
ρJ
]^_
S±^Z\e_gb_\]Zah\hfkdhie_gbb
ϑGϑ±kdhjhklvihlhdZb__baf_g_gb_ihgZijZ\e_gbx^\b`_gby
G+±ijbjZs_gb_]em[bguihlhdZ
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
αhdhwnnbpb_glDhjbhebkZ
GKlj±ihl_jbwg_j]bbgZlj_gb_
>Z\e_gb_ gZ k\h[h^ghc ih\_joghklb `b^dhklb ih^ ]Zah\uf kdhie_gb_f
ijZdlbq_kdb g_baf_ggh ihwlhfm iv_ahf_ljbq_kdbc gZihj \ h[_bo qZklyo
mjZ\g_gby fh`gh khdjZlblv Ihl_jb wg_j]bb gZ lj_gb_ GKlj bf_xl ^\_
khklZ\eyxsb_ihkl_gd_ljm[hijh\h^ZGKZbgZih\_joghklbjZa^_eZnZaGKL
ρ`
χ ϑ
G[ ⋅λ
⋅
GK Z =
ρ ` − ρ ] ϖ J
τ
GKL =
D
G[ ρ` − ρ] ϖ ⋅ J
]^_
ρ`ρ]±iehlghklv`b^dhklbb]ZaZ
λdhwnnbpb_gl>Zjkb
L
⋅
χkfhq_gguci_jbf_lj
ϖiehsZ^v`b\h]hk_q_gbyihlhdZ`b^dhklb
Z±^ebgZ]jZgbpujZa^_eZnZa
τL±dZkZl_evgh_gZijy`_gb_k^\b]ZaZkq_lkbef_`nZagh]hlj_gby
Iehlghklv]ZaZρ]gZ^\Zihjy^dZf_gvr_iehlghklb`b^dhklbρ`ihwlhfm
\ mjZ\g_gbyo _c fh`gh ij_g_[j_qv Ij_^klZ\bf ihl_jb wg_j]bb gZ
f_`nZagh_lj_gb_\\b^_mjZ\g_gby>Zjkb
GKL =
τ L ⋅ D G[ = τ L ⋅ D ⋅ ϑ G[ = τ L ⋅ D ⋅ ϖ ⋅ G[ ⋅ ϑ ρ` − ρ] ϖ ⋅ J
ρ `ϑ ϖ J
π ⋅ ρ `ϑ ' ϖ ' J
KjZ\gb\Zy mjZ\g_gb_ k mjZ\g_gb_f >Zjkb ijboh^bf d \u\h^m qlh
^hklZlhqgh kjZ\gblv dhwnnbpb_gl ]b^jZ\ebq_kdbo khijhlb\e_gbc λ k
dhfie_dkhf D ϖ
τ L
⋅ ⋅ ^ey khihklZ\e_gby GKZ b GKL Ih ^Zgguf
π ⋅ ρ `ϑ ' ϖ
=?Dhjh[dh\Z >@ agZq_gb_ f_`nZagh]h dZkZl_evgh]h gZijy`_gby
τL ρ `ϑ hp_gb\Z_lky \_ebqbghc \deZ^ hklZevguo \_ebqbg ihjy^dZ _^bgbpu Z
dhwnnbpb_gl>Zjkbbf__lihjy^hdKe_^h\Zl_evghkbeuf_`nZagh]hlj_gby
bf_xl\_ebqbgmf_g__kbe`b^dhklgh]hlj_gbyhkl_gdbljm[hijh\h^Z
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
IjbgbfZy \h \gbfZgb_ hij_^_e_gb_ ]b^jZ\ebq_kdh]h jZ^bmkZ 5] ϖ /χ b
\ujZ`_gb_h[t_fgh]hjZkoh^Z4 ϑ⋅ϖihemqbf
GK Z = λ
'
5]
⋅
G[ ϑ ⋅
=
' J
λ
 π'  J
' ⋅

 
= ⋅
λ
()
⋅ ϖR
' ϖ
