Ответы на вопросы по ХОБП (1128820), страница 4

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KlZpbhgZjgZy dbg_lbdZ n_jf_glZlb\guo j_Zdpbc F_lh^u h[jZ[hldbwdki_jbf_glZevguo^Zgguo<klZpbhgZjghcdbg_lbd_n_jf_glZlb\guoj_Zdpbckms_kl\mxl^\_ijhkl_crb_ko_fu– ko_fZ FboZwebkZ b ko_fZ :gjb dhlhju_ aZl_f fh]ml [ulv fh^bnbpbjh\Zgu ^ey [he__keh`guokemqZ_\kfKo_fZ FboZwebkZ ij_^iheZ]Z_l qlh j_Zdpby b^zl ih q_j_a h[jZlbfmx klZ^bxk1k2→ X h[jZah\Zgby ijhf_`mlhqgh]h ijh^mdlZ E + S ←→ E + P. Kbkl_fZ hibku\Z_lkyk−1dXdP= k1 ES0 − ( k−1 + k2 ) X , v0 == k2 X , E0 = E + X ± i_j\u_ ^\Z mjZ\g_gbydtdty\eyxlkyh[uqgufbdbg_lbq_kdbfbmjZ\g_gbyfb^eyj_Zdpbci_j\h]hb\lhjh]hihjy^dh\Zlj_lv_ \ujZ`Z_l mkeh\b_ fZl_jbZevgh]h [ZeZgkZ ih n_jf_glm AZibku\Zy mkeh\b_dXk +kk1 ES0 = ( k−1 + k2 ) X ⇒ E = −1 2 X ,klZpbhgZjghklb= 0, gZoh^bfdtk1S0mjZ\g_gbyfb22 k +k k2 E0k +k.

H[hagZqZy K m = −1 2E0 =  1 + −1 2  X , v0 =k +kk1S0 k11 + −1 2k1S0– dhgklZglZ FboZwebkZ,ijboh^bfdmjZ\g_gbxFboZwebkZF_gl_g v0 =k2 E0 S0. IjbK m + S0k−1 ± dhgklZglZ ^bkkhpbZpbb ijhf_`mlhqgh]hk1ijh^mdlZ h[uqgh n_jf_glkm[kljZlgh]h dhfie_dkZ >eywdki_jbf_glZevgh]h hij_^_e_gby iZjZf_ljh\ ko_fuFboZwebkZ bkihevamxl kihkh[ ij_^klZ\e_gguc gZ jbkmgd_vm = k2E0 – kdhjhklvj_ZdpbbijbS0 → ’Ko_fZ :gjb ij_^iheZ]Z_l qlh h[jZah\Zgb_ ijh^mdlZj_Zdpbb dhgdmjbjm_l k h[jZah\Zgb_fg_dh]hkh_^bg_gbyn_jf_glZkkm[kljZlhfWlhhagZqZ_lqlhk1k2→ X , E + S E + S ←→ E + P.k 2 k −1 K m ≈k−1Kbkl_fZ hibku\Z_lky mjZ\g_gbyfbdXdP= k1 ES0 − k−1 X , v0 == k A ES0 ,dtdtE0 = E + X .

Mkeh\b_ klZpbhgZjghklbE0k ESk K ESdXk= 0 ⇒ X = 1 S0 E , E =, v0 = k A S0 E = A 0 0 = A A 0 0 – mjZ\g_gb_:gjb]^_kkdtk −1K A + S0S0 1 + 11 + 1 S0k −1k −1kKA – dhgklZglZjZ\gh\_kbyh[jZah\ZgbyX: K A = −1 .k1>bkdjbfbgZpbyFboZwebkZb:gjbf_oZgbafh\<klZpbhgZjghfj_`bf_aZ\bkbfhklbv0 hlS0 ^ey ko_f FboZwebkZ b :gjb h^bgZdh\u kf]jZnbd \ >bkdjbfbgZpby \hafh`gZ lhevdh^ey ij_^klZpbhgZjghc dbg_lbdb \ ko_f_FboZwebkZ\j_f_ggu_aZ\bkbfhklbdhgp_gljZpbcaZ^ZxlkymjZ\g_gbyfbE0 S0kESk2 E0 S0()1 − e−(k1S0 + k−1 + k2 )t , P(t ) = 2 0 0 t +X (t ) =e−(k1 S0 + K m )t − 1 .

