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ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð, 2008, êãß 58, < 6, â. 738-754

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? 2008 ,,. Ô. ×. ÙÞâÝã
ôéÒ "×Àâ?fl ßêÒßêÛÝ" õãâÝã,âÝã,,ã ,,ãâëâê,ÒÜã,,ã êÒiÜÛ~ÒâÝã,,ã ëÜÛ,ÒâÛêÒê Ûß. ÷.?. ÕëßÜ, e-mail: petronyi@mail.ru øãâêëäÛÞ , ÒÝ^Û 02.04.2007 ,,. øÛÜflê , äÒ~êÈ 09.06.2008 ,,. øÒÞ,,Òêâfl Üã,fl ßãÒÞÈ äã^Òââ ,ãâäÛflêÛfl ÞÒßÒÜêÜã,,ã ,ÜÒ?ÜÒ,,ã âêÛßëÞ, ãâÜã,ÜÜfl Ü ÛÜßÛÝÒ ,ÜÛßÜÛfl âëÇÒÝê ,ãâäÛflêÛfl. ×,ãÛêâfl ÞãÝÞÈÜfl ÝãÞÛ~Òâê,ÒÜÜfl ßÒ ,ÜÛßÜÛfl Ü ãâÜã,Ò â,flÑÛ ,ÜÛßÜÛfl â ,ãÑÇëÛßãâêÈ ÜÞÛÑêã. øã,ãÛêâfl â,ÜÒÜÛÒ Ò?ÒÜÛfl äÒÞ,,ÒßãØ ßãÒÞÛ â ÒÑëÞÈêêßÛ ÝâäÒÛßÒÜê äã ÛââÞÒã,ÜÛ ÛÑßÒÜÒÜÛfl âäÒÒÞÒÜÛfl ,ãÑÇëÛßãâêÛ ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã , äã^ÒââÒ ,ãâäÛflêÛfl. øÒÞ,,Òêâfl êÝÚÒ éãßëÞ â,flÑÛ ,ÜÛßÜÛfl â ßäÞÛêëãØ ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ ÝÝ éëÜÝ^ÛÒØ ,ÒßÒÜÛ. ýÒãÒêÛ~ÒâÝfl ÛÜßÛÝ ßäÞÛêëÀ â,ÜÛ,Òêâfl â ÝâäÒÛßÒÜêÞÈÜãØ. øÛ,ãÛêâfl äÛßÒ ,ãââêÜã,ÞÒÜÛfl ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ Ü ãâÜã,Ò äÒÞ,,ÒßãØ êÒãÛÛ. × ßÝi ßãÒÞÛ ,À,ãÛêâfl ÑÝãÜ øÈÒãÜ - ñÇãÛÜ-óÒÇÒÒ,. ×ÀêÒÝfl ÛÑ ßãÒÞÛ Ñ,ÛâÛßãâêÈ ÒÝ^ÛÛ ãê ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ âããê,Òêâê,ëÒê ÑÝãÜë ûêÛ,ÒÜâ. ôÞ~Ò,ÀÒ âÞã,: ,ÜÛßÜÛÒ, âÒÞÒÝêÛ,ÜãâêÈ, ÒâëâÀ ,ÜÛßÜÛfl, êÒãÛfl ÛÜêÒ,,^ÛÛ äÛÑÜÝã,, ,,ÛÒÜê ,ÜÛßÜÛfl, ,ãÑÇëÛßãâêÈ äëÜÝêã, ÜÞÛÑêã, ßäÞÛêë ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ, ÑÝãÜ ûêÛ,ÒÜâ, ÑÝãÜ øÈÒãÜ-óÒÇÒÒ,-ñÇãÛÜ.

The Model of Attention Dynamics in Perception Process
Ô. V. Glasko
Department of the Higher Mathematics, Bauman State Technical University, Moscow, e-mail: petronyi@mail.ru A new model of perception of an elementary external stimulus is proposed on the basis of attention dynamics of a subject of perception. A local quantitative measure of attention is introduced with regard to connection of attention with analyzer excitability. The solution of the model is compared to the dynamics of distribution of the visual analyzer excitability in the process of perception measured experimentally. A formula of time dependence of attention on the evoked potential amplitude is presented. The theoretical amplitude dynamics is compared to the experimental results. The example of reconstruction of evoked potential on the basis of the model is given. Pieron's law is deduced in the framework of the model. The theoretical relationship between the reaction and stimulus intensity corresponds to the Stivens's law. Key words: attention, selective attention, attentional resources, feature-integration theory, gradients of attention, excitability, evoked potential amplitude, Stivens's law, Pieron-Lebedev-Zabrodin's law.

ùÜãØ ÛÑ ÜÛÇãÞÒÒ âã,ÒßÒÜÜÀi êÒãÛØ ,ÜÛßÜÛfl fl,ÞflÒêâfl êÒãÛfl Òâëâã, [15]. × ãêÞÛ~ÛÒ ãê âêëÝêëÜÀi êÒãÛØ ê êÒãÛfl âäãâãÇÜ ãÇflâÜÛêÈ äã,ÒÒÜÛÒ ~ÒÞã,ÒÝ , ëâÞã,Ûfli ,ãØÜÀi ÑÜÛØ, ê.Ò. âäÒÒÞÒÜÛfl ,ÜÛßÜÛfl. ýÒãÛfl ÜÒÛééÒÒÜ^Ûã,ÜÜÀi Òâëâã, ÜÒ , âãâêãflÜÛÛ ãÇflâÜÛêÈ ,ÚÜãâêÈ "âêëÝêëÜãØ ëÞÒÜÜãâêÛ" ßÒÚë ,ëßfl ÑÜÛflßÛ Þfl ÒÑëÞÈêêÛ,ÜãâêÛ Ûi ,ÀäãÞÜÒÜÛfl. áÞfl Ò?ÒÜÛfl êãØ äãÇÞÒßÀ ô. üÛÝÒÜâ [36] äÒÞãÚÛÞ ÝãÜ^Òä^Û ßÜãÚÒâê,ÒÜÜÀi Òâëâã,, äÒäã-