'
5]
()
⋅ ϖR
ϖ
'
5]
⋅ 4 G[ =
⋅ 4 G[
< ZgZeba_ n_ghf_gZ jZkkeh_ggh]h ^\b`_gby \ ljm[hijh\h^Zo
jZkkfZljb\ZxlkylZdb_]_hf_ljbq_kdb_oZjZdl_jbklbdb`b\h]hk_q_gbydZd
;_ajZaf_jgZy]em[bgZihlhdZ± Θ
+
= VLQ '
Θ
D
= VLQ '
χ
Θ
=
π' π
;_ajZaf_jgZy^ebgZ]jZgbpujZa^_eZnZa±
;_ajZaf_jguckfhq_gguci_jbf_lj
;_ajZaf_jguc]b^jZ\ebq_kdbcjZ^bmk Dhwnnbpb_glZaZiheg_gbyljm[u
5 ] = − VLQ Θ Θ
'
ϖ
ϖh
=
Θ − VLQ Θ
π
Z
+
Θ
'
Jbk=_hf_ljbq_kdb_oZjZdl_jbklbdb`b\h]hk_q_gby
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
JZkdju\Zy ϑGϑ dZd ϑ ϑ⋅GϑGϑ \ mjZ\g_gbb ij_g_[j_]Z_f
Gϑ dZd \_ebqbghc [he__ \ukhdh]h ihjy^dZ fZehklb Ihke_ ijb\_^_gby
ih^h[guoihemqZ_f
WJα =
()
G+
ϑ Gϑ
λ
+ α
+ ⋅ ⋅ ϖ R
G[
J G[
' ϖ
'
5]
⋅ 4 Baf_g_gb_ ]em[bgu ihlhdZ b kdhjhklgh]h gZihjZ ih ^ebg_ \
mklZgh\b\r_fky ^\b`_gbb `b^dhklb fh`_l ijhbkoh^blv eb[h ijb baf_g_gbb
^bZf_ljZ ljm[hijh\h^Z eb[h m]eZ _]h gZdehgZ d ]hjbahglm >ey we_f_glZjgh]h
mqZkldZ ljm[hijh\h^Z \ jZfdZo ij_^eh`_gghc jZkq_lghc ko_fu wlbo
khklZ\eyxsbo g_l J_rbf ihemq_ggh_ mjZ\g_gb_ hlghkbl_evgh dhwnnbpb_glZ
aZiheg_gby
WJα = ⋅
Dhwnnbpb_gl
λ
()
⋅ ϖR
' ϖ
'
5]
]b^jZ\ebq_kdh]h
⋅ 4 khijhlb\e_gby
\
k\hx
hq_j_^v
hij_^_ey_lkyj_`bfhflj_gbydhlhjucbg^bpbjm_lkyqbkehfJ_cghev^kZ
5H =
]^_
ϑ ⋅ 5]
4 ϖ 5 ]
=
⋅
⋅
ν
π' ⋅ν ϖ '
νdbg_fZlbq_kdZy\yadhklv`b^dhklb
H^gZdh ijb baf_g_gbb kl_i_gb aZiheg_gby kdhjhklv ^\b`_gby`b^dhklb
f_gy_lkyZke_^h\Zl_evghfh`_lf_gylvkybj_`bf^\b`_gby`b^dhklbbahgZ
lj_gby \ lmj[me_glghf j_`bf_ Ijb fZehc kl_i_gb aZiheg_gby ± eZfbgZjguc k
ihke_^mxsbf i_j_oh^hf \ lmj[me_glguc Z ijb hij_^_e_gguo mkeh\byo b
h[jZlgh GZ jbk bah[jZ`_gh baf_g_gb_ qbkeZ J_cghev^kZ \ aZ\bkbfhklb hl
dhwnnbpb_glZaZiheg_gbybj_`bfZl_q_gby`b^dhklb