>eyK m + S0K m + S0( K m + S0 )( k1S0 + k−1 + k2 )()()()E0 S0k K ESk A E0 S02−k S +K t1 − e − k1 ( S0 + K A )t , P(t ) = A A 0 0 t −e 1( 0 A ) − 1 .K A + S0K A + S0( K A + S0 ) k1L_i_jvko_fue_]dh^bkdjbfbgbjmxlkyihaZ\bkbfhklyfP(t).ko_fu:gjbX (t ) =()9. LjzoklZ^bcgZy ko_fZ n_jf_glZlb\gh]h dZlZebaZ.

AZ\bkbfhklv kdhjhklbj_Zdpbb hl dhgp_gljZpbb km[kljZlZ ^ey j_Zdpbb k mqZklb_f N ijhf_`mlhqguokh_^bg_gbcLjzoklZ^bcgZy ko_fZ oZjZdl_jgZ ^ey k_jbgh\uo ijhl_Za DhgklZglu mjZ\g_gby23k 2 k3K k, K m = S 3 ; ijb k2 k3 kkat ≈ k3k2 + k3k 2 + k3ebfblbjmxs_cklZ^b_cy\ey_lky^_Zpbebjh\Zgb_ijb k3 k2 kkat = k2 – Zpbebjh\Zgb_EA –Zpbebjh\Zggucn_jf_glF_oZgbafkmqZklb_fijhf_`mlhqguokh_^bg_gbcNKSkkkki +1n+132→ X 1 E + S ←E + P; ko_fZhibku\Z_lkymjZ\g_gbyfb→ X 2 → ... X i →... X n →FboZwebkZ fh]ml [ulv \uqbke_gu dZd kkat =dX idP= kn+1 X n = k2 X 1 ,= ki X i −1 − ki +1 X i = 0 ⇒ ki X i −1 = ki +1 X i . Mqblu\ZymjZ\g_gb_dtdtk ESK11fZl_jbZevgh]h [ZeZgkZ E0 = E + ∑ X i , gZc^zf v0 = kat 0 0 , kkat = n +1 , K m = S n +1 .11K m + S0k2i∑∑j =2 k ji = 2 kiv0 =?kebj-ZyklZ^byy\ey_lkyebfblbjmxs_clh kkat = k j , K m =KS k jk2.

L_fi_jZlmjgu_ aZ\bkbfhklb kdhjhkl_c n_jf_glZlb\guo j_ZdpbcL_jfhbgZdlb\Zpbyn_jf_glh\Hkh[_gghklbn_jf_glh\\u^_e_gguobal_jfhnbevguofbdjhhj]Zgbafh\L_fi_jZlmjgu_ aZ\bkbfhklb kdhjhkl_c n_jf_glZlb\guo j_Zdpbc ih^qbgyxlky≠≠HkT ∆RS − ∆RTe eh[uqgufaZdhghf_jghklyfobfbq_kdhcdbg_lbdb±mjZ\g_gbx:jj_gbmkZ k (T ) =h0b ijZ\bem <Zgl=hnnZ ijb ih\ur_gbb l_fi_jZlmju gZ kdhjhklv obfbq_kdhc j_Zdpbbm\_ebqb\Z_lky\kj_^g_f\jZaL_jfhbgZdlb\Zpby n_jf_glh\ ± ihl_jy dZlZeblbq_kdhc Zdlb\ghklb ijb ih\ur_gbbl_fi_jZlmju l_jfhbgZdlb\Zpby \ua\ZgZ ihkl_i_gghc ^_gZlmjZpb_c [_edZ b \ ijhkl_cr_fkemqZ_ih^qbgy_lkyaZ\bkbfhklb A(t ) = A0 e − kin (T )t , ]^_kin ih^qbgy_lkymjZ\g_gbx:jj_gbmkZLZdbf h[jZahf aZ\bkbfhklv Zdlb\ghklb n_jf_glZ hl l_fi_jZlmju ©dhehdhehh[jZagZª ijbgbadbo l_fi_jZlmjZo wg_j]by hl^_evguo qZklbp kebrdhf fZeZ ^ey lh]h qlh[u ij_h^he_lvwg_j]_lbq_kdbc [Zjv_j ± gbadZy Zdlb\ghklv ijb \ukhdbo l_fi_jZlmjZo n_jf_glbgZdlb\bjm_lky±lZd`_gbadZyZdlb\ghklv>eymf_gvr_gbykdhjhklbbgZdlb\Zpbyn_jf_glgm`gh klZ[bebabjh\Zlv kha^Zgb_f ^hihegbl_evguo k\ya_c \h^hjh^guo ^bkmevnb^guoh[jZah\Zgb_fkhe_\uofhklbdh\Hkh[_gghklbn_jf_glh\\u^_e_gguobal_jfhnbevguohj]Zgbafh\:<ukhdZyklZ[bevghklv<ukhdZywg_j]byZdlb\ZpbbGbadZyZdlb\ghklvijbdhfgZlghcl_fi_jZlmj_H^gbf ba lZdbo n_jf_glh\ y\ey_lky ]b^jh]_gZaZ ± [_ehd Zdlb\bjmxsbc fhe_dmem\h^hjh^ZHghq_gvmklhcqb\^Z`_\dbiys_c\h^_bfh`_l[ulvbkihevah\Zg\lhieb\guowe_f_glZo kbkl_fZo [bhnhlhebaZ \h^u dhg\_jkbb lhieb\ [bhdZlZeblbq_kdh]h\hkklZgh\e_gbyKH2.11.