Þ,,ë ÜÞÛ~ÛÒ âäÒ^ÛéÛ~ÒâÝÛi ÛÑãÞÛã,ÜÜÀi Òâëâã,, ãêÜãâflÛiâfl Ý ÑÜÀß âêëÝêëÜÀß âãâê,ÞflÛß âÛâêÒßÀ ãÇÇãêÝÛ ÛÜéãß^ÛÛ, ÚÒâêÝã ÑÒÞÒÜÜÀß äã ãäÒÒÞÒÜÜÀß Ý~Òâê,ÒÜÜÀß äÛÑÜÝß (ßãÞÈÜãâêÛ, âêÛÛ ãÇÇãêÝÛ, ÝãÀ). ùÜÝã äãâÞÒÜÛÒ ÝâäÒÛßÒÜêÞÈÜÀÒ ÜÜÀÒ äãÝÑÀ,ê, ~êã âêÒäÒÜÈ ÛÑãÞÛã,ÜÜãâêÛ Òâëâã, fl,ÞflÒêâfl ßÒÜÒÒ ,ÀÚÒÜÜãØ, ~Òß êã äÒäãÞ,,ÞãâÈ. ÷äÛßÒ, ?. ýÒØâßÜ [35] ãÇÜëÚÛÞ âëÒâê,ÒÜÜãÒ ÝãââßãÞÈÜãÒ ,ÑÛßãÒØâê,ÛÒ

738


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ßÒÚë ÑÜÛflßÛ, ,ÀäãÞÜflÒßÀßÛ , âÞëiã,ãØ Û ÑÛêÒÞÈÜãØ ßãÞÈÜãâêfli, iãêfl Û ßÒÜÈ?ÒÒ, ~Òß ,ÜëêÛßãÞÈÜãÒ ,ÑÛßãÒØâê,ÛÒ. øÒÞ,,Òßfl , ÜâêãflÒØ ÇãêÒ êÒãÛfl ,ÜÛßÜÛfl ãâÜã,Ü Ü äÒâê,ÞÒÜÛfli, äããÇÜÀi êÒãÛÛ Òâëâã,: âÒÞÒÝêÛ,ÜãâêÈ ,ÜÛßÜÛfl ãÇflâÜflÒêâfl ÜÒi,êÝãØ Òâëâã,, ê.Ò. (,,ÛäãêÒêÛ~ÒâÝÛß) ÑÝãÜãß âãiÜÒÜÛfl. × ÞÇãØ éÛÝâÛã,ÜÜÀØ ßãßÒÜê ,ÒßÒÜÛ ,ÜÛßÜÛÒ â~ÛêÒêâfl âäÒÒÞÒÜÜÀß äã ,âÒßë ßÜãÚÒâê,ë âêÛßëÞã,, ãâêëäÜÀi ,ãâäÛflêÛ, êã~ÜÒÒ äã ÇâêÝêÜãßë äâÛiÛ~ÒâÝãßë äãâêÜâê,ë (øø), , ÝãêããÒ êÛ âêÛßëÞÀ äãÒ^Ûëêâfl. û êÒ~ÒÜÛÒß ,ÒßÒÜÛ âäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl ÜÒäÒÀ,Üã ßÒÜflÒêâfl. ?êãê äã^Òââ ÛÑßÒÜÒÜÛfl (ÛÜßÛÝ ,ÜÛßÜÛfl) ãäÛâÀ,Òêâfl Ü ãâÜã,Ò ÛééÒÒÜ^ÛÞÈÜã,,ã ë,ÜÒÜÛfl , ~âêÜÀi äãÛÑ,ãÜÀi. ýÝÛß ãÇÑãß, ,ÜÛßÜÛÒ ë~âê,ëÒê Û Û,,Òê éëÜßÒÜêÞÈÜë ãÞÈ ÝÝ äÛ âãÑÜêÒÞÈÜãß, êÝ Û äÛ ÇÒââãÑÜêÒÞÈÜãß ,ãâäÛflêÛÛ (,êãßêÛ~ÒâÝãØ ãÇÇãêÝÒ), äÛ ,ãâäÛflêÛÛ ÝÝ ÞÒßÒÜêÜÀi éÛÑÛ~ÒâÝÛi, êÝ Û âÞãÚÜÀi âÒßÜêÛ~ÒâÝÛi âêÛßëÞã,. ûãÑÜêÒÞÈÜã ,ãâäÛÜÛßÒêâfl êãê âêÛßëÞ, Ýãêããßë ëÒÞflÒêâfl ÜÛÇãÞÈ?ÒÒ ,ÜÛßÜÛÒ. × ßÝi êÝÛi äÒâê,ÞÒÜÛØ ã~Ò,ÛÜÀß ãÇÑãß ãÇflâÜflÒêâfl, Ý äÛßÒë, ééÒÝê â âãÇâê,ÒÜÜÀß ÛßÒÜÒß: iãêfl ã ßãßÒÜê Ñ,ë~ÜÛfl ÛßÒÜÛ ßÝâÛßëß ,ÜÛßÜÛfl äÛiãÛÞâfl Ü ë,,ãØ âêÛßëÞ, Üã Û êã~ÝÒ øø, Ýãêãë , äãâÞÒâê,ÛÛ äãÒ^ÛëÒêâfl âãÇâê,ÒÜÜãÒ Ûßfl, ëÒÞflÞãâÈ ÜÒÇãÞÈ?ãÒ (Üã ÜÒ ÜëÞÒ,ãÒ) ÝãÞÛ~Òâê,ã ,ÜÛßÜÛfl. × ßãßÒÜê Ñ,ë~ÜÛfl ÛßÒÜÛ Ü~ÛÜÒêâfl äÒÒâäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl, , ÒÑëÞÈêêÒ Ýãêãã,,ã ßÝâÛßëß ,ÜÛßÜÛfl äÛiãÛêâfl ëÚÒ Ü êã~Ýë øø, âããê,Òêâê,ëë ,ãâäÛflêÛ ÛßÒÜÛ, Û âãÑÜÜÛÒ äÒÒÝÞ~Òêâfl Ü ,ãâäÛflêÛÒ ÛßÒÜÛ. × ßÝi äÒÞ,,ÒßãØ êÒãÛÛ ,ãÑßãÚÜã ãäÛâÜÛÒ ,ÑÛßãÒØâê,Ûfl ßÒÚë ÑÞÛ~ÜÀßÛ äâÛiÛ~ÒâÝÛßÛ äã^ÒââßÛ , Ñ,ÛâÛßãâêÛ ãê ââêãflÜÛfl ßÒÚë ÜÛßÛ , øø Û iÝêÒÛâêÛÝ âêÛßëÞã,, Ûi äããÚÛi. ýÝÛß ãÇÑãß, ÝãÜ^Òä^Ûfl ÚÒâêÝãØ ÛÑãÞfl^ÛÛ Òâëâã, ÑßÒÜflÒêâfl ÝãÜ^Òä^ÛÒØ Ñ,ÛâÛßãâêÛ âêÒäÒÜÛ ,ÑÛßãÒØâê,Ûfl ãê ââêãflÜÛfl, ãäëâÝÒØ, Ý äÛßÒë, ÝãââßãÞÈÜãÒ ,ÑÛßãÒØâê,ÛÒ, iãêfl, ,ãÑßãÚÜã, Û ÇãÞÒÒ âÞÇãÒ, ~Òß ,ÜëêÛßãÞÈÜãÒ. ÷ÒãâêêÝãß ÒâëâÜãØ êÒãÛÛ fl,ÞflÒêâfl êÝÚÒ êã, ~êã "ÜÒ ÇÀÞã âÒÞÜã äãäÀêãÝ äÒÒÇãâÛêÈ ßãâê ~ÒÒÑ äãäâêÈ, ãêÒÞflë ÝãÜ^Òä^Û âäÒÒÞÒÜÛfl Òâëâã, ãê ÒÒ âêëÝêëÜãØ ÒÞÛÑ^ÛÛ , ÜÒØãÜÜÀi âÒêfli" [15]*. ÿãêfl ,êã ÜâêãflÒØ *