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
±eZfbgZjguc
j_`bfl_q_gby
±]b^jZ\ebq_kdb
]eZ^db_ljm[u
±d\Z^jZlbqgZy
ahgZlj_gby
5HI±qbkeh
J_cghev^kZ\
gZihjghf
j_`bf_l_q_gby
5H 5HI
Jbk±Baf_g_gb_iZjZf_ljZJ_cghev^kZ
ϖ
ϖh
Hlghr_gb_
5H
5H I ϖ
ϖ
ϖ
ϖ
^hklb]Z_lk\h_]hfZdkbfmfZ
= = \ahg_]eZ^dh]hlj_gby = 5H
5H I ϖ
5H I
= \eZfbgZjghfj_`bf_l_q_gby
5H
5H I ϖ
5H
= \ahg_d\Z^jZlbqgh]hlj_gby
= GZ hkgh\Zgbb wdki_jbf_glZevguo bkke_^h\Zgbc =?Dhjh[dh\uf >@
[ueb ij_^eh`_gu aZ\bkbfhklb dhwnnbpb_glZ >Zjkb ^ey [_agZihjgh]h
eZfbgZjgh]hl_q_gby
λ=
λ=
5H
bahgu]eZ^dh]hlj_gby
5H
ih]j_rghklvdhlhjuog_ij_\urZ_l
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
Bkihevamy nhjfmem Dhev[jmdZ ^ey ahg kf_rZggh]h b d\Z^jZlbqgh]h
lj_gby >@ Z lZd `_ j_dhf_g^Zpbb F<Emjv_ ^ey ZiijhdkbfZpbb i_j_oh^gh]h
j_`bfZ©dhwnnbpb_glhfi_j_f_`Z_fhklbª>@
γ H[S^⋅5H`
ihemqbf ke_^mxsbc Ze]hjblf ^ey hij_^_e_gby dhwnnbpb_glZ ]b^jZ\ebq_kdh]h
khijhlb\e_gby
λ=
λ=
λ=
5H
− γ + γ 5H
5H
5H
^ey5H
^ey5H
'

^ey5H 
N
 w
'

 N
= − ⋅ OJ w +
 ^ey5H!  
λ
 ' 5H λ 
Nw
]^_
Nw ± dhwnnbpb_gl wd\b\Ze_glghc r_jhoh\Zlhklb \gmlj_gg_c
ih\_joghklbljm[u
:G:EBAIH<?>?GBY=B>JH>BG:FBQ?KDHCKBKL?FU
K p_evx h[h[s_gby b ZgZebaZ ihemq_ggh]h j_r_gby \\_^_f \
jZkkfhlj_gb_ jZkoh^ iheguf k_q_gb_f 4I ih^ dhlhjuf [m^_f ihgbfZlv
ijhba\h^bl_evghklv mqZkldZ ljm[hijh\h^Z \ mkeh\byo dh]^Z ]b^jZ\ebq_kdbc
mdehg jZ\_g m]em gZdehgZ hkb d ]hjbahglm Wlhl j_`bf ij_^iheZ]Z_l l_q_gb_
`b^dhklb ih^ ^_ckl\b_f lhevdh ]jZ\blZpbhgguo kbe Z ^Z\e_gb_ ih ^ebg_
mqZkldZhklZ_lkyihklhygguf
4I =
WJα ⋅ '
⋅ λ I
]^_
λI ± dhwnnbpb_gl ]b^jZ\ebq_kdbo khijhlb\e_gbc hij_^_ey_lky ih
deZkkbq_kdhcf_lh^bd_
λ=
5H
^ey5H
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX

 N
= − ⋅ OJ w +
 ^ey5H!