Bg]b[bjh\Zgb_n_jf_glh\G_h[jZlbfh_ bg]b[bjh\Zgb_ ± h[jZah\Zgb_ ijhqghc g_ jZajmrZ_fhc \ mkeh\byoijh\_^_gby dZlZebaZ obfbq_kdhc k\yab bg]b[blhjZ k nmgdpbhgZevgh \Z`gufb ]jmiiZfbkZdlb\gh]hp_gljZn_jf_glZG_h[jZlbfh_bg]b[bjh\Zgb_hibku\Z_lkyko_fhc E + I → EI .KqblZy I 0 E0 , aZibr_f dbg_lbq_kdh_ mjZ\g_gb_ ^ey j_Zdpbb \lhjh]h ihjy^dZ Ijbf_jg_h[jZlbfh]hbg]b[bjh\Zgby±ZkibjbgbijhklZ]eZg^bgGkbgl_lZaZ24H[jZlbfh_ bg]b[bjh\Zgb_ h[jZah\Zgb_ dhfie_dkh\ n_jf_gl±bg]b[blhj fh`_l [ulvdhgdmj_glgufbg_dhgdmj_glguf.Ki→ EI ,< ijhp_kk_ dhgdmj_glgh]h bg]b[bjh\Zgby ijhl_dZxl j_Zdpbb E + I ←Kmkkat→ ES →E + S ←E + P; E0 S0 , E0 I 0 . <_ebqbgu EI b ES fh`gh aZibkZlv q_j_aE ⋅ I0E ⋅ S0, ES =; lh]^Z mkeh\b_dhgklZglu jZ\gh\_kby khhl\_lkl\mxsbo j_Zdpbc EI =KiKmSI fZl_jbZevgh]h [ZeZgkZ ih n_jf_glm ijbf_l \b^ E0 E + ES + EI = E  1 + 0 + 0  . Kdhjhklv Km Ki hij_^_eyxs_c y\ey_lky klZ^by h[jZah\Zgby J ihwlhfmgZ[ex^Z_fZy kdhjhklv j_Zdpbb hij_^_ey_lky mjZ\g_gb_fk E ⋅ S0kkat E0 S0dP= kkat ES = kat=.i_j\h]h ihjy^dZ v0 =dtKmI K m  1 +  S0 Ki LZdbfh[jZahfbg]b[blhjg_\eby_lgZij_^_evgh_mjZ\g_gb_(S0 → ’ ko_fu FboZwebkZF_gl_g kf vm = kkatE0,mf_gvrZ_l gZ[ex^Z_fmx kdhjhklv j_Zdpbb gh m\_ebqb\Z_lgZ[ex^Z_fh_ agZq_gb_ Km.