ÇãêÀ ÜÒ äÒêÒÜëÒê Ü Ò?ÒÜÛÒ êãØ äãÇÞÒßÀ, ÑÒâÈ äÒÞ,,Òêâfl Ü ëã,ÜÒ ÛÒØ ,Ò ÑÞÛ~ÜÀi ÛÜêÒäÒê^ÛÛ ÛÑÞ,,ÒßãØ êÒãÛÛ , ßâ?êÇÒ ÜÒØãÜÜÀi âÒêÒØ. øÒ,fl ÛÑ ÜÛi ãâÜã,Ü Ü êãß, ~êã ,âÒ éÛÑÛãÞã,,Û~ÒâÝÛÒ äã^ÒââÀ, äãÛâiãflÛÒ , ÜÒØãÜÜãØ âÒêÛ, ÜëÚêâfl , ,ÒÒâê,i, äÒÒÜãâÛßÀi ÚÛÝãâêflßÛ ,ÜëêÛ ßãÑ,,, ÜäÛßÒ Ýã,È (âß. êÝÚÒ [10]). ?êÛ ÚÛÝãâêÛ ÛÞÛ âãÒÚÛÒâfl , ÜÛi ,ÒÒâê, Û Û,,ê ãÞÈ ã,,ÜÛ~ÒÜÜÀi Òâëâã,. ×êãfl ÛÜêÒäÒê^Ûfl ãâÜã,Ü Ü ÜÞã,,ÛÛ ßÒÚë ,ÜÛßÜÛÒß Û êÒäÞãêãØ, ê.Ò. ßÒÚë âäãâêÜÒÜÛÒß ,ãÑÇëÚÒÜÛØ , ÜÒØãÜÜãØ âÒêÛ, âãäã,ãÚÒßãß ÞêÒÞÈÜÀß Û ,ãÑ,êÜÀß êãßãÚÒÜÛÒß Û âäãâêÜÒÜÛÒß êÒäÞ (,ãÑÇëÚÒÜÛØ êãßã,) , ÝÛâêÞÞÛ~ÒâÝãØ Ò?ÒêÝÒ. × ÜâêãflÒØ ÇãêÒ ÛÑÞ,,êâfl ãâÜã,À äÒÞ,,ÒßãØ êÒãÛÛ: Ò~È ÛÒê ã ,ãâäÛflêÛÛ ãêÒÞÈÜã,,ã ÞÒßÒÜêÜã,,ã âêÛßëÞ, ÜäÛßÒ ß,,Üã,ÒÜÜãØ êã~Ò~ÜãØ ,âäÀ?ÝÛ â,Òê Ü ÝÜÒ, êãÜã,ãØ äãâÀÞÝÛ ÛÞÛ êã~Ò~Üã,,ã äÛÝãâÜã,ÒÜÛfl Ý äã,ÒiÜãâêÛ ÝãÚÛ. øßÒêãß, iÝêÒÛÑëÛß "ÑÜ~ÛßãâêÈ" ÛÞÛ "âÛÞë" êÝã,,ã âêÛßëÞ, fl,ÞflÒêâfl Ò,,ã ÛÜêÒÜâÛ,ÜãâêÈ. ùÇãÇÒÜÛÒ êÒãÛÛ Ü ,ãâäÛflêÛÒ âÞãÚÜÀi âêÛßëÞã,, äã ÝØÜÒØ ßÒÒ ÑÛêÒÞÈÜÀi, ,ãÑßãÚÜã Ü ãâÜã,Ò âÛÜêÒÑ â êÒãÛÒØ ÛÜêÒ,,^ÛÛ äÛÑÜÝã, ?. ýÒØâßÜ [15, 21], äÛ ãêÝÑÒ ãê äãÚÒÝêãÜÀi äÒâê,ÞÒÜÛØ ã ,ÜÛßÜÛÛ. ×ßÒâêã Þë~ äãÚÒÝêã, ÛßÒÒ,,ã âêã,,ë ,,ÜÛ^ë Û âäãâãÇÜã,,ã ÞÛ?È â?ÛflêÈâfl ÛÞÛ âëÚêÈâfl, Üã ÜÒ ßÒÜflêÈâfl äã ÛÜêÒÜâÛ,ÜãâêÛ, äÒÞ,,Òêâfl ÜÒäÒÀ,ÜãÒ âäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl äã ,âÒßë øø, ÝãêããÒ, ãÜÝã, ßãÚÒê ÇÀâêã ëÇÀ,êÈ äÛ ëÞÒÜÛÛ ãê "^ÒÜê ,ÜÛßÜÛfl" Û ÇÀêÈ âëÒâê,ÒÜÜã ãêÞÛ~ÜÀß ãê ÜëÞfl êãÞÈÝã , ÜÒÝãêããØ ãÝÒâêÜãâêÛ êã,,ã ^ÒÜê, âããê,Òêâê,ëÒØ Þë~ë ?. ýÒØâßÜ (Ûâ. 1). øããÇÜë ÛÒ (ÛÒ ",,ÛÒÜê ,ÜÛßÜÛfl") ÜÒÒ ,ÀâÝÑÀ,ÞÛ áÚ. õÜ,,ëÜ Û û. ÿÛÞÞÛ [28, 29]. øÛ êãß äÒÞ,,ÒßãÒ , ÜâêãflÒØ ÇãêÒ ë,ÜÒÜÛÒ ßãÚÒê ãäÛâÀ,êÈ ÛÜßÛÝë ,ÜÛßÜÛfl , äÒÒÞi ãêÒÞÈÜÀi Ýê ?. ýÒØâßÜ. ÷ÒÝãêãÀÒ ÛÒÛ ãÇãÇÒÜÛfl äÒÞ,,ÒßãØ ÑÒâÈ êÒãÛÛ Ü ,ãâäÛflêÛÒ âÞãÚÜÀi âêÛßëÞã, Û âÛâêÒß ÞÒßÒÜêÜÀi âêÛßëÞã, ÛÑÞãÚÒÜÀ êÝÚÒ , Çãêi [7, 8]. øÒÞ,,Òßfl êÒãÛfl ÜÒ ãÇflâÜflÒê êÝÛi fl,ÞÒÜÛØ, ÝÝ ÑêëiÜÛÒ ãÛÒÜêÛã,ã~Üã,,ã ÒéÞÒÝâ äÛ ßÜã,,ãÝêÜÀi äã,êãÒÜÛfli âêÛßëÞ Û Ò,,ã ,ãââêÜã,ÞÒÜÛÒ äÛ ÛÑßÒÜÒÜÛÛ âêÛßëÞ. ü~Òê êÛi fl,ÞÒÜÛØ ,ãÑßãÚÒÜ Ü ãâÜã,Ò ãÇÒÛÜÒÜÛfl äÒÞ,,ÒßãØ êÒãÛÛ â êÒãÛÒØ
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5 r

