развитие метода интегральных уравнений для расчета свч

=HKM>:JKL<?GGUCG:MQGUCP?GLJJHKKBCKDHCN?>?J:PBB BGKLBLMLNBABDB<UKHDBOWG?J=BC BN<W± <?L_jy_\ J:A<BLB?F?LH>:BGL?=J:EVGUOMJ:<G?GBC >EYJ:KQ?L:K<Q−J?AHG:LHJH< NbebZeBgklblmlZy^_jghcnbabdbKHJ:G Ijhl\bgh M>D F :gghlZpby L_jy_\ <? JZa\blb_ f_lh^Z bgl_]jZevguo mjZ\g_gbc êy jZkq_lZ K<Qj_ahgZlhjh\ Ij_ijbgl BN<W±Ijhl\bgh±kjbklZ[e[b[ebh]j JZkkfhlj_gZ aZ^ZqZ jZkq_lZ ^\mf_jguo h[t_fguo K<Q−j_ahgZlhjh\ f_lh^hf bgl_]jZevguo mjZ\g_ gbc =jZgbqgu_ bgl_]jZevgu_ mjZ\g_gby knhjfmebjh\Zgu hlghkbl_evgh lZg]_gpbZevghc dhfihg_glu fZ]gblgh]h ihey b ih\_joghklghc iehlghklb lhdZ J_rZxsbf nZdlhjhf ihemq_gby \ukhdhc lhqghklb jZkq_lZy\ey_lkybkihevah\Zgb_dm[bq_kdh]hkieZcgZêyZiijhdkbfZpbbbkdhfuoihe_cgZih\_joghklb − j_ahgZlhjZ<l_klh\uoaZ^ZqZo^_fhgkljbjm_lkylhqghklvjZkq_lh\j_ahgZgkghcqZklhlu êyg_ kbff_ljbqguolbih\dhe_[Zgbc\ukhdh]hihjy^dZ $EVWUDFW 7HU\DHY9('HYHORSPHQWRIWKH%RXQGDU\,QWHJUDO0HWKRGIRU5)&DYLW\$QDO\VLV,+(33UHSULQW ±3URWYLQR±SILJWDEOHUHIV 7KH WZRGLPHQVLRQDO SUREOHP IRU 5) FDYLW\ DQDO\VLV LV FRQVLGHUHG 7KH ERXQGDU\ LQWHJUDO HTXDWLRQ DUH IRUPXODWHGZLWKUHVSHFWWRWDQJHQWLDOFRPSRQHQWRIDPDJQHWLFILHOGDQGVXUIDFHFXUUHQWGHQVLW\7KHPDLQIDFWRU RIGHULYLQJRIDKLJKDFFXUDF\LVWKHXVHRIDFXELFVSOLQHIRUDSSUR[LPDWLRQRIXQNQRZQFRPSRQHQWVRIILHOGVRQ − D VXUIDFH RI D FDYLW\ ,Q WKH WHVWV WKH DFFXUDF\ RI UHVRQDQFH IUHTXHQF\ RI IRU KLJK RUGH GLSROH PRGHV LV GHPRQVWUDWHG =hkm^Zjkl\_ggucgZmqgucp_glj JhkkbckdhcN_^_jZpbb Bgklblmlnbabdb\ukhdbowg_j]bc <\_^_gb_ <gZklhys__\j_fyêyjZkq_lZj_ahgZlhjh\ijbf_gy_lkyjy^\uqbkebl_evguoijh]jZff Wlh ba\_klgu_ ijh]jZffu 683(5),6+ 850(/7 0$),$ b hl_q_kl\_ggu_ ijh]jZffu 683(5/$16$=,087+358'> @Hgbj_rZxlmjZ\g_gbyFZdk\_eeZ\^bnn_j_gpbZevghc nhjf_Bkihevah\Zgb_bgl_]jZevguomjZ\g_gbcFZdk\_eeZêyjZkq_lZj_ahgZlhjh\f_g__jZa \blh Wlh k\yaZgh k g_h[oh^bfhklvx ]jhfha^dbo \uqbke_gbc bgl_]jZeh\ ih ih\_joghklb keh`ghcnhjfubkljm^ghklvxgZoh`^_gbyj_ahgZgkguoqZklhlfh^hkh[_ggh\ukrbolbih\ H^gbfbakihkh[h\ij_h[jZah\Zgbybgl_]jZevgh]hmjZ\g_gbydkbkl_f_ebg_cguomjZ\g_ gbcy\ey_lkyf_lh^dheehdZpbc=jZgbqgu_mkeh\byêyihe_cgZih\_joghklbmklZgZ\eb\Zxl kylhqgh\uiheg_ggufb\^bkdj_lghfqbke_lhq_ddheehdZpbbLhqghklvj_r_gbyaZ^ZqbaZ\b kblhlqbkeZlhq_dk_ldbbhl\u[jZgghcZiijhdkbfZpbbihe_cgZih\_joghklbf_`^mlhqdZfb <^ZgghcjZ[hl_ij_^klZ\e_gihôh^dhlhjucj_rZ_lijh[e_fulhqghklbbgZ^_`ghklb \uqbke_gbyj_ahgZgkguoqZklhlfh^êyf_jghc]_hf_ljbb J_rZxsbf \ ^Zgghf ihôh^_ y\ey_lky bkihevah\Zgb_ l_ogbdb ZiijhdkbfZpbb bkdh fuo ihe_c gZ ih\_joghklb ijh\h^gbdZ dm[bq_kdbf kieZcghf KieZcg fh`gh jZkkfZljb\Zlv dZddhg_qgucwe_f_glk[hevrbfqbkehf\gmlj_ggbomaeh\lhq_ddheehdZpbbQbkehdhg_q guowe_f_glh\aZ\bkblhlkeh`ghklb]_hf_ljbb>eyijhklhc]_hf_ljbbgZijbf_jkn_ju^hk lZlhqgh h^gh]h dhg_qgh]h we_f_glZ Lhqghklv j_r_gby jZkl_l k m\_ebq_gb_f qbkeZ maeh\ kieZcgZ<i_j\u_l_ogbdmkieZcgZêyf_jguoaZ^Zqwe_dljhklZlbdbjZa\beB\Zgh\>@bih emqbe\_kvfZlhqgu_j_amevlZlu Dhwnnbpb_glu fZljbpu hibku\Zxs_c kbkl_fm ebg_cguo mjZ\g_gbc \uqbkeyxlky bgl_]jbjh\Zgb_fnmgdpbb=jbgZmfgh`_gghcgZebg_cgu_nmgdpbbihjh`^Z_fu_kieZcghf >ey \uqbke_gby ^bZ]hgZevguo dhwnnbpb_glh\ fZljbpu ]^_ lhqdZ dheehdZpbb ijbgZê_`bl ih\_joghklb bgl_]jbjh\Zgby nmgdpby =jbgZbf__lbgl_]jbjm_fmxhkh[_gghklv dhlhjZy\u ^_ey_lkyZgZeblbq_kdb Ijhp_^mjZ gZoh`^_gby j_ahgZgkghc qZklhlu khklhbl \ jZkq_l_ qZklhlghaZ\bkbfuo we_f_glh\ dhfie_dkghc fZljbpu \ aZ^Zgghf ^bZiZahg_ qZklhl <[ebab j_ahgZgkghc qZklhlu fgbfZy qZklv fbgbfZevgh]h kh[kl\_ggh]h agZq_gby fZljbpu y\ey_lky nmgdpb_c qZklhlu [ebadhc d ebg_cghc Ijhklhc ZgZeblbq_kdbc ijbf_j ijb\h^bfuc gb`_ ih^l\_j`^Z_l lZdh_ ih\_^_gb_Dhj_gvwlhcnmgdpbbkhhl\_lkl\m_lj_ahgZgkghcqZklhl_bgZoh^blkyaZfZeh_qbk ehbl_jZpbcihqZklhl_IhbkdfbgbfZevgh]hkh[kl\_ggh]hagZq_gbyfZljbpuhkms_kl\ey_lky f_lh^hf h[jZlguo bl_jZpbc b aZgbfZ_l g_[hevrmx qZklv \j_f_gb ih kjZ\g_gbx k jZkq_lhf kZfhcfZljbpu JZg__ him[ebdh\Zggu_ j_amevlZlu >@ ij_^klZ\eyeb ^h\hevgh ihegmx fZl_fZlbq_kdmx nhjfmebjh\dmaZ^Zqb ghqbke_ggucZe]hjblfg_h[_ki_qb\ZegZ^_`gh]hblhqgh]h\uqbke_ gbyj_ahgZgkguoqZklhl Bgl_]jZevgh_mjZ\g_gb_ H[hagZqbfbg^_dkhf L lhqdmgZ[ex^_gbybf_xsmxjZ^bmk\_dlhj ! L baZibr_fbgl_ ! kha^Z\Z_fh]h we_dljbq_kdbfb lhdZfb ]jZevgmx nhjfmem >@ êy fZ]gblgh]h ihey + L iehlghklvx - ! jZkiheh`_ggufbgZih\_joghklb 6 ijh\h^gbdZhdjm`Zxs_]hh[t_f 9 \ dhlhjhf bs_f j_r_gby êywe_dljhfZ]gblguoihe_c>jm]b_bklhqgbdbihey gZijbf_jfZ] gblgu_lhdbihdZg_jZkkfZljb\Z_f ! = - ! × U ⋅ I NU G6 + L ∫ 6 ]^_h[hagZq_gh I NU = + LNU ⋅ H − LNU ⋅ Ω U JZ^bmk\_dlhj U = ! L − ! jbkgZijZ\e_ghllhqdbbklhqgbdZkjZ^bmkhf\_dlhjhf ! jZkiheh`_gghcgZih\_joghklb 6 dlhqd_gZ[ex^_gbykjZ^bmkhf\_dlhjhf ! L 7Zdbfh[jZ ahfjZkkfZljb\Z_f\heguk\hegh\ufqbkehf N gZijZ\e_ggu_hlbklhqgbdZiheyIZjZf_lj Ω y\ey_lkyl_e_kgufm]ehfih^dhlhjuf\b^_gbkke_^m_fuch[t_fbalhqdbgZ[ex^_gby>@ Hg^hihegy_lm]heijbgyluc\>@^h π ?keblhqdZgZ[ex^_gbygZoh^blky\gmljbh[t_fZ hdjm`_ggh]h ih\_joghklvx 6 lh Ω = π êy j_]meyjghc qZklb ih\_joghklb Ω = π < ^\mf_jguo aZ^ZqZo lhqd_ gZ[ex^_gby khhl\_lkl\m_l iehkdbc m]he Λ gZ dhglmj_ b lh]^Z Ω = Λ >eylhq_dgZj_]meyjghcqZklbdhglmjZ Λ = π GZ ih\_joghklb b^_Zevgh]h ijh\h^gbdZ jbk fZ]gblgh_ ihe_ b iehlghklv lhdZ F\yaZgu]jZgbqgufmkeh\b_f ρ = - ρ QL × + L L GhjfZev d ih\_joghklb Q L gZijZ\e_gZ gZjm`m ijh\h^gbdZ < m]eh\hc lhqd_ ghjfZev fh`_l ijbgZê_`Zlvex[hcbakf_`guoih\_joghkl_c V = ; ρL Ω ρ U - Q + < Jbk=jZgbqgh_mkeh\b_ Jbk Ijbf_j dh]^Z lhqdZ gZ[ex^_gby L gZoh ^blky\h\gmlj_gg_fm]emih\_joghklb 6 lhdZ LZdbfh[jZahfbabihemqZ_fbgl_]jZevgh_mjZ\g_gb_hlghkbl_evghiehlghklb ∫ Q × - ρ × U ⋅ I NU G6 = - ρ L L 6 <_dlhj iehlghklb lhdZ gZ ih\_joghklb ijh\h^gbdZ jZaeh`bf ih hjlh]hgZevguf gZ ijZ\e_gbyfk_^bgbqgufb\_dlhjZfb b ! ehdZevghckbkl_fudhhj^bgZl - = - τ τ ϕ ⋅ + - ϕ τ ϕ ⋅ ! AZl_f^hfgh`ZykdZeyjghihhq_j_^bgZ_^bgbqgu_\_dlhju L b ! L \lhqd_gZ[ex^_gby L ihemqbfbgl_]jZevgh_mjZ\g_gb_êydhfihg_gliehlghklblhdZ ∫ > - τ L ⋅ QL × × U + - ϕ L ⋅ QL × ! × U @ ⋅ I NU G6 = -Lτ 6 τ ϕ ϕ ∫ > - !L ⋅ QL × × U + - !L ⋅ QL × ! × U@ ⋅ I NU G6 = -L 6 <gmlj_ggxxaZ^Zqmwe_dljh^bgZfbdbfh`ghknhjfmebjh\Zlvhlghkbl_evgheb[hfZ] gblgh]h ihey eb[h we_dljbq_kdh]h ihey Bgl_]jZevgh_ \ujZ`_gb_ êy we_dljbq_kdh]h ihey \u]ey^bl[he__]jhfha^dhq_fêyfZ]gblgh]hihey>@ (!L = −  - L ⋅ U ⋅ U  L  − LNU  N - L × U × U  L  −  +  − L −  ⋅ H G6  ∫ Ωξ F 6  U U NU   NU  N U <uibr_f]jZgbqgh_mkeh\b_êywe_dljbq_kdh]hihey\lhqd_gZ[ex^_gby L ρ = L GLY- ρ QL ⋅ ( L L & Bgl_]jZevgh_ mjZ\g_gb_ hlghkbl_evgh iehlghklb lhdZihemqZ_fh_ba b nhjfm ebjm_lkyZgZeh]bqghbgl_]jZevghfmmjZ\g_gbx k[he__keh`gufbij_h[jZah\Zgbyfb>Z e__h]jZgbqbfkyjZkkfhlj_gb_f[he__ijhklh]hbgl_]jZevgh]hmjZ\g_gbyihemq_ggh]hba jZkkfhlj_gbyfZ]gblgh]hihey :dkbZevghkbff_ljbqgZyaZ^ZqZ IjbZdkbZevghckbff_ljbbehdZevgmxdhhj^bgZlm τ \u[_j_f\^hevh[jZamxs_cnb ]mju \jZs_gby f_jb^bZgZ k _^bgbqguf \_dlhjhf ZehdZevgZydhhj^bgZlZ ϕ kh\iZ^_lk m]eh\hcdhhj^bgZlhcpbebg^jbq_kdhckbkl_fubf_xs_c\wlhclhqd_gZijZ\e_gb__^bgbqgh ]h \_dlhjZ ! Dhfihg_glu ih\_joghklghc iehlghklb lhdZ ]Zjfhgbq_kdb aZ\bkyl hl m]eZ ϕ JZkdeZû\Zy\_dlhjiehlghklblhdZihhjlh]hgZevgufgZijZ\e_gbyf b ! ihemqZ_f - τ ϕ = - τ τ ⋅ FRV Pϕ ⋅ + - ϕ τ ⋅ VLQ Pϕ ⋅ ! ]^_ P ±ZabfmlZevgh_qbkeh - τ b - ϕ −nmgdpbblhevdhdhhj^bgZlu τ J_amevlZl\_dlhjguohi_jZpbc\pbebg^jbq_kdhckbkl_f_k_^bgbqgufb\_dlhjZfbba ihdZaZg\Ijbeh`_gbbBgl_]jbjh\Zgb_ihiehsZ^bkwe_f_glhf G6 = 5 ⋅ Gτ ⋅ Gϕ ijb\h ^bl d bgl_]jbjh\Zgbx \^hev h[jZamxs_c / ih iZjZf_ljbq_kdhc dhhj^bgZl_ τ bkdhfuo nmgdpbc - τ b - ϕ by^jZ * µη y\eyxsbokynmgdpbyfb τ b τ L Bgl_]jbjh\Zgb_ihm]em ϕ \dexq_gh\\uqbke_gb_dhfihg_gly^jZ ∫ > - τ τ ⋅ * ττ τ τ L + - ϕ ⋅ * τϕ τ τ L @Gτ = - τ τ L / τ ϕτ ϕ ϕϕ τ ∫ > - τ ⋅ * τ τ L + - ⋅ * τ τ L @Gτ = - τ L / <_jogbcbg^_dky^jZgZijbf_j * τϕ τ τ L ihdZau\Z_l ijh_dpbx\_ebqbgufZ]gbl gh]hihey\lhqd_kdhhj^bgZlhc τ L kha^Z\Z_fh]h_^bgbqghciehlghklvx ϕ cdhfihg_glulh dZkdhhj^bgZlhc τ π * ττ = 5 ∫ I NU ⋅ − 5L FRV γ = + ' FRV ϕ ⋅ FRV Pϕ ⋅ Gϕ π * τϕ = − 5 ∫ I NU ⋅ VLQ Pϕ ⋅ VLQ ϕ ⋅ Gϕ π * ϕτ = 5 ∫ I NU ⋅ 5L FRV γ =L FRV γ 5 − ' FRV γ 5L ⋅ VLQ Pϕ ⋅ VLQ ϕ ⋅ Gϕ π * ϕϕ = 5 ∫ I NU ⋅ 5 FRV γ = L − 'L FRV ϕ ⋅ FRV Pϕ ⋅ Gϕ A^_kv I NU babh[hagZq_gh U = 5 + 5L − 55L FRV ϕ + = L − = ' = 5 FRV γ = + = L − = FRV γ 5 'L = 5L FRV γ L = − = L − = FRV γ L 5 Dhhj^bgZlu lhqdb bgl_]jbjh\Zgby 5 = 5 τ = = = τ b gZijZ\eyxsb_ dhkbgmku we_f_glZ ih\_joghklbdhkyf FRV γ 5 FRV γ = y\eyxlkynmgdpbyfb τ \_ebqbgukbg^_dkhf L nmgdpbb dhhj^bgZlulhqdbgZ[ex^_gby τ L jbkM^\h_gb_\hagbdZ_l\k\yabkl_fqlhkmq_lhfq_l gh]hbebg_q_lgh]hoZjZdl_jZihûgl_]jZevghcnmgdpbbijh\h^bfbgl_]jbjh\Zgb_g_ihihe ghfmm]emZ\ij_^_eZohl ^h π = L 5L γ =L γ 5L = L 5 Jbk <aZbfgh_ jZkiheh`_gb_ gZ dhglmj_ / lhqdb gZ[ex^_gby L k dhhj^bgZlZfb = L 5L b lhqdb bgl_] / Uτ ϕ Q = 5 γ = γ 5 jbjh\Zgbykdhhj^bgZlZfb = 5 τ γ γ= 5 Kbff_ljbqgu_lbiudhe_[Zgbc >ey^bihevguob\ukrbolbih\dhe_[Zgbcdh]^Z P ≠ \j_ahgZlhjZoijhba\hevghc nhjfukpbebg^jbq_kdhckbff_ljb_cih\_^_gb_ihe_cg_\hafh`ghdeZkkbnbpbjh\Zlvih ( beb + -lbiZf dhe_[Zgbc dZd wlh bf__l f_klh ijb jZkkfhlj_gbb j_ahgZlhjh\ ki_pbZevghc nhjfupbebg^jZbebkn_juGhêykbff_ljbqguolbih\ P = lZdZydeZkkbnbdZpbybf__l f_klhKemqZcdh]^Zkms_kl\m_llhevdhf_jb^bZgguclhd - τ khhl\_lkl\m_l ( lbiZfdhe_ [Zgbcdh]^Zkms_kl\m_llhevdhZabfmlZevguclhd - ϕ khhl\_lkl\m_l + lbiZf Bgl_]jZevgh_mjZ\g_gb_bf__lke_^mxsbc\b^ ∫ - τ ⋅ * τ τ Gτ = - τ L L / ]^_êy ( lbih\h[hagZqbf - = τ * = * τ êy + lbih\ - = ϕ * = * ϕ Y^jZ * τ b * ϕ ihemqbfba * ττ b * ϕϕ ijb P = π * τ = 5 ∫ I NU ⋅ − 5L FRV γ = − ' FRV ϕ Gϕ π * ϕ = 5 ∫ I NU ⋅ 5 FRV γ =L − 'L FRV ϕ Gϕ >\mf_jgZyaZ^ZqZ\^_dZjlh\hckbkl_f_dhhj^bgZlJ_]meyjguc\hegh\h^ AZ^ZqZ h djblbq_kdbo lbiZo dhe_[Zgbc \ j_]meyjghf \hegh\h^_ jZkiZ^Z_lky gZ aZ^Zqb êy ( b + lbih\ : >ey ( lbih\ kms_kl\m_l lhevdh dhfihg_glZ iehlghklb lhdZ - = τ gZijZ\e_ggZy \^hev\hegh\h^Zbkhhl\_lkl\_gghdhfihg_gluihe_c ( = + ; + < H[hagZqbfq_j_a τ [ \ iZjZf_ljbq_kdmxdhhj^bgZlmlhqdbih\_joghklbBgl_]jZev gh_ij_^klZ\e_gb_êywe_dljbq_kdh]hihey ( = aZibku\Z_lkyq_j_anmgdpbx=jbgZ L * NU = − + NU y\eyxsmxkynmg^Zf_glZevgufj_r_gb_ff_jgh]hmjZ\g_gby=_evf]hevpZ>@ ∆* + N * = δ U Ijh^hevgZy dhfihg_glZ we_dljbq_kdh]h ihey \ujZ`Z_lky bgl_]jZehf \^hev h[jZamxs_c / \hegh\h^Zbbf__l\b^ πωµ ( = ρ L = L Ω / ∫ - τ ⋅ * NU Gτ π mqblu\Z_ldhgnb]mjZpbxih\_joghklb\lhqd_gZ[ex^_gbydZdb\\ujZ Ω `_gbb JZ^bmk\_dlhj U τ τ L = !L τ L − !