λ
 ' 5H λ 
LZdbf h[jZahf jZkoh^ iheguf k_q_gb_f mqblu\Z_l b m]he gZdehgZ
mqZkldZd]hjbahglmbj_heh]bq_kdb_k\hckl\Zi_j_dZqb\Z_fhckj_^u
GZ ]jZnbd_ bah[jZ`_gu djb\u_ aZ\bkbfhkl_c hlghkbl_evghc
ijhba\h^bl_evghklb mqZkldZ ljm[hijh\h^Z
4
ϖ
hl _]h kl_i_gb aZiheg_gby
4I
ϖh
ijbjZaebqguobkoh^Zokf_gj_`bfh\
Hlghkbl_evgZyijhba\h^bl_evghklv
Dhwnnbpb_glaZiheg_gby
Jbk±Ijhba\h^bl_evghklvmqZkldZljm[hijh\h^Z\aZ\bkbfhklbhl
dhwnnbpb_glZ_]haZiheg_gby
±eZfbgZjgucj_`bfl_q_gby`b^dhklb
±lmj[me_glgucj_`bfl_q_gby`b^dhklb\ahg_]eZ^dh]hlj_gby
± ahgZ lj_gby d\Z^jZlbqgZy \h \k_f ^bZiZahg_ dhwnnbpb_glZ
aZiheg_gby
Ohly l_g^_gpby ZgZeh]bqgZ b gZ ]jZnbdZo \h \k_o kemqZyo gZ[ex^Z_lky
lhqdZ fZdkbfmfZ gh _]h \_ebqbgZ b agZq_gb_ dhwnnbpb_glZ aZiheg_gby ijb
dhlhjhffZdkbfmfgZ[ex^Z_lkyjZaebqgu
Hlghkbl_evgmxijhba\h^bl_evghklvfh`ghhij_^_eblvba\ujZ`_gby
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
ϖ λ I 5]
4
=
4I ϖ λ '
Mqblu\Zy \ujZ`_gby q_j_a p_gljZevguc m]he Θ [_ajZaf_jgh]h
]b^jZ\ebq_kdh]hjZ^bmkZbdhwnnbpb_glZaZiheg_gbyZlZd`_mjZ\g_gby
^ey hij_^_e_gby dhwnnbpb_glh\ ]b^jZ\ebq_kdh]h khijhlb\e_gby λ fh`gh
ihemqblv ZgZeblbq_kdb_ aZ\bkbfhklb ^ey hlghkbl_evghc ijhba\h^bl_evghklb \
^bZiZahg_p_gljZevguom]eh\Θ\ij_^_eZoh^ghcahgulj_gby
(Θ − VLQ Θ)
4
= Θ
4I
^ey
(Θ − VLQ Θ) 4
= 4I
Θ
^eyahgu]eZ^dh]hlj_gby (Θ − VLQ Θ) 4
= 4I
Θ
^eyahgud\Z^jZlbqgh]hlj_gby
Qbke_ggh_ j_r_gb_ wlbo mjZ\g_gbc ^Z_l ke_^mxsb_ agZq_gby
eZfbgZjgh]h
j_`bfZ
l_q_gby
fZdkbfmfh\
4 
4 
 I
4 
4 
 I
= ^eyeZfbgZjgh]hl_q_gby
PD[
= ^ey]b^jZ\ebq_kdb]eZ^dboljm[ PD[
4 
4 
 I
Θ = Θ =
= ^eyd\Z^jZlbqghcahgulj_gby
PD[
Θ = Baf_g_gb_ kl_i_gb aZiheg_gby \ aZ\bkbfhklb hl m]eZ gZdehgZ mqZkldZ
ljm[hijh\h^Z∅ff^eyjZaebqguoj_`bfh\l_q_gby`b^dhklb\yadhklvx
kKl\^bZiZahg_jZkoh^h\>«[email protected][jZ`_ghgZjbk
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
5Hdj
5H,
5H,,
ϖ
ϖ
fk
4
Jbk±Kl_i_gvaZiheg_gbyljm[hijh\h^Z\aZ\bkbfhklbhlijhba\h^bl_evghklb
WJα WJα WJα WJα Djb\u_ aZiheg_gby ihemq_gu ba mjZ\g_gbc 4
IΘ⋅4I ^ey
khhl\_lk\mxsbo j_`bfh\ l_q_gby =jZgbpu ahg lj_gby hij_^_eyxlky
nhjfmeZfb