úÛâ. 1. øÛ t1 > t2 > t3 ÛâëÜãÝ ÛÞÞâêÛëÒê Ò?ÒÜÛÒ ë,ÜÒÜÛfl êÒäÞãäã,ãÜãâêÛ (2) Þfl âÞë~fl, Ýã,, , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ âëÇâêÜ^Ûfl âÝãÜ^ÒÜêÛã,Ü , êã~ÝÒ x = 0. û êÒ~ÒÜÛÒß ,ÒßÒÜÛ ãÜ äãâêÒäÒÜÜã ââÒÛ,Òêâfl äã äãâêÜâê,ë. øÛ t1 < t2 < t3 ÛâëÜãÝ ÛÞÞâêÛëÒê Ò?ÒÜÛÒ (9) ë,ÜÒÜÛfl (8) â ãäãÞÜÛêÒÞÈÜÀß ëâÞã,ÛÒß (6) Ü äÒ,ãß êäÒ äã^Òââ ,ãâäÛflêÛfl: âäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl , ãÝÒâêÜãâêÛ äãÒÝ^ÛÛ O âêÛßëÞ , äâÛiÛ~ÒâÝãß äãâêÜâê,Ò , êÛ äãâÞÒã,êÒÞÈÜÀi ßãßÒÜê ,ÒßÒÜÛ. ÙéÛÝÛ ÒßãÜâêÛëê äãâêÒäÒÜÜë ÝãÜ^ÒÜê^Û ,ÜÛßÜÛfl Ü âêÛßëÞÒ. ?ÒÒÑ r ãÇãÑÜ~ÒÜ ,ÒÞÛ~ÛÜ ãêÝÞãÜÒÜÛfl ãê êã~ÝÛ x = 0. Fig. 1. For t1 > t2 > t3 the figure illustrate the solution of the diffusion equation (2) for the case, when by t = 0 a substance is concentrated in the point x = 0. Next it is dissipating in the space. For t1 < t2 < t3 the figure illustrate the solution (9) of the equation (8) by the condition (6) on the first phase of the perception process: the distribution of the attention in the neighborhood of the projection O of the stimulus in the psychical space in moments t1, t2, t3. The graphs demonstrate that the attention is concentrating on the stimulus. r is the magnitude of the deviation from the point x = 0.