τ gZijZ\e_ghlbklhqgbdZiheydlhqd_gZ[ex ]^_fgh`bl_ev ^_gbyNmgdpby=Zgd_ey + NU = - + L<NU \ujZ`Z_lkyq_j_anmgdpbb;_kk_eybhibku\Z_l\hegmjZkoh^ysmxkyhlbklhqgbdZ DZdb\ur_nhjfmebjm_f\gmlj_ggxxaZ^Zqmwe_dljh^bgZfbdbhlghkbl_evghfZ]gbl gh]hiheydhlhjh_gZoh^bfbamjZ\g_gbyFZdk\_eeZ +=− URW ( Lωµ =jZgbqgh_mkeh\b_ Q L × + L = - L êyfZ]gblgh]hiheygZb^_Zevghijh\h^ys_cih\_jo ghklb\lhqd_gZ[ex^_gbykdhhj^bgZlhc τ L ijb\h^bldbgl_]jZevghfmmjZ\g_gbxhlgh kbl_evghih\_joghklghciehlghklblhdZ ∫ - τ ⋅ * τ τ Gτ = - τ L / y^jhdhlhjh]hbf__l\b^ * τ τ L = FRV γ L ; b FRV γ hkyf ; b < L < L  LπN \ − \ τ [ − [τ  + NU FRV γ ; L L − FRV γ <L L Ω U τ τ L U τ τ L   y\eyxlky gZijZ\eyxsbfb dhkbgmkZfb we_f_glZ ih\_joghklb \ lhqd_ τ L d U τ τ L = [L − [τ + \L − \ τ Nmgdpby=Zgd_ey + NU = - NU + L< NU \ujZ`_ggZyq_j_anmgdpbb;_kk_eyihy\ey_lkyihke_^bnn_j_gpbZevguohi_jZpbc ;>eydjblbq_kdbo + lbih\\\hegh\h^_kms_kl\m_llhevdhihi_j_qgZydhk_\hceb gbb\hegh\h^Zdhfihg_glZiehlghklblhdZ -τ τ gZijZ\e_ggZy\^heviZjZf_ljbq_kdhcdhhj ^bgZlu τ bdhfihg_gluihe_c + = ( ; (< Bgl_]jZevgh_\ujZ`_gb_êy\uqbke_gbyfZ] gblgh]hiheybf__l\b^ + = !L = ∫ - τ ⋅ * τ τ L Gτ / ]^_ * τ τ L = L πN  \ − \ τ [ − [τ  − FRV γ τ L + FRV γ ; τ L  Ω U τ τ L U τ τ L   ke_^m_ljZaebqZlvk Ij_h[jZah\Zgb_bgl_]jZevgh]hmjZ\g_gbydkbkl_f_ebg_cguomjZ\g_gbc <f_lh^_dheehdZpbc>@ bgl_]jZevgh_mjZ\g_gb_ \uihegy_lkylhqgh\^bkdj_l ghf 1 qbke_lhq_dih\_joghklb\lhqdZodheehdZpbbF_`^mlhqdZfbêybkdhfhcnmgdpbb - ij_îheZ]Z_lkydZdZyeb[hZiijhdkbfZpbyWlhiha\hey_lij_h[jZah\Zlvbgl_]jZebamjZ\ g_gbydkmff_ ∫ - τ * τ τ 1 , / Gτ = ∑ - M $LM M = bbgl_]jZevgh_mjZ\g_gb_dkbkl_f_ 1 ebg_cguomjZ\g_gbc  $ ττ  τϕ $ $ ϕτ   - τ   - τ   =  $ ϕϕ  - ϕ  - ϕ  A^_kv $ −ih^fZljbpujZaf_jhf 1 × 1 Z - −ih^\_dlhjuêbghc 1 >eyiehkdhcaZ^Zqbbêykbff_ljbqguolbih\dhe_[ZgbcZdkbZevghkbff_ljbqghcaZ ^ZqbqbkehmjZ\g_gbcjZ\ghqbkemlhq_ddheehdZpbb 1 $ ⋅ - = - ]^_ - ijbgbfZ_lagZq_gb_ - τ beb - ϕ GZb[he__ ijhklhc \b^ dhwnnbpb_glu $LM fZljbpu bf_xl ijb ZiijhdkbfZpbb - eb g_cghcnmgdpb_c\ij_^_eZo M ]hwe_f_glZih\_joghklb ghc\ij_^_eZo GZijbf_jijb ihklhyg ihemqbfwe_f_glih^fZljbpu $ $LM = ∫ * ττ L Gτ /M ]^_ * ττ L ih^klZ\ey_fbabebba Klhqdbaj_gbyf_lh^Zdhg_qguowe_f_glh\dmkhqghihklhyggZybebg_cgZyZiijhdkb fZpbywd\b\Ze_glgZij_^klZ\e_gbxbkdhfhcnmgdpbbjy^hfijyfhm]hevguobeblj_m]hevguo bgl_jiheypbhgguonmgdpbc GZ 6 fbgl_j\Ze_êbghc K6 bagZq_gbyfb - 6 b - 6 + gZdhgpZobgl_j\ZeZkdhhj^b gZlZfb τ 6 b τ 6 + nmgdpbyij_^klZ\e_gZ\ujZ`_gb_f - 6 τ = beb\fZljbqghf\b^_ ]^_ - 6 τ 6 + − τ τ −τ 6 -6 + - 6 + K6 K6 - τ = &τ ⋅ - 6 ±\_dlhjklhe[_p 1 agZq_gbcnmgdpbb\maeZok_ldb & & &τ =  − &   − &   _klv e_glhqgZy fZljbpZ bgl_jiheypbhgguo nmgdpbc jZaf_jhf 1 × 1 + >ey dmkhqgh ihklhygghcZiijhdkbfZpbb &τ \ujh`^Z_lky\_^bgbqgmx^bZ]hgZevgmxfZljbpmjZaf_jhf 1 -RQJ b $GDPV >@ ijh^_fhgkljbjh\Zeb ijbf_g_gb_ dmkhqghihklhygghc ZiijhdkbfZ pbbêyf_jghcaZ^ZqbjZkq_lZj_ahgZlhjh\f_lh^hfbgl_]jZevguomjZ\g_gbcLhqghklvjZk q_lh\j_ahgZgkghcqZklhlukhklZ\eyeZJZg__ZgZeh]bqgZylhqghklvkbkihevah\Zgb _fdmkhqghihklhygghcZiijhdkbfZpbbihemq_gZZ\lhjhf^ZgghcjZ[hluijbjZkq_l_hk_kbf f_ljbqguo j_ahgZlhjh\ M\_ebq_gb_ jZaf_jh\ k_ldb g_ ijb\h^beh d m\_ebq_gbx lhqghklb >eymemqr_gbylhqghklbklZehg_h[oh^bfufjZkkfhlj_lvZiijhdkbfZpbx[he__\ukhdh]hih jy^dZ L_ogbdZkieZcgZiijhdkbfZpbbêyj_r_gbybgl_]jZevgh]hmjZ\g_gby <i_j\u_l_ogbdmdm[bq_kdh]hkieZcgZêyj_r_gbydjZ_\hcaZ^ZqbmjZ\g_gbyEZieZkZ f_lh^hfbgl_]jZevguomjZ\g_gbcjZajZ[hlZeB\Zgh\>@LhqghklvjZkq_lZihl_gpbZeZ\l_klh \uoaZ^ZqZoij_\urZeZgZihjy^hdlhqghklvihemq_ggmxbkihevah\Zgb_fiZjZ[hebq_kdhcZi ijhdkbfZpbb b gZ q_luj_ ihjy^dZ ij_\urZeZ lhqghklv dmkhqghihklhygghc ZiijhdkbfZpbb ijbl_o`_jZaf_jZojZkq_lghck_ldb<ukhdZylhqghklvj_amevlZlh\kbkihevah\Zgb_fkieZcgZ ih\b^bfhfmk\yaZgZkl_fqlhdm[bq_kdbckieZcgh[eZ^Z_lk\hckl\hffbgbfZevghcdjb\bagu kj_^b^jm]bobgl_jihebjmxsbonmgdpbcckl_i_gb>@ KieZcg fh`gh jZkkfZljb\Zlv dZd h^ghf_jguc dhg_qguc we_f_gl k [hevrbf qbkehf \gmlj_ggbomaeh\ 1 ?]hm^h[ghaZibkZlvq_j_a[_ajZaf_jgu_iZjZf_ljujbk τ −τ6 K6 τ −τ6 = K6 Z6 = − Z6 Z6 = Z6 > Z6 − @ Z6 = Z6 > Z6 − @ τ 6 ±dhhj^bgZlZmaeZ K6 ±êbgZbgl_j\ZeZ τ K6 − τ6 Z6 6 Z6 K6 6 + Jbk JZkiheh`_gb_ maeh\ gZ ]jZgbqghc ebgbb h[eZklb b h[hagZq_gby dhhj^bgZl êy hij_^_e_ gby kieZcgZ Z6 ± ehdZevgZy dhhj^bgZlZ baf_ gyxsZykyhl ^h τ 6 + AgZq_gb_nmgdpbbgZ 6 fbgl_j\Ze_jZ\gh - 6 τ = - 6 Z6 τ + - 6 +Z6 τ + 0 6 Z6 τ + 0 6 +Z6 τ ]^_ dhwnnbpb_glu 0 6 \ujZ`Zxlky q_j_a agZq_gby nmgdpbb - 6 \ maeZo < fZljbqghf \b^_ dhwnnbpb_glujZ\gu 0 = + −'- A^_kv + b ' −e_glhqgu_fZljbpujZaf_jhf 1 × 1 - _klv\_dlhjklhe[_pbj_amevlZlu