AZ\bkbfhklv v hl S0 ij_^klZ\e_gZgZjbkmgd_G_dhgdmj_glgh_ bg]b[bjh\Zgb_ ijhl_dZ_l ih ij_^klZ\e_gghc ko_f_ Bkihevamy\_ebqbgu EI, ES, ihemq_ggu_ ^ey kemqZy dhgdmj_glgh]h bg]b[bjh\Zgby gZc^zfSII S E ⋅ I 0 ⋅ S0. E0 = E + ES + EI + ESI = E 1 + 0 + 0 + 0 0  .ESI =K m Ki K m K i K m Ki S0kkat S0E0=K m 1 + S0 + I 0 + I 0 S0K m Ki K m Kibaf_gy_lgZ[ex^Z_fh_agZq_gb_ Km. AZ\bkbfhklv v(S0)ij_^klZ\e_gZgZjbkmgd_>bkdjbfbgZpbydhgdjmj_glgh]hbg_dhgdmj_glgh]hbg]b[bjh\Zgby hkms_kl\ey_lkyih aZ\bkbfhklyf /v0 hl 1/S0dZd ihdZaZgh gZ jbkmgd_kijZ\Z±dhgdmj_glgh_bg]b[bjh\Zgb_ke_\Z±v0 =kkat E01 + I 0 / Ki.

Bg]b[blhj \eby_l gZ kdhjhklv j_Zdpbb gh g_K m + S025g_dhgdmj_glgh_<ebygb_pH gZkdhjhklvn_jf_glZlb\guoj_ZdpbcN_jf_glZlb\gu_ijhp_kkuijhl_dZxsb_kmqZklb_fijhlhgZij_^klZ\e_gugZko_f_E⋅H+E− ⋅ H +,, \ujZabf q_j_a E b ESAZibku\Zy dhgklZglu jZ\gh\_kbc K1 =K=2EH +Edhgp_gljZpbb g_h[oh^bfu_ ^ey aZibkb mjZ\g_gby fZl_jbZevgh]h [ZeZgkZ ih n_jf_glm H + K2  H + K2 + +  + ES  1 ++E = E + EH + + E − + ES + EH + S + ES − = E  1 +=K1 H K1 H + S0   H + K 2 E0= E 1 ++ + ⇒ E =. 1 +K1 H S0   H + K 2  Km  +1 + 1 +K1 H +  Km  k E ⋅ S0kkat E0 S0dP.v0 == kkat ES = kat=dtKm H + K2 ( K m + S0 ) 1 + + + K1 H AZ\bkbfhklv lg v(pH) ij_^klZ\e_gZ gZ jbkmgd_ H[hagZqZyvm = kkatE0S0, gZc^zf aZ\bkbfhklb lg v(pH) ^ey g_dhlhjuoh[eZkl_c]jZnbdZ<dbkehch[eZklbvKH + K1 , K 2 ⇒ v = m + 1 , lg v = const + pH.