,ÒâêÜfl â,flÑÈ ,ÜÛßÜÛfl Û ,ÒßÒÜÛ ÒÝ^ÛÛ (×ú) Ü êÒâêÛëÛÒ âêÛßëÞÀ [15]. ÕãÞÒÒ ÝãÜÝÒêÜã, äÞãêÜãâêÈ ,ÜÛßÜÛfl I(x, t) ãäÒÒÞflÒêâfl ÝÝ ,ÒÞÛ~ÛÜ, äãäã^ÛãÜÞÈÜfl ÛÑßÒÜÒÜÛ ,ãÑÇëÛßãâêÛ (,ÒÞÛ~ÛÜÀ, ãÇêÜã äãäã^ÛãÜÞÈÜãØ ×ú [23]). ýÝãÒ ãäÒÒÞÒÜÛÒ ,ãÑßãÚÜã ÇÞ,,ãfl ßÒêãë, ÑÇãêÜÜãßë , ?ÝãÞÒ æ.ð. ÕãØÝã [3, 16, 24] Û ééÒÝêÛ,Üã ÛâäãÞÈÑëÒßëâfl Þfl ÞãÝÞÈÜã,,ã ÛÑßÒÒÜÛfl ,ãÑÇëÛßãâêÛ [23]. ôãßÒ êã,,ã, ,ÜÛßÜÛÒ, ÝÝ ÛÑ,ÒâêÜã [15], ,ÞÛflÒê êÝÚÒ Ü ßäÞÛêëÀ ÝãÞÒÇÜÛØ ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ (×ø). ?êã êÝÚÒ äãÑ,ãÞflÒê ÛÑßÒflêÈ äÞãêÜãâêÈ ,ÜÛßÜÛfl. × ÑÒÞi 3, 4, 5 äã,ãÛêâfl â,ÜÒÜÛÒ äÒâÝÑÜÛØ ßãÒÞÛ â ÝâäÒÛßÒÜêÞÈÜÀßÛ ÒÑëÞÈêêßÛ: ÛÜßÛÝãØ ,ãÑÇëÛßãâêÛ ÑÞÛ~ÜÀi äëÜÝêã, ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã , äã^ÒââÒ ^ÒÞÒÜä,ÞÒÜÜã,,ã ,ãâäÛflêÛfl [22], ÛÜßÛÝãØ ßäÞÛêëÀ ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ (×ø), ÑÝãÜãß ûêÛ,ÒÜâ [20]. × ßÝi ßãÒÞÛ ,À,ãÛêâfl êÝÚÒ ÛÑ,ÒâêÜÀØ ÝâäÒÛßÒÜêÞÈÜÀØ ÑÝãÜ øÈÒãÜ-ñÇãÛÜ-óÒÇÒÒ, [11, 12]. 1. ôÔ?æûý×æ÷÷?æ ùûùÕæ÷÷ùûýð áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð? ÿÝêÒÜãØ Ý~Òâê,ÒÜÜãØ ãâãÇÒÜÜãâêÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl fl,ÞflÒêâfl â,ãØâê,ã âÒÞÒÝêÛ,ÜãâêÛ ,ÜÛßÜÛfl. üâÛÞÒÜÛÒ ,ÜÛßÜÛfl Ý ãÜãßë ÛÑ ,ãâäÛÜÛßÒßÀi (,ããÇÚÒßÀi, ßÀâÞÛßÀi Û ä.) âêÛßëÞã, â ÜÒãÇiãÛßãâêÈ äÛ,ãÛê Ý ãâÞÇÞÒÜÛ ,ÜÛßÜÛfl Ý ë,,Ûß âêÛßëÞß [1, 2, 15]. øããÇÜfl ãäãÞÜÛêÒÞÈÜãâêÈ ,ãâäÛflêÛfl ÛßÒÒê ßÒâêã ÝÝ ,ÜëêÛ ãÜãØ ßãÞÈÜãâêÛ, êÝ Û ßÒÚë ÑÞÛ~ÜÀßÛ ßãÞÈÜãâêflßÛ. × ßÝi êÒãÛÛ Òâëâã, [15] âÒÞÒÝêÛ,ÜãâêÈ ,ÜÛßÜÛfl ãÇflâÜflÒêâfl ÜÒi,êÝãØ ÝãÞÛ~Òâê,ÒÜÜã ã,,ÜÛ~ÒÜÜÀi Òâëâã,, ê.Ò. Ü ãâÜã,Ò ÑÝãÜ âãiÜÒÜÛfl. úÑ,Û,fl êë ÛÒ, ãêßÒêÛß âÞÒëÒÒ [10]. ûÒÞÒÝêÛ,ÜãÒ â,ãØâê,ã ,ÜÛßÜÛfl Òê Ý~Òâê,ÒÜÜë ãâÜã,ë Þfl ,,ÛäãêÒÑÀ ã âãiÜÒÜÛÛ ,ÜÛßÜÛfl. ÕãÞÒÒ êã,,ã, ãÜã ëÝÑÀ,Òê Ü ã~Ò,ÛÜë ÜÞã,,Û ßÒÚë ,ÜÛßÜÛÒß Û éÛÑÛ~ÒâÝÛßÛ âëÇâêÜ^ÛflßÛ êÛä ,,Ñ, âê,ã ÛÞÛ êÒäÞ. áÒØâê,ÛêÒÞÈÜã, ÇÞ,,ãfl êãßë â,ãØâê,ë ,ÜÛßÜÛÒ ÒâêÒâê,ÒÜÜã êÝêã,êÈ ÝÝ ÜÒÝãêãë âãiÜflëâfl ^ÒÞãâêÜãâêÈ: ,ÜÛßÜÛÒ "ÜÒ ,ãÑÜÛÝÒê ÜÛãêÝë Û ÜÒ Ûâ~ÒÑÒê , ÜÛÝë", ÞÛ?È äÒÒâãâÒãêã~Û,Òêâfl ÛÞÛ äÒÒâäÒÒÞflÒêâfl â ãÜã,,ã âêÛßëÞ (,ÜÒ?ÜÒ,,ã ÛÞÛ ,ÜëêÒÜÜÒ,,ã) Ü ë,,ãØ, ÛÑ ãÜã,,ã "ßÒâê" , ë,,ãÒ.