mfgh`_gbygZg_]hlZd`_y\eyxlkyklhe[pZfb −     µ λ     µ λ +=     µ 1 − λ1 −    −   ]^_ λ6 = K µ 6 = − λ6 bh[hagZq_gh α 6 = 6 − α6 + K6    α +  '=      − α α + α + α − α α + α α 1 − + IjbjZ\ghf_jghck_ld_we_f_glufZljbpijhklu_ − α 1 −        α 1 − + α 1 −       −          ' =   + =             −   Mkeh\by gZ ]jZgbpZo kieZcgZ ij_^hklZ\eyxl k\h[h^m \u[hjZ < ^Zgguo \ujZ`_gbyo dhwnnbpb_glu klhe[pZ '- '- = b '- 1 = qlh khhl\_lkl\m_l jZ\_gkl\m gmex \lhjhc ijhba\h^ghcnmgdpbbgZdhgpZokieZcgZ KieZcgaZibr_f\fZljbqghcnhjf_ - τ = : τ + : τ 5 - = &τ - A^_kv - τ −\_dlhjklhe[_pZiijhdkbfbjm_fuonmgdpbcjZaf_jhf 1 − ( )  Z τ Z τ   Z τ Z τ      : τ =   : τ =     Z1− τ Z1 −  Z1 − τ Z1 −    _klv fZljbpu iZjZf_ljh\ jZaf_jhf 1 × 1 − 5 = + − ' − ijhba\_^_gb_ fZljbp ba FZljbpZ &τ jZaf_jhf 1 × 1 − \hlebqb_hliheghklvxaZiheg_gZ Ijbih^klZgh\d_\bgl_]jZeijboh^bfdkmff_bgl_]jZeh\ih 1 − bgl_j\Z eZf /6 1 −  1   ∑ &VM τ - L *6 τ τ L Gτ τ τ τ τ * G = ∑ L ∫/ ∫   V = / 6  M =  I_j_klZ\ey_ff_klZfbkmffbjh\Zgb_ih V b M ∫ - τ * τ τ L Gτ = /  1 −    τ τ τ τ & * G ∑ M ∑ ∫ VM 6 L   M =  6 = /6  1 IhemqZ_fdhwnnbpb_glu $LM kbkl_fuebg_cguomjZ\g_gbc $LM = 1 − ∑ ∫& 6 = / 6 VM τ *6 τ τ L Gτ AZibr_fdhwnnbpb_gluy\ghq_j_awe_f_glufZljbp & b 5 1 − ( ) $LM µν = , LMµν ε M1 + , LMµν ε M1 + ∑ 5 MV ,LVµν + 5 M V +, LVµν 6 = A^_kv 1 b 1 −ghf_jZgZqZevghcbdhg_qghclhq_dkieZcgZ>eyh^bghqgh]hkieZcgZ 1 = 1 = 1 Bg^_dku µ ν ijh[_]ZxlagZq_gby ϕ b τ kbf\he ε jZ\_g  L ≠ M ε LM =   L = M <\oh^bl\uqbke_gb_bgl_]jZeh\dhlhju_fh`ghaZibkZlvh[sbf\ujZ`_gb_f , NLV = τ 6 + ∫ω N V τ *6 τ τ L Gτ τ6 Bg^_dk N ijbgbfZ_l agZq_gby hl ^h b bg^_dkbjm_l nmgdpbb ω µη N τ \ \ujZ`_gbyo bnmgdpbb * = * µν \u[bjZ_f >ey g_kbff_ljbqguo lbih\ dhe_[Zgbc bg^_dkbjm_f , = , ba\ujZ`_gbc>eykbff_ljbqguolbih\ih^klZ\ey_fnmgdpbb * ba\ujZ`_gbcbeb êyiehkdhcaZ^Zqbba\ujZ`_gbcbebBg^_dk V mdZau\Z_lgZijbgZê_`ghklv dhhj^bgZlbgl_j\Zem τ 6 τ 6 + LZdbf h[jZahf dhwnnbpb_glu $ kbkl_fu ebg_cguo mjZ\g_gbc \dexqZxl \uqbke_ gb_lbih\bgl_]jZeh\êyg_kbff_ljbqguofh^dhe_[Zgbcbeblbih\êykbff_ljbq guofh^biehkdhcaZ^Zqb IjhklZy ]_hf_ljby gZijbf_j kn_jZ fh`_l [ulv ij_^klZ\e_gZ h^gbf dhg_qguf kieZcgwe_f_glhfKeh`gZy]_hf_ljbyhibku\Z_lkyg_kdhevdbfbkieZcgZfbijbgZê_`Zsbfb _kl_kl\_ggufmqZkldZf]_hf_ljbb −^m]ZfijyfufAgZq_gbykieZcgh\\kf_`guolhqdZo]jZ gbpu krb\Zxlky l_ klZ\blky mkeh\b_ g_ij_ju\ghklb iehlghklb lhdZ - =jZgbqgu_ lhqdb we_f_glh\ ijbgZê_`Zl kf_`guf kieZcgZf Wlh khhl\_lkl\m_l lhfm qlh fZljbpZ 5 ba P khklhysZybaih^fZljbp 5 jZaf_jhf 1 P × 1 P i_j_dju\Z_lkyk\hbfbm]eh\ufbdhwn nbpb_glZfb >jm]hc ijb_f jZkkfhlj_gguc B\Zgh\uf>@ khklhbl\lhf qlhh^gZblZ`_kf_`gZy lhqdZgZijbf_j M ijbgZê_`ZsZy\lhjhfmkieZcgmbg^_dkbjm_lkydZd M + Mkeh\b_krb \Zgby - M = - M + hagZqZ_l qlh \ khhl\_lkl\mxs_c L hc kljhd_ fZljbpu $ [m^_l $LM = $L M + = − Z\k_hklZevgu_we_f_glujZ\gugmexIhjy^hdkbkl_fum\_ebqb\Z_lkygZqbkeh kf_`guolhq_dFZljbpZ 5 khklhblbag_i_j_k_dZxsbokyih^fZljbp 5 P <uqbke_gb_bgl_]jZeh\ Ijb \uqbke_gbb bgl_]jZeh\ ih mqZkldZf L b L + jbk ijbe_`Zsbf lhqd_ gZ [ex^_gby V = L dh]^Z dhhj^bgZlu ϕ → b τ → τ L g_h[oh^bfh mqblu\Zlv qlh ihûgl_ ]jZevgu_nmgdpbbbf_xlbgl_]jbjm_fmxhkh[_gghklvIjb ϕ → banmgdpbcdhg_qgu fb hklZxlky * ττ b * ϕϕ Ijb τ → τ L hkh[_gghklv ijbkmlkl\m_l \ bgl_]jZeZo ,LL b , L L − QZklbbgl_]jZeh\kfgh`bl_e_f τ − τ L hkh[_gghklvxg_h[eZ^Zxl * τ τ L Jbk Ihûgl_]jZevgZy nmgdpby k hkh[_g ghklvxijb V = L b__ZkbfilhlbdZ FRV γ =L OQτ − τ L 5L τ 6 − , LL = τ L + ∫Z τ τ L * τ τ L Gτ = τ L + τL , L L − τL τ L + ∫ * τ τ Gτ − ∫ L τL τL τL V =L τ6 τ 6 + τ −τL * τ τ L Gτ KL τL τ −τ = ∫ Z τ τ L * τ τ L Gτ = ∫ * τ τ L Gτ − ∫ L * τ τ L Gτ KL − τ L − τ L − τ L − τ H[hagZqbfbg^_dkhf bgl_]jZeukhkh[_gghklvx , ττ = ∫ * ττ τ τ L Gτ / , ϕϕ = ∫ * ϕϕ τ τ L Gτ / KlZg^Zjlgucijb_f\uqbke_gbybgl_]jZeh\khkh[_gghklvxaZdexqZ_lky\bkihevah\Zgbb Zkbfilhlbdb ihûgl_]jZevghc nmgdpbb GZ i_j\hf wlZi_ \uql_fb^h[Z\bfnmgdpbb=jbgZ Φ b Φ dhevpZkhklZpbhgZjguflhdhf , = ∫ (*τ τ − Φ L / H^ghkeZ]Z_fh_ Φ ) τ τ L + Φ τ τ L Gτ \ujZabfdZdZkbfilhlbdmihûgl_]jZevghcnmgdpbb Φ τ τ L = * τ τ L ijb P = ϕ → τ → τ L <lhjmxqZklv Φ ijhbgl_]jbjm_fihm]em ϕ b\ujZabfq_j_aihegu_weebilbq_kdb_bgl_ ]jZeui_j\h]h (η b\lhjh]h .η jh^Zbkihevamyba\_klgh_\ujZ`_gb_êynmgdpbb=jbgZ dhevpZklhdhfIhemqbfihe_agu_nhjfmeuêy\klj_qZxsbokybgl_]jZeh\ π   O + 55L  − .η + (η  O   FRV ϕ ∫ U Gϕ = 55 O + 55 L L π Gϕ ∫U = O O + 55L (η ]^_ η = O U = 5 + 5L − 55, FRV ϕ + = − = L jbk O + 55, <lhjhc wlZi Hkh[_gghklv \ Φ k\yaZgZ k weebilbq_kdbf bgl_]jZehf .η b ghkbl eh]Zjbnfbq_kdbc oZjZdl_j <uql_f qbke_gguc bgl_]jZe hl Zkbfilhlbq_kdh]h ij_^_eZ Φ τ τ L τ →τ L = − OLP τ →τ L Φ = − FRV γ =L OQO 5L b ^h[Z\bf ZgZeblbq_kdbc ij_^_e FRV γ =L  KL  OQ −  5L   Ko_fZ\uqbke_gbybgl_]jZeh\khkh[_gghklvxke_^mxsZy ( ) , = ∫ * τ τ L − * τ τ L P = ϕ → τ →τ L + Φ τ − Φ τ → τ L Gτ + OLP τ →τ L Φ / <uibr_f\ujZ`_gbyêybgl_]jZeh\k\u^_e_gghchkh[_gghklvx , ττ =  55L FRV γ = − ' O + 55L 5L   ττ '  (η + .