< g_cljZevghcH+h[eZklb H K1 , H + K 2 ⇒ v ≈ vm . < s_ehqghc h[eZklbH + K1 , K 2 ⇒ v =vm H +, lg v = const − pH.K2 :dlb\gu_ p_glju n_jf_glh\ DZlZeblbq_kdb_ b khj[pbhggu_ ih^p_gljuHkgh\gu_kljmdlmjgu_ we_f_glu Ki_pbnbqghklv b wnn_dlb\ghklv n_jf_glZlb\gh]hdZlZebaZKfDZlZeblbq_kdbc pbde ± ihke_^h\Zl_evghklv [hevrh]h qbkeZ hl^_evguo we_f_glZjguoklZ^bc dhlhju_ y\eyxlky [ukljufb g_ebfblbjmxsbfb aZ kqzl j_Zebamxsboky]b^jhnh[guo we_dljhklZlbq_kdbo \aZbfh^_ckl\bc \h^hjh^guo k\ya_c Z ihlhfmijb[eb`_gudi_j_oh^ghfmkhklhygbxkfbgbfZevghcwg_j]b_cIj_^eh`_ghg_kdhevdhh[tykg_gbc\ukhdhcki_pbnbqghklbn_jf_glh\ Dhgp_ipby ©dexq±aZfhdª ± oZjZdl_jgh_ kljh_gb_ Zdlb\gh]h p_gljZ n_jf_glZ^himkdZxs__lhevdhkhhl\_lkl\mxsbc_fmihkljh_gbxkm[kljZl Dhgp_ipby ©^u[uª ± n_jf_gl Zdlb\bjm_l km[kljZl jZkly]b\Zy b ^_klZ[bebabjmyk\yab Dhgp_ipby bg^mpbjh\Zggh]h khhl\_lkl\by ± lhevdh ©hl^_evgu_ª km[kljZlukihkh[gu\ua\Zlvg_h[oh^bfu_dhgnhjfZpbhggu_baf_g_gby\[_ed_Djhf_ ©h[uqghcª ki_pbnbqghklb ih km[kljZlm n_jf_glu aZqZklmx h[eZ^Zxlkl_j_hki_pbnbqghklvx ± ^_ckl\mxl lhevdh gZ h^bg ba wgZglbhf_jh\ ijbqbgZ lZdh]hwnn_dlZ khklhbl \ hjb_glZpbb ]b^jhnh[gh]h njZ]f_glZ dhlhjuc hl\_qZ_l aZ k\yau\Zgb_km[kljZlZimlzf]b^jhnh[gh]h\aZbfh^_ckl\byP_ibi_j_ghkZaZjy^Z±dq_fmwlh"" < k\h[h^ghf Zdlb\ghf p_glj_ gmde_hnbe h[eZ^Z_l gbadhc j_Zdpbhgghckihkh[ghklvxkms_kl\_gghgb`_q_fHG–bebZedhdkbevgucbhg < dhfie_dk_ k \ukhdhki_pbnbqguf km[kljZlhf n_jf_glZ gmde_hnbe [ebahd d26ZedhdkbevghfmbhgmGZklZ^bb^_Zpbebjh\Zgby\Zpben_jf_gl_j_ZdpbhggZykihkh[ghklv\h^u[ebadZdj_Zdpbhgghckihkh[ghklb]b^jhdkbevgh]hbhgZ F_lh^u [bhbgnhjfZlbdb <ujZ\gb\Zgb_ ihke_^h\Zl_evghklb Zfbghdbkehlwgljhiby R_gghgZ dZd djbl_jbc dhgk_j\Zlb\ghklb Zfbghdbkehl \ k_f_ckl\Zon_jf_glh\;bhbgnhjfZlbdZ ± gZmdZ h dhfivxl_jghf ZgZeba_ ]_g_lbq_kdbo l_dklh\Zfbghdbkehlguoihke_^h\Zl_evghkl_cijhkljZgkl\_gghckljmdlmjubnmgdpbb[_edh\>ey kjZ\g_gby Zfbghdbkehlguo ihke_^h\Zl_evghkl_c bkihevamxl lZd gZau\Z_fh_\ujZ\gb\Zgb_ ± kjZ\g_gb_ iheh`_gbc kh\iZ^Zxsbo mqZkldh\ <ujZ\gb\Zgb_ bkihevamxl^ey fh^_ebjh\Zgby ijhkljZgkl\_gghc kljmdlmju ih ]hfheh]bb Z lZd`_ ihbkdZ koh^guoh[t_dlh\ih[ZaZf^Zgguo<b^u\ujZ\gb\Zgby:Ihdhebq_kl\m\h\e_qzgguoihke_^h\Zl_evghkl_c±iZjgh_bfgh`_kl\_ggh_IhoZjZdl_jmkoh^kl\Z±ehdZevgh_bh[s__Ihkljmdlmj_hklZldh\±kijhimkdZfb\g_dhlhjuop_iyo\hafh`gujZaju\uf_`^mkh\iZ^ZxsbfbmqZkldZfbbg_ij_ju\gh_KlZlbklbq_kdZy\_jhylghklvihiZ^Zgby ihc Zfbghdbkehlu \ j-h_njiheh`_gb_ pij = i j ; wlZ \_ebqbgZ∑ niiiha\hey_lhij_^_eblvwgljhibxR_gghgZ^eyiheh`_gbyjjjH j = −∑ pi log 2 pi .

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