ÜÒØãÜÜãØ ßãÒÞÛ âêÛßëÞ æ.÷. ûãÝãÞã, [19]. × âÞÒëÒß ÑÒÞÒ äÒÒ~ÛâÞflêâfl ãâÜã,ÜÀÒ (Ü Ü? ,Ñ,,Þfl) Ý~Òâê,ÒÜÜÀÒ ãâãÇÒÜÜãâêÛ ÛÜßÛÝÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl. ÷ ãâÜã,Ò êÛi â,ãØâê, ,ÜÛßÜÛfl , ÞÈÜÒØ?Òß âêãÛêâfl ßêÒßêÛ~ÒâÝfl ßãÒÞÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl ÞÒßÒÜêÜã,,ã éÛÑÛ~ÒâÝã,,ã ,ÜÒ?ÜÒ,,ã âêÛßëÞ [10], ÇÑÛëflâfl Ü ë,ÜÒÜÛÛ Þfl äÞãêÜãâêÛ ,ÜÛßÜÛfl I(x, t). ûäãâãÇÀ ÛÑßÒÒÜÛfl äÞãêÜãâêÛ ,ÜÛßÜÛfl ãäÒÒÞflêâfl , ÑÒÞi 3, 4. øÛ êãß ÛâäãÞÈÑëÒêâfl äÒÚÒ ,âÒ,,ã ÛÑ-

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

741

×êãfl Ý~Òâê,ÒÜÜfl ãâãÇÒÜÜãâêÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl ãÇÀ~Üã ÜÒ ,ÀÒÞflÒêâfl , Ý~Òâê,Ò ãêÒÞÈÜã,,ã â,ãØâê, , âÛÞë â,ãÒØ ã~Ò,ÛÜãâêÛ. × äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÒ?ÜÒ,,ã âêÛßëÞ äãâÞÒÜÛØ âÜ~Þ äÛ,ÞÒÝÒê Ý âÒÇÒ ,ÜÛßÜÛÒ, ÑêÒß ,ÜÛßÜÛÒ ãê,ÞÒÝÒêâfl ãê ÜÒ,,ã. × âÛÞë âÒÞÒÝêÛ,ÜãâêÛ (âãiÜÒÜÛfl) ãâê ,ÜÛßÜÛfl Ý âêÛßëÞë ãÑÜ~Òê ÝãÜ^ÒÜê^Û ,ÜÛßÜÛfl, äãÜÛÚÒÜÛÒ ,ÜÛßÜÛfl Ý âêÛßëÞë - ââÒflÜÛÒ ,ÜÛßÜÛfl (äã ãêÜã?ÒÜÛ Ý ÜÒßë). ðêÝ, , äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÛßÜÛÒ âÜ~Þ ÝãÜ^ÒÜêÛëÒêâfl Ü âêÛßëÞÒ, ÑêÒß ââÒÛ,Òêâfl äã ãêÜã?ÒÜÛ Ý ÜÒßë. ýÒêÈfl Ý~Òâê,ÒÜÜfl ãâãÇÒÜÜãâêÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl âãâêãÛê , êãß, ~êã ~Òß "âÛÞÈÜÒÒ" âêÛßëÞ, êÒß ÇÀâêÒÒ ãÜ äÛ,ÞÒ~Òê Ý âÒÇÒ ,ÜÛßÜÛÒ Û êÒß ÇãÞÈ?ÒÒ ,ÜÛßÜÛÒ ãÜ Ý âÒÇÒ äÛ,ÞÒ~Òê. øÛ êãß , âÞë~Ò ÞÒßÒÜêÜã,,ã âêÛßëÞ äã "âÛÞãØ" äãÜÛßÒêâfl Ò,,ã ÛÜêÒÜâÛ,ÜãâêÈ. ýÝ, ,ÜÒÑäÜÀØ ,ÑÀ, äÒêÀ Ñ ãÝÜãß ß,,Üã,ÒÜÜã äÛ,ÞÒÝÒê Ý âÒÇÒ äã,À?ÒÜÜãÒ ,ÜÛßÜÛÒ (ãê,ÞÒÝfl ãê ë,,Ûi ÒÞ), , êã ,Òßfl ÝÝ ?ããi ÞÛâêÈÒ, ãÇÀ~Üã ãâêÒêâfl ÜÒÑßÒ~ÒÜÜÀß. ÷ ãâÜã,Ò äÒÒ~ÛâÞÒÜÜÀi â,ãØâê, ,ÜÛßÜÛfl , ÞÈÜÒØ?Òß âêãÛêâfl ßãÒÞÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl ÞÒßÒÜêÜã,,ã éÛÑÛ~ÒâÝã,,ã âêÛßëÞ. 2. õÔýæõÔýð?æûôÔ? õùáæó? øúùåæûûÔ ×ùûøúð?ýð? ?óæõæ÷ýÔú÷ùÙù ×÷æ?÷æÙù ûýðõüóÔ øãâêãÛß ßêÒßêÛ~ÒâÝë ßãÒÞÈ ÛÜßÛÝÛ ,ÜÛßÜÛfl ÛâäÀêëÒßã,,ã , äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÒ?ÜÒ,,ã âêÛßëÞ. û êãØ ^ÒÞÈ ââßãêÛß âÜ~Þ ÇâêÝêÜãÒ ßÒêÛ~ÒâÝãÒ øø S â ãäÒÒÞÒÜÜãØ Ü ÜÒß ßÒãØ* Å Û ,,ÒÒß éãßÞÈÜã , êãß äãâêÜâê,Ò äÞãêÜãâêÈ ,ÜÛßÜÛfl I(x, t), x S, t - (ÇÒÑÑßÒÜãÒ, ãêÜãâÛêÒÞÈÜãÒ) ,Òßfl. ýã,, ,,ÛäãêÒÑ ã âãiÜÒÜÛÛ ,ÜÛßÜÛfl (â,ãØâê,ã âÒÞÒÝêÛ,ÜãâêÛ) ÑäÛ?Òêâfl , ,ÛÒ

êÝÚÒ ÒêÞÛ Ò,,ã âêëÝêëÀ ÜÒ fl,Þflêâfl äÒßÒêãß ãÇâëÚÒÜÛfl ÜâêãflÒØ ÇãêÀ, ãÜÛ ãäÒÒÞflêâfl âäÒ^ÛéÛÝãØ ÝêÛã,ÜÛfl [26]. áÞfl ÜâêãflÒØ ÇãêÀ âëÒâê,ÒÜÜã êãÞÈÝã, ~êãÇÀ øø ÇÀÞã ÞãÝÞÈÜã ãêãÚÒâê,Ûßã â ãÇÞâêflßÛ ,ëißÒÜã,,ã Ò,ÝÞÛã, ÞÛÜÒØÜã,,ã äãâêÜâê, R2, ê.Ò. ãÝÒâêÜãâêÛ ãêÒÞÈÜÀi êã~ÒÝ øø ßãÚÜã ÇÀÞã ââßêÛ,êÈ ÝÝ äÞãâÝÛÒ ãÇÞâêÛ. ýÝÛÒ ãÇÞâêÛ ßãÚÜã êÝêã,êÈ, â ãÜãØ âêããÜÀ, ÝÝ ÝêÀ ?. ýÒØâßÜ, â ë,,ãØ - ÝÝ ÞãÝÞÈÜÀÒ ãÇÞâêÛ âÞãÒ, ÝãÀ ,,ãÞã,Üã,,ã ßãÑ,, (ôÙõ). × ÜâêãflÒØ ÇãêÒ Ò~È äãØÒê ã ,ãâäÛflêÛÛ ÞÒßÒÜêÜã,,ã ,ÜÒ?ÜÒ,,ã ÑÚÛêÒÞfl - êã~Ò~ÜÀØ Ûâêã~ÜÛÝ â,Òê, ÝããêÝfl êãÜã,fl äãâÀÞÝ Û äã~ÒÒ, - iÝêÒÛÑëÒßã,,ã ÛÜêÒÜâÛ,ÜãâêÈ , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i. × ãÇÒß âÞë~Ò äã ßãÚÜã äãÜÛßêÈ ÜÒÝãêãë ãÇãÇÒÜÜë iÝêÒÛâêÛÝë âêÛßëÞ, ë~ÛêÀ,ë Ò,,ã âÒßÜêÛ~ÒâÝãÒ âãÒÚÜÛÒ [8]. æâÞÛ ÛÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ ãâêêã~Üã ßÞ, êã ,ÀÑ,ÜÜãÒ (ÜÒäãâÒâê,ÒÜÜã) ÒØâê,ÛÒß âêÛßëÞ äÒÒâäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl äãÛâiãÛê , ãâÜã,Üãß , äÒÒÞi ßÞãØ ãÝÒâêÜãâêÛ S0 êã~ÝÛ O øø, , Ýãêãë ãÜ äãÒ^ÛëÒêâfl. ?êë ãÝÒâêÜãâêÈ ßÀ Û ÇëÒß â~ÛêêÈ äÞãâÝãØ ãÇÞâêÈ, äãÒÝ^Û âêÛßëÞ , øø äÛßÒß Ñ Ü~Þã ÝããÛÜê O(0; 0) , êãØ ãÇÞâêÛ. ×,Ûë âÝÑÜÜã,,ã ÑÝãÜ âãiÜÒÜÛfl äÛÇÞÛÚÒÜÜã ,ÀäãÞÜflÒêâfl , äÒÒÞi ãÇÞâêÛ S0
S


0

I ( x, t ) x = const

(1)


S

I ( x, t ) dÅ = const,

(äãÞÜãÒ ÝãÞÛ~Òâê,ã ,ÜÛßÜÛfl , øø ÒâêÈ ,ÒÞÛ~ÛÜ äãâêãflÜÜfl). ÙÞãÇÞÈÜfl âêëÝêë øø,
*õÒêÛ~ÒâÝãÒ äãâêÜâê,ã - êã ßÜãÚÒâê,ã, Þfl Ýãêãã,,ã ,,ÒÒÜã äãÜflêÛÒ ââêãflÜÛfl ßÒÚë ÞÒßÒÜêßÛ (ßÒêÛÝÛ). õÒ - êã ãÇãÇÒÜÛÒ äãÜflêÛfl äÞãÛ ÛÞÛ ãÇÒß Ü äãÛÑ,ãÞÈÜÀÒ ßÜãÚÒâê,. õÒ äãÑ,ãÞflÒê âêãÛêÈ ÛÜêÒ,,Þ.

(äãêãÝ ,ÜÛßÜÛfl ~ÒÒÑ ,,ÜÛ^À ãÇÞâêÛ äÒÜÒÇÒÚÛßã ßÞ). æâÞÛ ÚÒ ÛÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ ãêÜãâÛêÒÞÈÜã ,ÒÞÛÝ, ãÜ ,ÀÑÀ,Òê ,,ÞãÇÞÈÜãÒ (ßÒÚßãÞÈÜãÒ) äÒÒâäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl äã ,âÒßë øø. × ÜâêãflÒØ ÇãêÒ ââßêÛ,Òêâfl âÞë~Ø "ßÞãØ" ÛÜêÒÜâÛ,ÜãâêÛ** Û âêãÛêâfl ë,ÜÒÜÛÒ, ãäÛâÀ,ÒÒ ÛÜßÛÝë ,ÜÛßÜÛfl , äÒÒÞi ãÇÞâêÛ S0 Ñ ãâêêã~Üã ßÞÀØ äãßÒÚëêãÝ ,ÒßÒÜÛ (äãflÝ ×ú). ?êã ë,ÜÒÜÛÒ ãäÛâÀ,Òê äã^Òââ, ,ÀÑ,ÜÜÀØ ÜÒäãâÒâê,ÒÜÜã ÒØâê,ÛÒß âêÛßëÞ. ùÜÝã êãê äã^Òââ ßãÚÒê ÛÜÛ^ÛÛã,êÈ Üã,ÀÒ äã^ÒââÀ , ÑÞÛ~ÜÀi (ââã^ÛêÛ,ÜÀi) ãÇÞâêfli øø. ×ÒãflêÜã, êÛ äã^ÒââÀ ãäÛâÀ,êâfl êÒß ÚÒ ë,ÜÒÜÛÒß, êãÞÈÝã ãÞÈ Þfl ÜÛi, ,ãÑßãÚÜã, Û,,Òê ëÚÒ ÜÒ ÛÜêÒÜâÛ,ÜãâêÈ ÛâiãÜã,,ã âêÛßëÞ, ÜÒÝãêãfl iÝêÒÛâêÛøã~ÒÝÜÒß, ~êã êÒßÛÜ "ßÞÀØ" âÞÒëÒê äãÜÛßêÈ , ëÝÑÜÜãß ,À?Ò âßÀâÞÒ, ÜÒ , êãß âßÀâÞÒ, ~êã ãÜ ÇÞÛÑãÝ Ý ÇâãÞêÜãßë äãã,,ë ,ãâäÛflêÛfl.
**