η  * τ τ  + L ∫ O 5L π / O + 55L     FRV γ =L FRV γ = L  KL  OQ O  Gτ − +  OQ −  5L 5L    , ϕϕ =  5 FRV γ =L − 'L O + 55L 5L '   ϕϕ   (η + L .η  τ τ * + L ∫  π / 5L O O + 55L     FRV γ =L FRV γ =L  KL  + OQ O  Gτ −  OQ −  5L 5L    ]^_h[hagZq_gh ττ * π = 5 ∫ I NU (− 5 L FRV γ = − ' FRV ϕ )Gϕ * ϕϕ π ( = 5 ∫ I NU 5 FRV γ L = ) − ' L FRV ϕ Gϕ  + LNU − LNU  FRV Pϕ − H Ω  U ΩU U + 5 − 5 L FRV γ 5 I NU = I NU − ' = 5 FRV γ = ' L = 5 L FRV γ L = = − 5 − 5 L FRV γ    L 5 IZjZf_lj O → τ − τ L ihdZaZggZjbkHklZevgu_h[hagZq_gbyl_`_qlhb\b γ ] = γ5 5 5L τ = − =L O / JbkH[hagZq_gbyijb\uqbke_gbbbgl_]jZeh\khkh[_gghklvx >ey kbff_ljbqguo ( b + lbih\ dhe_[Zgbc P = bgl_]jZeu k hkh[_gghklvx \u qbkeyxlky ih nhjfmeZf b khhl\_lkl\_ggh Ihûgl_]jZevgu_ \ujZ`_gby b iehkdhcaZ^Zqbg_h[eZ^Zxlhkh[_gghklvx Ijb\uqbke_gbbbgl_]jZeh\\oh^ysbo\kmffmbkihevamxlkyd\Z^jZlmjgu_ nhjfmeu=ZmkkZ>@H[hagZqbfihûgl_]jZevgu_nmgdpbbq_j_a I τ b I τ ϕ >eyhl ^_evgh]h V ]hbgl_j\ZeZêbghc O6 = τ 6 + − τ 6 ihemqZ_f τ 6 + ∫ τ6 π I τ G τ ∫ I τ ϕ G ϕ = O6 π Q   \ I τ ∑  L L ∑ \ M I τ L ϕ M  L =  M =  Q O π [ M + τ L = 6 [L + Z \L [L ± lZ[ebqgu_ agZq_gby \_kh\ b Z[kpbkk d\Z^jZ lmjguo nhjfme ihjy^hd dhlhjuo Q b Q \u[bjZHlky bkoh^y ba g_h[oh^bfhc lhqghklb \u ]^_ ϕ M = qbke_gbc Ihbkdj_ahgZgkguoqZklhl &bkl_fZh^ghjh^guoebg_cguomjZ\g_gbc ($N − , )- = ddhlhjhcijb\h^blkyjZkkfZljb\Z_fZykbkl_fZbf__lj_r_gb_dh]^Z GHW ($N − , ) = ]^_ , ±_^bgbqgZy^bZ]hgZevgZyfZljbpZIhke_hij_^_e_gbydhjg_c N = N nmgdpbb I N = GHW ($N − , ) b khhl\_lkl\_ggh \uqbke_gby fZljbpu $ N ba fh`ghgZclb\_dlhjj_r_gby - >ey wlh]hh^bgbawe_f_glh\ - kqblZ_fba\_klgufbj_rZ_fmf_gvr_ggmxgZ_^bgbpmg_h^ghjh^ gmxkbkl_fmhlghkbl_evghhklZevguowe_f_glh\ - >jm]hcihôh^hkgh\ZggZZgZeba_kh[kl\_gguoagZq_gbc λ fZljbpuMjZ\g_gb_hlgh kbl_evgh λ aZibku\Z_fke_^mxsbfh[jZahf ($N − , )- = λ N - Ihgylgh qlh ijb N = N fbgbfZevgh_ kh[kl\_ggh_agZq_gb_ λPLQ N fZljbpu kh]eZkgh ^he`ghh[jZsZlvky\gmevZkh[kl\_gguc\_dlhj - [m^_lj_r_gb_fkbkl_fu:e]hjblfhij_ ^_e_gby λPLQ hkgh\ZggZh[jZlguobl_jZpbyo>@ $ N − , - Q + = - Q Ijb[hevrhfqbke_bl_jZpbc Q hlghr_gb_êbg\_dlhjh\ ^_ebfwlhhlghr_gb_ke_^mxsbfh[jZahf Q b - Q + koh^blkyd λPLQ Hij_ - L Q ∑ Q + L = - L A^_kv 1 ±jZaf_jghklv\_dlhjZ - >Zggh_hij_^_e_gb_g_kljh]hjZ\gh λPLQ ghhghihe_agh Q N = λPLQ 1 l_f qlh kh^_j`bl agZd b jZ\gh gmex\lhqd_j_ahgZgkZ<u[hjgZqZevgh]hagZq_gby\_dlhjZ - agZq_gbyg_bf__lb\[ebab N = N ]^_ λPLQ N → bl_jZpbbkoh^ylky[ukljh Ihke_\uqbke_gbydhwnnbpb_glh\fZljbpu $N − , hgZijb\h^blkyf_lh^hfbkdex q_gby=ZmkkZd\_jog_clj_m]hevghcnhjf_>@Ihke_q_]hj_r_gb_kbkl_fubbl_jZpbb aZgbfZxlf_gvr__fZrbggh_\j_fyq_f\j_fy\uqbke_gbykZfhcfZljbpu LZdbfh[jZahfijb N = N ^he`gu\uihegylkyke_^mxsb_mkeh\by Z GHW $ N − , = \ 5H λPLQ N = k ,P λPLQ N = Qbke_ggu_bkke_^h\ZgbyihdZaZebke_^mxsb_hkh[_gghklbnmgdpbc Fh^mev^_l_jfbgZglZ\[ebabj_ahgZgkZklZgh\blkyfZeufghg_kljh]hgme_\ufWlhmdZ au\Z_lgZlhqlhfgbfu_b^_ckl\bl_evgu_qZklb_]hklZgh\ylkygme_\ufbg_ijbh^ghfb lhf`_agZq_gbb N Fh^mev^_l_jfbgZglZ\^Zebhlj_ahgZgkZ\_^_lk_[yfhghlhgghGh\[ebabj_ahgZgkZijb i_j_oh^_q_j_a N = N i_j\Zyijhba\h^gZyf_gy_lagZdjbkWlhaZljm^gy_lihbkdfb gbfmfZlZdhc9h[jZaghcnmgdpbb < kemqZ_ dh]^Z j_ahgZgku [ebadb d \ujh`^_gbx ih\_^_gb_ ^_l_jfbgZglZ klZgh\blky [ebadbfd8h[jZaghfmkhkeZ[h\ujZ`_ggufbfbgbfmfZfbjbkLhqghklvhij_^_e_gby j_ahgZgkZijbwlhfiZ^Z_l Ohjhrbfbk\hckl\Zfbh[eZ^Z_lih\_^_gb_fgbfhcqZklb ,P λPLQ N F_`^mj_ahgZgkZfb bf_xlky jZaju\u Z \[ebab j_ahgZgkZ wlZ nmgdpby [ebadZ d ebg_cghc Dhjgb nmgdpbb ,P λPLQ N gZ^_`gh \uqbkeyxlky \ l_klh\uo aZ^ZqZo k \ukhdhc lhqghklvx jZ\gu ZgZeblbq_kdbfj_ahgZgkgufagZq_gbyfbbkihevamxlkyêyhij_^_e_gbyj_ahgZgkZ ,PλPLQ ( + GHW$N, úñ$ Jbk>\Z[ebadhjZkiheh`_gguoj_ahgZgkZPbebg^jbq_kdbcj_ahgZlhj5 f+ P :gZeblbq_kdb_qZklhlu )( = F=p ) G = F=p Qbke_ggucjZkq_l )( = F=p )G = F=p :gZeblbq_kdbcl_klêybeexkljZpbbf_lh^ZihbkdZj_ahgZgkguoqZklhl JZkkfhljbfh^ghf_jgucj_ahgZlhjh[jZah\Zgguc^\mfyiZjZee_evgufbijh\h^ysbfb iehkdhklyfbIh\_joghklguclhdiehlghklvx - b - gZijZ\e_g\^hevhkb ] jbk - - + + + + = < G ; JbkH^ghf_jgucj_ahgZlhjJZkkfZljb\Zxlkylhevdhiehkdb_\hegu Bgl_]jZevgZy nhjfmeZ êy fZ]gblgh]h ihey ijb\h^bl d kbkl_f_ ^\mo ebg_cguo mjZ\g_gbc + - ; + +; = − + ; + + ; = - Dhfihg_glufZ]gblguoihe_cgZiehkdhklyobba\_klguêyh^ghf_jghciehkdhcaZ^Zqb + ; = +; = - HLNG = − - HLNG + ; = + ; I_j_g_kyijZ\u_qZklb\e_\hi_j_c^_fdh^ghjh^ghckbkl_f_mjZ\g_gbc HLNG HLNG - = beb\fZljbqghf\b^_ % ⋅ - = - Wlhckbkl_f_khhl\_lkl\m_loZjZdl_jbklbq_kdh_mjZ\g_gb_ − λ HLNG = H LNG − λ Ihemqbf^_l_jfbgZglbkh[kl\_ggh_agZq_gb_ GHW % = − HL NG λ = ± HL NG ]jZnbdbdhlhjuoihdZaZgugZjbkJ_ahgZgkgu_qZklhlukhhl\_lkl\mxldhjgyfnmgdpbc ,P λ N 5H λ N GHW %N l_ N j_a G = Qπ ÿ&) $)$ % ⋅ - Q + = - Q j_amevlZldhlhjh]h^Z_lke_^mxs__ λPLQ   -Q - Q  λ = OLP Q → ∞  Q + + Q +  =  -   λ  -  π π π ≤ NG ≤ ≤ NG ≤ $EVGHW ,Pλ1 , ,Pλ2 5Hλ1 5Hλ2 <b^ghqlhlhqdbj_ahgZgkZm^h[ghhij_^_eylvihdhjgyffgbfhcqZklbkh[kl\_gguoagZ q_gbckbkl_fu. λ1 λ2 λ1 NGπ) λ2 