4=
]^_
5H⋅ ' ⋅ν ⋅ Θ
5H 5Hdj ^ey jZa]jZgbq_gby ahgu eZfbgZjgh]h l_q_gby `b^dhklb b
]b^jZ\ebq_kdb]eZ^dboljm[
5H 5H,±ahg]eZ^dh]hbkf_rZggh]hlj_gby
5H 5H,,±ahgkf_rZggh]hbd\Z^jZlbqgh]hlj_gby
LZdbf
h[jZahf
g_h[oh^bfuf
gh
g_
^hklZlhqguf
mkeh\b_f
kms_kl\h\Zgby ]Zah\ha^mrgh]h kdhie_gby gZ mqZkld_ ljm[hijh\h^Z y\ey_lky
khhlghr_gb_
44PD[
]^_
4±f]gh\_ggZyijhba\h^bl_evghklvljm[hijh\h^Z
4PD[±fZdkbfZevgh\hafh`gZyijhba\h^bl_evghklvmqZkldZ\[_agZihjghf
j_`bf__]hwdkiemZlZpbb
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
<U<H>
Iheh`_gb_ ]Zah\ha^mrgh]h kdhie_gby \ ihehklb ljm[hijh\h^Z h[mkeh\e_gh
]b^jh^bgZfbq_kdbfbmkeh\byfb
kdhie_gb_ jZkiheZ]Z_lky gZ gbkoh^ys_f mqZkld_ ljZkku gZqbgZy k
gZb\ukr_ci_j_\Zevghclhqdb
g_h[oh^bfufmkeh\b_fkms_kl\h\Zgbykdhie_gbyy\ey_lkyih^^_j`Zgb_
ijhba\h^bl_evghklb\ij_^_eZo4 >«4PD[@
iehsZ^v ihi_j_qgh]h k_q_gby kdhie_gby gZ dZ`^hf mqZkld_
ljm[hijh\h^Zj_]eZf_glbjm_lky_]hdhwnnbpb_glhfaZiheg_gby
ϖ
ϖ
>ebgZ]Zah\h]hkdhie_gbyhij_^_ey_lkygZebqb_f]ZaZ
EBL?J:LMJ:
>hg_pD=Bkke_^h\Zgb_jZ[hlug_nl_ijh^mdlhijh\h^h\\i_jbh^jZaju\Z
kiehrghklbihlhdZmi_j_\ZeZdZg^^bkkFFBGOb=I
.DOLQVNH$$5REHUWVRQ,0(QWHUDLQPHQWRIDLULQIORZLQJZDWHU7UDQVDFWLRQV
$PHULFDQ6RFLHW\RI&LYLO(QJLQHHUV±YRO±SS
FZkeh\EKM^Ze_gb_\h^ub\ha^moZbaljm[hijh\h^h\\imkdh\hci_jbh^
Kljhbl_evkl\hljm[hijh\h^h\±‹
;Zof_lv_\;:HjZ\ghf_jghf^\b`_gbb`b^dhklb\dZgZeZobljm[Zo±
E
Qm]Z_\JJ=b^jZ\ebdZL_ogbq_kdZyf_oZgbdZ`b^dhklbBa^Zgb__±E
Wg_j]hba^Zl±k
Rl_j_gebol><=b^jZ\ebdZ±FWg_j]hZlhfba^Zl±k
0XQVRQ%5<RXQJ')2NLLVKL7+)XQGDPHQWDOVRI)OXLG0HFKDQLFV6HFRQG
(GLWLRQ±1<-RKQ:LOH\6RQV,QFS
=m`h\:BKh\f_klguck[hjbljZgkihjlg_nlbb]ZaZ±FG_^jZ±
k
7HLWHO<'XNOHU$(%DUQHD'0RGHOOLQJ)ORZ3DWWHUQ7UDQVLWLRQVIRU6WHDG\
8SZDUG*DV/LTXLG)ORZLQ9HUWLFDO7XEHV$,&K(-9RO±SS
Ljm[hijh\h^gucljZgkihjlg_nl_ijh^mdlh\BLBrfmoZf_lh\KEBkZ_\
F<Emjv_KIFZdZjh\±FG_nlvb]Za±k
Dhjh[dh\=?>\b`_gb_g_nl_cbg_nl_ijh^mdlh\\ljm[hijh\h^Zo
g_aZiheg_ggufk_q_gb_f^bkkdZg^l_oggZmd±MnZ±k
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
‹G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX
Похожие документы
Скачать