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19
() () ( )
()()
,,,,,0
,,,0 ,, ,
∞
−∞
∞
−∞
=ξτ−τξ+
∫∫∫∫
−τξ ξ τ ν⋅
∫∫∫
(4.10)
=
, v —
V
()
()
σ
—
τ
() ()
,,
+∞
−∞ Σ
∂
=τ ξτ⋅⋅ν Σ
∫∫∫
∂ξ
. (4.11)
Σ.
.
t x n
x,
y -
,,.
()
[]
Σ
∂
=⋅ν⋅∗⋅Σ
∫∫
∂ξ
. (4.12)
19
∞
XQ ( [, W ) = ∫ GW ∫∫∫ IL (ξ, τ )*QO ( [, W − τ, ξ,0 ) G9 +
&
−∞ 9
(4.10)
∞
∫ GW ∫∫ *QO ( [, W − τ, ξ,0 )7L X (ξ, τ ) , ν ⋅ G6 ,
−∞ 6
]^_ 7L = FLMNO $)QN O , v — _^bgbqgZy ghjfZev d ih\_joghklb jZaju\Z Wlh \u
jZ`_gb_ l_hj_fu ij_^klZ\e_gby ;_llb ^ey kemqZy gme_\uo gZijy`_gbc gZ
ih\_joghklb jZaju\Z L_hj_fZ ij_^klZ\e_gby iha\hey_l aZf_gblv h[eZklv
h[t_fZ V k jZaju\hf gZ ^\_ h[eZklb [_a jZaju\Z ijh^he`Zy jZaju\ gZ
[_kdhg_qghklv
GZ ijhly`_gbb ih\_joghklb jZaju\Z \_dlhju kf_s_gbc XQ ( [ W ) b
gZijy`_gbc σQ ( [ W ) — g_ij_ju\gu Ijb i_j_oh^_ q_j_a ih\_joghklv jZa
ju\Z l_gahj =jbgZ *QO b l_gahj gZijy`_gbc τLM lZd`_ g_ij_ju\gu
Kf_s_gby \ ijhba\hevghc lhqd_ ijhkljZgkl\Z \ujZ`_ggu_ q_j_a
kf_s_gby gZ jZaju\_
LZdbf h[jZahf \_dlhj kf_s_gby \ ex[hc lhqd_ ijhkljZgkl\Z fh`_l
[ulv \ujZ`_g q_j_a kdZqhd kf_s_gbc gZ jZaju\_ Z bf_ggh
+∞ ∂*NO
XL ( [, W ) = ∫ G τ∫∫ XL (ξ, τ ) ⋅ FLMNO ⋅ ν M
&
GΣ . (4.11)
−∞ Σ ∂ξ
Wlh y\ey_lky ke_^kl\b_f l_hj_fu _^bgkl\_gghklb B hlkx^Z ke_^m
_l mijm]h_ ihe_ hl jZaju\Z kh\iZ^Z_l k ihe_f dhlhjh_ ^Z\ZeZ [u kj_^Z
[_a jZaju\Z k bklhqgbdhf jZkij_^_e_gguf gZ ih\_joghklb Σ. DZ`^uc
we_f_gl jZaju\Z wd\b\Ze_gl_g g_dhlhjhfm lhq_qghfm bklhqgbdm.
< lh \j_fy dZd nmgdpby =jbgZ ij_^klZ\ey_l kh[hc kf_s_gb_ kha^Z
\Z_fh_ _^bgbqghc khkj_^hlhq_gghc kbehc ijbeh`_gghc \ fhf_gl \j_f_
gb t \ lhqd_ x b gZijZ\e_gghc ih n __ ijhba\h^gZy ih dhhj^bgZlZf [m^_l
hibku\Zlv kf_s_gby kha^Z\Z_fu_ _^bgbqghc iZjhc kbe Ijbq_f _keb gZ
ijZ\e_gb_ __ ^_ckl\by hjb_glbjh\Zgh ih hkb x, lh fhf_gl hij_^_ey_lky
hlghkbl_evgh hkb y LZdbf h[jZahf lhq_qguc bklhqgbd hibku\Z_lky -x
iZjZfb \aZbfh^_ckl\mxsbo kbe khhl\_lkl\mxsbo \hafh`guf dhf[bgZ
pbyf bg^_dkh\ L, M, O .
Kf_s_gb_ gZ ih\_joghklb fh`_l [ulv aZibkZgh lZd`_ k ihfhsvx
l_hj_fu h k\_jld_
∂
XQ ( [ W ) = ∫∫ [XL ] ⋅ νL ⋅ FLMNO ∗
&
⋅ *QS G Σ . (4.12)
Σ ∂ξ
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