NGπ) NGπ) Jbk>_l_jfbgZglbkh[kl\_ggu_agZq_gbyh^ghf_jgh]hj_ahgZlhjZ@bjghc ebgb_c\u^_e_gj_amevlZlbl_jZpbhggh]hijhp_kkZ\uqbke_gby λ PLQ <uqbke_gb_ihe_cbiZjZf_ljh\j_ahgZlhjh\ J_amevlZlhf jZkq_lZ fhû y\eyxlky __ qZklhlZ b dhfihg_glu iehlghklb lhdZ \ maeZo k_ldb Ihey b iZjZf_lju j_ahgZlhjZ jZkkqblu\Zxlky hl^_evghc ijhp_^mjhc <_ebqbgu k\y aZggu_ k ih\_joghklvx \uqbkeyxlky \_kvfZ [ukljh Wlh gZijy`_gghklb fZ]gblguo b we_d ljbq_kdbo ihe_c gZ ih\_joghklb ihl_jb \ kl_gdZo >ey jZkq_lZ gZdhie_gghc wg_j]bb µ : = ∫ + G 9 bkihevam_lkyihe_agZynhjfmeZij_h[jZah\Zgbyh[t_fgh]hbgl_]jZeZ\bgl_ ]jZeihih\_joghklb>@ µ ∫ + G9 = µ + − ξ ( U ⋅ Q G 6 ∫ A^_kv ghjfZev Q we_f_glZ ih\_joghklb gZijZ\e_gZ gZjm`m JZ^bmk\_dlhj U gZijZ\e_g ba ijhba\hevghclhqdbgZijbf_jbagZqZeZdhhj^bgZl<f_jghcaZ^Zq_bgl_]jbjh\Zgb_\_^_l kyihdhhj^bgZl_ τ <_ebqbgZ U ⋅ Q = 5 FRV γ = − = FRV γ 5 y\ey_lkynmgdpb_c τ >eyjZkq_lZihe_c\lhqdZo\gmljbj_ahgZlhjZg_h[oh^bfhbgl_]jbjh\Zgb_ih\k_cih \_joghklbihwlhfmihkljh_gb_dZjlbguihe_c\h[t_f_aZgbfZ_lagZqbl_evgh_\j_fy ;ukljuf ihjlj_lhf fhû fh`_l kem`blv dZjlbgZ jZkij_^_e_gby ih\_joghklghc iehl ghklblhdZGZjbkihdZaZgihjlj_lfhûpbebg^jbq_kdh]hj_ahgZlhjZ<\_jomihkljh_gu ebgbbjZ\gh]hmjh\gy - = FRQVW gZiehkdhklbdhhj^bgZlghckbkl_fu ϕ − τ ]^_ ϕ baf_gy_l kyhl ^h π b τ hl ^h / / −êbgZh[jZamxs_cEbgbbmjh\gyihdZau\ZxlgZijZ\e_ gb_ fZ]gblgh]h ihey gZ ih\_joghklb Z ]jZ^b_gl mdZau\Z_l gZijZ\e_gb_ \_dlhjZ iehlghklb lhdZ <uibr_f \ujZ`_gbyêy\uqbke_gbydhfihg_glihe_c ihemqZ_fuobabgl_]jZevguo nhjfmeb :dkbZevgZy kbff_ljby Ijhba\hevgu_ lbiu dhe_[Zgbc FZ]gblgh_ ihe_ \ lhqd_ k dhhj^bgZlZfb 5L = L ihemqZ_f kmffbjh\Zgb_f dhfihg_gl kha^Z\Z_fuo ϕ b τ khklZ\eyx sbfbih\_joghklghciehlghklblhdZy\eyxsbfbkynmgdpbyfbdhhj^bgZl 5 τ = τ + 5 = + 5ϕ + + 5τ + ϕ = + ϕϕ + + ϕτ + = = + =ϕ + + =τ Dhfihg_glufZ]gblgh]hiheyihemqZ_fu_babf_xl\b^ π + 5ϕ = ∫ - ϕ τ 5 = L − = G τ ∫ I NU FRV Pϕ FRV ϕ G ϕ / π + 5τ = −∫ - τ τ 5' G τ ∫ I NU VLQ Pϕ VLQ ϕ G ϕ / π + ϕϕ = ∫ - ϕ τ 5 = L − = G τ ∫ I NU VLQ Pϕ VLQ ϕ G ϕ / + τ ϕ = ∫ - τ π τ 5 G τ ∫ 5L FRV γ = − ' FRV ϕ I NU FRV Pϕ G ϕ / π + =ϕ = ∫ - ϕ τ 5 G τ ∫ 5 − 5L FRV ϕ I NU FRV Pϕ G ϕ / + τ = = 5L ∫ - τ π τ 5 FRV γ 5 G τ ∫ I NU VLQ Pϕ VLQ ϕ G ϕ / A^_kv I NU jZ\gh j_Zevghc qZklb dhfie_dkghc nmgdpbb ijb agZq_gbb Ω = π ' b U h[hagZq_gu\Bg^_dkhf L h[hagZqbfdhhj^bgZlulhqdb\dhlhjhcjZkkfZljb\Z_lkyihe_ <ujZ`_gb_ êy \uqbke_gby we_dljbq_kdh]h ihey \u]ey^bl keh`g__ <_dlhj we_d ljbq_kdh]hihey ( jZaeZ]Z_lkyihhjlh]hgZevgufgZijZ\e_gbyf U b θ kn_jbq_kdhckbkl_fu dhhj^bgZlDhfihg_glujZaeh`_gbyjZkkfZljb\ZxlkydZdkmffZihe_ckha^Z\Z_fuo ϕ b τ dhfihg_glZfbih\_joghklghciehlghklblhdZBlZdh_jZaeh`_gb_g_h[oh^bfhijh^_eZlvêy dZ`^hcbadhfihg_glihey\pbebg^jbq_kdhckbkl_f_dhhj^bgZl (5 = (5ϕU + (5ϕθ + (5τU + (5τθ (ϕ = (ϕϕU + (ϕϕθ + (ϕτU + (ϕτθ (= = (=ϕU + (=ϕθ + (=τU + (=τθ LZdbfh[jZahfihemqZ_fbgl_]jZeh\êy\uqbke_gbywe_dljbq_kdh]hihey ( ϕU 5 = − 5L ∫ / ϕ π 5 G τ ∫ I NU 5L − 5 FRV ϕ VLQ Pϕ VLQ ϕ G ϕ π (ϕϕU = 5L ∫ - ϕ 5 G τ ∫ I NU FRV Pϕ VLQ ϕ G ϕ / π ( =ϕU = − 5L ∫ - ϕ 5'= G τ ∫ I NU VLQ Pϕ VLQ ϕ G ϕ / π ( 5τU = ∫ - τ 5 G τ ∫ '= FRV γ = − 5 − 5L FRV ϕ FRV γ 5 5L − 5 FRV ϕ I NU FRV Pϕ G ϕ / π (ϕτU = ∫ - τ 5 G τ ∫ '= FRV γ = − 5 − 5L FRV ϕ FRV γ 5 I NU VLQ Pϕ VLQ ϕ G ϕ / π ( =τU = ∫ - τ 5'= G τ ∫ '= FRV γ = − 5 − 5L FRV ϕ FRV γ 5 I NU FRV Pϕ G ϕ / π ( 5ϕθ = ∫ - ϕ 5 G τ ∫ ' = + 5 5 − 5L FRV ϕ I NU VLQ P ϕ VLQ ϕ G ϕ / π (ϕϕθ = ∫ - ϕ 5 G τ ∫ 5L − 5 FRV ϕ 5 − 5L FRV ϕ − ' = FRV ϕ I NU FRV P ϕ G ϕ / ( ϕθ = = − 5L ∫ - ϕ π 5' = G τ ∫ I NU VLQ P ϕ VLQ ϕ G ϕ / π ( 5τθ = ∫ - τ 5 G τ ∫ '= 5L FRV γ = − ' FRV ϕ − 55L FRV γ 5 VLQ ϕ I NU FRV Pϕ G ϕ / π (ϕτθ = ∫ - τ 5 G τ ∫ 5L FRV γ 5 5L − 5 FRV ϕ + '= ' I NU VLQ Pϕ VLQ ϕ G ϕ / ( τθ = = −∫ - τ / H[hagZq_gh π 5 G τ ∫ 5L FRV γ = 5L − 5 FRV ϕ + ' 5 − 5L FRV ϕ I NU FRV Pϕ G ϕ '= τ = = L − = τ 'τ = 5 FRV γ = + = L − = FRV γ 5 I NU =   FRV NU + VLQ NU   πξ FU  NU  I NU =   N  −  FRV NU + VLQ NU    πξ FU   N U NU   U ϕ τ = 5 + 5L − 55L FRV ϕ + = L − = Dhhj^bgZlulhqdbih\_joghklb = b 5 bgZdehgu FRV γ = FRV γ 5 we_f_glZih\_jogh klbdhkyfy\eyxlkynmgdpbyfbdhhj^bgZlu τ >eyhibkZgbynmgdpbb - τ aZ^ZgghckieZcghfbkihevam_lkydm[bq_kdh_ij_^klZ\e_ gb_>@ ihemqZ_fh_ba dh]^ZagZq_gby - L \maeZok_ldbm`_ba\_klgubdhwnnbpb_glu 0 L \uqbke_gukh]eZkghGZdZ`^hfihûgl_j\Ze_ >τ 6 τ 6 + @ - τ = - 6 + E6 τ − τ 6 + F6 τ − τ 6 + G 6 τ − τ 6 ]^_ E6 = - 6 + − - 6 − K6 0 6 + + 0 6 K6 F6 = 0 6 0 6 + − 0 6 K6 G6 = :dkbZevgZykbff_ljby ( lbidhe_[Zgbc P = Kms_kl\m_llhevdh - τ −dhfih g_glZih\_joghklghciehlghklblhdZ + ϕ −dhfihg_glZfZ]gblgh]hiheyb (5 = (5τU + (5τθ b ( = = ( =τU + ( =τθ −dhfihg_gluwe_dljbq_kdh]hihey +ϕ = + τ ϕ = ∫ / τ π τ 5 G τ ∫ 5L FRV γ = − ' FRV ϕ I NU G ϕ Khhl\_lkl\mxsb_ \ujZ`_gby êy \uqbke_gby dhfihg_gl we_dljbq_kdh]h ihey \u[bjZ_f ba \ur_ijb\_^_gguoh[sbo\ujZ`_gbcijbagZq_gbb P = :dkbZevgZykbff_ljby + lbiudhe_[Zgbc P = Kms_kl\m_llhevdh - ϕ −dhf ihg_glZ ih\_joghklgh]h lhdZ + 5 = + 5ϕ b + = = + =ϕ − dhfihg_glu fZ]gblgh]h ihey b (ϕ = (ϕϕU + (ϕϕθ −dhfihg_glZwe_dljbq_kdh]hihey<ujZ`_gbyêydhfihg_glihemqZ_fba h[sbo\ujZ`_gbcijb P = >_dZjlh\Zy^\mf_jgZykbkl_fZdhhj^bgZl ( lbiuKms_kl\m_lijh^hevgZydhfih g_glZwe_dljbq_kdh]hihey ( = \uqbkey_fZydZdj_ZevgZyqZklvbihi_j_qgh_fZ]gblgh_ ihe_kdhfihg_glZfb + ; b + < \uqbkey_fufbba ( = [L \ L = ωµ - τ ⋅ - NU G τ ∫/ + ; [L \ L = \ − \ τ N G τ - τ ⋅ < NU L ∫ / U + < [L \ L = − [ − [τ N Gτ - τ ⋅ < NU L ∫ / U ]^_ U = U [L \ L τ = [L − [ τ + \L − \ τ >_dZjlh\Zykbkl_fZdhhj^bgZl + lbiuKms_kl\mxldhfihg_gluihe_c + = ( ; (< <uqbke_gb_fZ]gblgh]hiheyijhba\h^blkyihnhjfmeZfNhjfmeuêyjZkq_lZ we_dljbq_kdh]hiheyihemqZ_fbamjZ\g_gbyFZdk\_eeZ = URW + ( Lωξ Ijb\uqbke_gbbihe_ci_j_oh^bfhldhfie_dkguo\_ebqbgd^_ckl\bl_evguf ( ; [L \L = = - τ ⋅ * ; [L \L τ Gτ ∫/ = (< [L \L = − ∫ - τ ⋅ *< [L \L τ Gτ / Nmgdpbb=jbgZêywe_dljbq_kdh]hiheyjZ\gu  ∂ U ∂U  ∂U ∂ U  ∂U   FRV γ ; <′NU FRV FRV * ; =  FRV γ ; < NU N + − − γ γ \ \ ∂\L  ∂\L ∂[L ∂\L  ∂[L  ∂\L   ∂ U ∂ U  ∂U  ∂U ∂U  <′NU  FRV γ ; − FRV γ \ − FRV γ \ *< =  FRV γ ; < NU + N  ∂[L ∂\ L ∂[L  ∂\L ∂[L  ∂[L   ]^_ U = U [L \L τ dZdb\ur_ = = µ Ijhba\h^gZynmgdpbb;_kk_eyjZ\gZ ε <′NU = < NU − 5 Ebgbbwe_dljbq_kdh]hihey\ iehkdhklb 5 − = j_ahgZlhjZ EbgbbfZ]gblgh]hiheygZih\_joghklb ϕ Ebgbbmjh\g_c π - < NU NU - = FRQVW τ Lhj_p Pbebg^j Lhj_p / Dhfihg_gluiehlghklblhdZ - = ϕ - τ τ Jbk KjZ\g_gb_ jZkkqblZgguo dZjlbg ihe_c \ h[t_f_ j_ahgZlhjZ b gZ ih \_joghklbLbidhe_[Zgbc ( \pbebg^jbq_kdhfj_ahgZlhj_DZjlbgZgZih \_joghklbkljhblky[ukljhbfh`_lkem`blvihjlj_lhffhû Ijh]jZffZ0$;:(//bl_klh\u_jZkq_lu GZ hkgh\_ baeh`_ggh]h f_lh^Z jZajZ[hlZgZ ijh]jZffZ k ]jZnbq_kdbf bgl_jn_ckhf jZ[hlZxsZyih^06'26beb:,1'2:6Ij_^_evgucjZaf_jfZljbpu × khhl\_lkl \m_lk_ld_kmaeZfbêyfh^kZabfmlZevgufb\ZjbZpbyfbbmaeZfbêykbff_ljbqguo fh^ Ijh]jZffZ kdZgbjm_l k rZ]hf ih qZklhl_ \ aZ^Zgghf ^bZiZahg_ qZklhl <j_fy jZkq_lZ fZljbpumdZaZggh]hij_^_evgh]hjZaf_jZbj_r_gb_kbFl_fumjZ\g_gbc\h^ghclhqd_qZklhlu khklZ\ey_lhlh^ghc^hg_kdhevdbofbgmlêy3HQWLXPF=pbaZ\bkblhllhqghklbbgl_]jb jh\Zgby hij_^_ey_fhc\u[hjhfihjy^dZd\Z^jZlmjguonhjfme=ZmkkZ >eyhij_^_e_gby j_ahgZgkghc fhû g_h[oh^bfh ijhba\_klb jZkq_l \−lhqdZoqZklhluKmf_gvr_gb_fjZa f_jghklb k_ldb \j_fy jZkq_lZ khdjZsZ_lky d\Z^jZlbqgh >ey ]_hf_ljbb ijhklhc nhjfu pb ebg^jZ kn_ju ^hklZlhqgh k_ldb k − maeZfb b \j_fy jZkq_lZ \ h^ghc lhqd_qZklhlukh klZ\ey_l g_kdhevdh k_dmg^ K_ldZ k maeZfb gZ ih\_joghklb khhl\_lkl\m_l ijbf_jgh ijh kljZgkl\_gghc k_ld_ k lukyqZfb maeh\ êy ijh]jZff 850(/7 683(5),6+ beb 6XSHU/DQV>@ L_klh\u_ jZkq_lu ijh\h^bebkv êy kn_jbq_kdh]h b pbebg^jbq_kdh]h j_ahgZlhjh\ Z lZd`_ êy pbebg^jbq_kdh]h b ijyfhm]hevgh]h \hegh\h^h\ Ih\_^_gb_ ^_l_jfbgZglZ b kh[kl \_ggh]hagZq_gbyfZljbpu\^bZiZahg_qZklhlho\Zlu\Zxs_f^bihevguofh^pbebg^jbq_ kdh]hj_ahgZlhjZihdZaZghgZjbk ,PλPLQ GHW$N, 5HλPLQ úñ$ JbkJ_amevlZljZkq_lZpbebg^jbq_kdh]hj_ahgZlhjZ 5 = P + = P >bihevgu_ fhû P = J_ahgZgkgu_qZklhlukhhl\_lkl\mxldhjgyfnmgdpbb ,P λPLQ H[eZklvk[ebadh jZkiheh`_ggufbfh^Zfb\jZchg_F=pihdZaZgZ[he__ih^jh[ghgZjbk >eybeexkljZpbblhqghklb\lZ[ebp_ijb\_^_guj_amevlZlujZkq_lh\j_ahgZgkguoqZk lhl^bihevguofh^kn_jbq_kdh]hj_ahgZlhjZjZ^bmkhf kfkcfhûihxbkjZ\g_ gb_bokZgZeblbq_kdbfbagZq_gbyfbK_ldZ 1 = Hrb[dZg_ij_\urZ_l − Ghf_jfhû :gZeblbq_kdh_ agZq_gb_ qZklhlu F=p JZkq_lF=p Ijh\h^behkvkjZ\g_gb_lhqghklbjZkq_lh\j_ahgZgkguoqZklhl^hfh^ba\_klgu fbijh]jZffZfb850(/76XSHU/DQVêyg_kbff_ljbqguofh^b6XSU)LVKêykbff_ljbqguo fh^jbkIjbmdZaZgguogZjbkmgd_jZaf_jZok_lhd\uqbkebl_evgu_j_kmjkub\j_fyjZk q_lh\jZagufbijh]jZffZfb[ueb[ebadbLhqghklvjZkq_lh\j_ahgZgkguoqZklhlpbebg^jb q_kdh]hj_ahgZlhjZkhklZ\beZ − kn_jbq_kdh]h− − Lhqghklvg_iZ^ZeZkm\_ebq_gb_f qZklhlubghf_jZfhûijbjZaf_jZok_ldb 1 = − maeh\ 6XSHU)LVK 1 = × /RJ))) 6XSHU/DQV 1 = × 6XSHU/DQV 850(/7 1 = × 13 = /RJ))) 0$;:(// 1 = 0$;:(// 1 = )úñ$ )0ñ$ Kbff_ljbqgu_fhû P = G_kbff_ljbqgu_fhû P = Pbebg^jbq_kdbcj_ahgZlhj 5 = f / = f 6XSHU )LVK 1 /RJ)) ) 6XSHU/DQV 1 = × 6XSHU/DQV 1 = × 0$;:(// 1 = 13 = = × 850(/7 /RJ) )) 0$;:(// 1 = )0ñ$ )úñ$ Kbff_ljbqgu_fhû P = G_kbff_ljbqgu_fhû P = Kn_jbq_kdbcj_ahgZlhj 5 = kf JbkLhqghklvijh]jZff850(/76XSHU)LVK6XSHU/DQVb0$;:(//DZ`^ZylhqdZkhhl\_l kl\m_lj_ahgZgkghcqZklhl_ ) :gZeblbq_kdh_agZq_gb_qZklhlu ) IhdZaZgujZaf_juk_lhd Mf_gvr_gb_lhqghklbjZkq_lh\j_ahgZgkghcqZklhlukmf_gvr_gb_fjZaf_jZk_ldbih dZaZghgZjbkG_dhlhju_\ukrb_lbiudhe_[ZgbcklZgh\ylkyg_jZaebqbfuWlhijhbkoh ^blmlZdbolbih\êydhlhjuoqbkeZlhq_dkieZcgZg_^hklZlhqghêyZiijhdkbfZpbbj_adh baf_gyxsbokyihe_c\^hevdZdh]heb[hmqZkldZih\_joghklb\^ZgghfkemqZ_\^hevlhjpZbeb h[_qZcdbpbebg^jZ>eygbarbolbih\dhe_[ZgbclhqghklvhklZ_lky\ukhdhc^Z`_ijbjZaf_ jZok_ldb± <ujh`^_ggu_fhûij_^klZ\eyxljZkq_lgu_ljm^ghklbêy\kydh]hf_lh^Z\uqbke_gbc Ki_pbnbdZijh]jZffu0$;:(//aZdexqZ_lky\kdZgbjh\ZgbbihqZklhl_\aZ^Zgghf^bZiZ ahg_?kebrZ]kdZgbjh\Zgby[hevr_jZkklhygbyf_`^mqZklhlZfb[ebadbofh^lh_klvhiZk ghklv ijhkdhqblv fh^m MdZaZgb_f gZ gZebqb_ [ebadbo fh^ kem`bl ih\_^_gb_ fh^mey ^_l_j fbgZglZfZljbpu\aZ\bkbfhklbhlqZklhluNmgdpbyi_j_klZ_l[ulv9h[jZaghc\[ebabj_ ahgZgkZbklZgh\blky[ebadhcd8h[jZaghc <ur_ gZjbk ihdZaZgijbf_j^\mo[ebadbofh^\pbebg^jbq_kdhfj_ahgZlhj_5 f/ f<lZdbof_klZog_h[oh^bfhkdZgbjh\Zlvk[he__f_edbfrZ]hfihqZklhl_ 1 /RJ)) ) /RJ)) ) 1 )úñ$ )úñ$ JbkIZ^_gb_lhqghklb0$;:(//ijbmf_gvr_gbbjZaf_jZk_ldbG_dRlhju_\ukrb_lbiudhe_ [ZgbcklZgh\ylkyg_jZaebqbfuhj^bgZlZjZ\gZPbebg^jbq_kdbcj_ahgZlhj 5 = f / = f G_kbff_ljbqgu_lbiu P = Lhqdbkhhl\_lkl\mxlj_ahgZgkgufqZklhlZf ) AZdexq_gb_ F_lh^ bgl_]jZevguo mjZ\g_gbc êy ^\mf_jguo aZ^Zq ^Ze \hafh`ghklv bkihevah\Zlv ZiijhdkbfZpbxj_r_gbyh^ghf_jgufkieZcghfWlhgZjy^mkZddmjZlgufbgl_]jbjh\Zgb_fb f_lh^hfjZkq_lZj_ahgZgkghcqZklhluiha\hebehihemqblv\ukhdmxlhqghklvj_r_gby\l_k lh\uoaZ^ZqZoAZiZkihlhqghklb^Z_lgZ^_`ghklvêyZgZebaZj_ahgZgkh\h[eZkl_cbf_xsbo keh`gmx]_hf_ljbx G_ij_^klZ\ey_l[hevrhcljm^ghklbgZjy^mkwe_dljbq_kdbfblhdZfb\\_klb\jZkkfhl j_gb_fZ]gblgu_lhdbbkhhl\_lkl\_ggh]jZgbqgh_mkeh\b_êywe_dljbq_kdh]hiheyb^Ze__ gZwlhchkgh\_\\_klb\aZ^Zqmebg_cgu_^bwe_dljbdbbn_jjhfZ]g_lbdb Wlhl ihôh^ ]h^blky lZd`_ êy j_r_gby aZ^Zqb baemq_gby êy q_]h g_h[oh^bfh ^h[Z \blvj_abklb\gu_]jZgbqgu_mkeh\byb]jZgbqgu_mkeh\byêybaemqZl_eyAZ^Zqm`_baemq_ gbyhldjuluoZgl_ggbgl_]jZevguff_lh^hflhevdhbfh`ghj_rZlv AZfZgqb\uf y\ey_lky ijbf_gblv f_lh^ bgl_]jZevguo mjZ\g_gbc êy f_jguo aZ^Zq we_dljh^bgZfbdbbkihevamxêyZiijhdkbfZpbbj_r_gby^\mf_jguckieZcgbeb^jm]mx^\m f_jgmxZiijhdkbfZpbx\ukhdh]hihjy^dZ Ijbeh`_gb_ AZibr_f\ujZ`_gbyêy_^bgbqguo\_dlhjh\\^_dZjlh\hckbkl_f_dhhj^bgZl = 7; L + 7< M + 7= N U = 5; L + 5< M + 5= N ! = Φ ; L + Φ< M + Φ = N L L L L = 7; L + 7< M + 7= N I !L = Φ L; L + Φ<L M + Φ L= N QL = 1 ;L L + 1<L M + 1 =L N <ujZabfdhfihg_glu_^bgbqguo\_dlhjh\q_j_abodhhj^bgZlu\pbebg^jbq_kdhckbk l_f_dhhj^bgZl ; = FRV γ 5 ⋅ FRV φ 7< = FRV γ 5 ⋅ VLQ φ 7= = FRV γ = 5; = 5L − 5 ⋅ FRV ϕ 5< = − 5 ⋅ VLQ ϕ 5= = = L − = Φ ; = − VLQ ϕ Φ < = FRV ϕ I Φ = = 7; L = FRV γ 5 L 7< L = 7= L = FRV γ = L L Φ; = Φ< L = Φ= L = 1; L = − FRV γ = 1< L = 1= L = FRV γ 5 L L GZijZ\eyxsb_ dhkbgmku we_f_glZ ih\_joghklb d hkyf 5 b = h[hagZq_gu FRV γ 5 FRV γ = FRV γ 5L FRV γ 5L jbkBg^_dk L khhl\_lkl\m_llhqd_gZ[ex^_gbykdhhj^bgZlhc τ L Dhhj^bgZlu khhl\_lkl\mxsb_ lhqd_ bklhqgbdZ 5 = 5 τ = = = τ b dhkbgmku m]eh\ FRV γ 5 τ FRV γ = τ y\eyxlkynmgdpbyfbehdZevghcdhhj^bgZlu τ Zdhhj^bgZlu khhl\_l FRV γ 5 L = FRV γ 5 τ L 5L = 5 τ L = L = = τ L kl\mxsb_ lhqd_ gZ[ex^_gby FRV γ 5 L = FRV γ = τ L _klv nmgdpbb τ L M]he ϕ hlkqblu\Z_lky hl m]eh\hc dhhj^bgZlu lhqdb gZ[ex^_gbyêydhlhjhcijbgylh ϕ L = Kibkhdebl_jZlmju >@ &RPSXWHU &RGHV IRU 3DUWLFOH $FFHOHUDWRU 'HVLJQDQG$QDO\VLV$&RPSHQGLXP/$85/RV$OD PRV$FFHOHUDWRU&RGH*URXS/RV$ODPRV6HFRQG(GLWLRQ0D\ >@ . +ROEDFK 5) +ROVLQJHU 683(5),6+ ± $ &RPSXWHU 3URJUDP IRU (YDOXDWLRQ RI 5) &DYLWLHV ZLWK &\OLQGULFDO6\PPHWU\3DUWLFOH$FFHOHUDWRUV9ROSS >@ %0)RPHOHWDO$QHZFRGHIRUHYDOXDWLRQRIWKHHOHFWURPDJQHWLFILHOGVDQGUHVRQDQFHIUHTXHQFLHVRID[L V\PPHWULF5)FDYLWLHV3DUWLFOH$FFHOHUDWYS >@ :>=jb]hjv_\b^jWe_dljhggZyl_ogbdZK_jWe_dljhgbdZK<Q\uik >@ :=>Zcdh\kdbcb^jIj_ijbglBN<WIjhl\bgh >@ 0 GH -RQJ ) $GDPV&DYLW\ 5) 0RGH $QDOLV\V8VLQJD%RXQGDU\,QWHJUDO0HWKRG3URFRIWKH 3DUWLFOH$FFHOHUDWRU&RQI3$&9ROSS >@ <YB\Zgh\FFDZjebg_j<?L_jy_\<IYdh\e_\Ijbf_g_gb_f_lh^Z]jZgbqguobgl_]jZev guomjZ\g_gbcêyjZkq_lZ\ukhdhqZklhlguoj_ahgZlhjh\@mjgZe\uqbkebl_evghcfZl_fZlbdbb fZl_fZlbq_kdhcnbabdb<uiFk >@ <YB\Zgh\<IBevbgJ_r_gb_kf_rZgguodjZ_\uoaZ^ZqêymjZ\g_gbyEZieZkZf_lh^hfbgl_ ]jZevguo mjZ\g_gbc Lbih\u_ ijh]jZffu j_r_gby aZ^Zq fZl_fZlbq_kdhc nbabdb Kb[bjkdh_ hl^_ e_gb_:GKKKJGh\hkb[bjkd >@ :Ih^`h?Fbee_j<dg<uqbkebl_evgu_f_lhû\we_dljh^bgZfbd_FFbjk >@ <<GbdhevkdbcWe_dljh^bgZfbdZbjZkijhkljZg_gb_jZ^bh\hegFGZmdZ >@ :N<_jeZgv<KKbabdh\Bl_]jZevgu_mjZ\g_gbyDb_\GZmdh\Z>mfdZ >@ :>=jb]hjv_\<;Ygd_\bqJ_ahgZlhjubj_ahgZlhjgu_aZf_êyxsb_kbkl_fuK<QFJZ^bhb k\yav >@ <K<eZ^bfbjh\MjZ\g_gbyfZl_fZlbq_kdhcnbabdbFGZmdZ >@ E>EZg^Zm?FEbnrbpWe_dljh^bgZfbdZkiehrguokj_^FGZmdZk >@ >`NhjkZclFFZevdhevfDFhme_jFZrbggu_f_lhûfZl_fZlbq_kdbo\uqbke_gbcFFbj >@ Mbedbgkhg JZcgr KijZ\hqgbd Ze]hjblfh\ gZ yaud_ :E=HE Ebg_cgZy Ze]_[jZ F FZrbgh kljh_gb_ >@ F:[jZfh\bpBKlb]ZgKijZ\hqgbdihki_pbZevgufnmgdpbyfFGZmdZk JmdhibkvihklmibeZbxey]h^Z <?L_jy_\ JZa\blb_f_lh^Zbgl_]jZevguomjZ\g_gbcêyjZkq_lZK<Qj_ahgZlhjh\ Hjb]bgZefZd_lih^]hlh\e_gkihfhsvxkbkl_fu:25' J_^ZdlhjG<?`_eZL_ogbq_kdbcj_^ZdlhjG<Hjeh\Z BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB IhîbkZghdi_qZlbNhjfZloHnk_lgZyi_qZlv I_qeMqbaêLbjZÀZdZaBg^_dk EJ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB =GPJNBgklblmlnbabdb\ukhdbowg_j]bc Ijhl\bghFhkdh\kdhch[e Bg^_dk IJ?IJBGLBN<W

развитие метода интегральных уравнений для расчета свч

Related documents

Products

Support

развитие метода интегральных уравнений для расчета свч

Related documents

Add this document to collection(s)

Add this document to saved

Suggest us how to improve StudyLib