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,,ÞâÝã

Ý äÒ,Û~Üã,,ã äã^Òââ (ÛÜêÒÜâÛ,ÜãâêÈ ",ÜëêÒÜÜÒ,,ã" âêÛßëÞ). øãâêãÛß ë,ÜÒÜÛÒ Þfl éëÜÝ^ÛÛ I(x, t) , ãÇÞâêÛ S0. ÕëÒß ãâÜã,À,êÈâfl Ü ãäÛâÜÜÀi ,À?Ò Ý~Òâê,ÒÜÜÀi ãâãÇÒÜÜãâêfli ÛÜßÛÝÛ ,ÜÛßÜÛfl. ×,Ûë ,ÒÜâê, (1) Û ëÝÑÜÜãØ ,À?Ò ÜÞã,,ÛÛ ßÒÚë ÛÜßÛÝãØ ,ÜÛßÜÛfl Û ÛÜßÛÝãØ êÒäÞ, ,,Ñ ÛÞÛ âê,ã, ÒâêÒâê,ÒÜÜã ÛâÝêÈ Ò,,ã , éãßÒ ë,ÜÒÜÛfl êÒäÞãäã,ãÜãâêÛ (ë,ÜÒÜÛfl ÛééëÑÛÛ) I t = a0 I ,
2 2 0

(4), ÝãÒÝêÜ. áÞfl êã,,ã ~êãÇÀ ÝãÜ^ÒÜê^Ûfl ,ÜÛßÜÛfl ~ÒÒÑ ÜÒÝãêããÒ ,Òßfl âßÒÜflÞâÈ ââÒflÜÛÒß, ãÇ,Ûß , ä,ë ~âêÈ ë,ÜÒÜÛfl (3) "ÝÞââÛ~ÒâÝãÒ" âÞ,,ÒßãÒ â äãÞãÚÛêÒÞÈÜÀß, ,ãÑâêÛß â êÒ~ÒÜÛÒß ,ÒßÒÜÛ ÝãééÛ^ÛÒÜêãß a0 I t = - ---- I + k ( ) t I , 2 t I ( x, + ) = ( x ) .
2

(5)

ãäãÞÜÛêÒÞÈÜãÒ ëâÞã,ÛÒ (4) ÑäÛ?Òß , ,ÛÒ
k=0

(2)

(6)

,,Ò a - äãÞãÚÛêÒÞÈÜÀØ äãâêãflÜÜÀØ ÝãééÛ^ÛÒÜê, It - äãÛÑ,ãÜfl äÞãêÜãâêÛ ,ÜÛßÜÛfl I(x, t) äã ,ÒßÒÜÛ, - ãäÒêã óäÞâ. ?êã ë,ÜÒÜÛÒ ãäÛâÀ,Òê ,ãÞ^Û âäÒÒÞÒÜÛfl ÜÒäÒÀ,ÜãØ âëÇâêÜ^ÛÛ (,,Ñ, êÒäÞ Û ê..), iÝêÒÛÑëÒßãØ äÞãêÜãâêÈ I(x, t), äã äãâêÜâê,ë äÛ ÑÜÜãß ÒÒ âäÒÒÞÒÜÛÛ , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ. ×ÚÜÒØ?ÒØ Þfl Üâ ãâãÇÒÜÜãâêÈ ë,ÜÒÜÛfl (2) fl,ÞflÒêâfl êã, ~êã Ò,,ã Ò?ÒÜÛÒ ëã,ÞÒê,ãflÒê ÑÝãÜë âãiÜÒÜÛfl (1). ùÜÝã Ò,,ã Ò?ÒÜÛÒ ëã,ÞÒê,ãflÒê 2 êÝÚÒ Û ÑÝãÜë ,ãÑâêÜÛfl ÜêãäÛÛ ( a 0 > 0): ÝÝ ÇÀ ÜÛ ÇÀÞ âäÒÒÞÒÜ âëÇâêÜ^Ûfl I(x, t) , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ, â êÒ~ÒÜÛÒß ,ÒßÒÜÛ ãÜ äãâêÒäÒÜÜã ,ÜãßÒÜã âäÒÒÞflÒêâfl äã äãâêÜâê,ë ("ââÒÛ,Òêâfl"). ýÝ, ÒâÞÛ , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ âëÇâêÜ^Ûfl ÇÀÞ âÝãÜ^ÒÜêÛã,Ü , êã~ÝÒ x = 0, êã â êÒ~ÒÜÛÒß ,ÒßÒÜÛ ãÜ ÇëÒê ,ãÞ^ÛãÜÛã,êÈ êÝ, ÝÝ äãÝÑÜã Ü Ûâ. 1, ,,Ò t1 > t2 > t3, r = ÁR = = Á|x|. × êã ÚÒ ,Òßfl ,ÜÛßÜÛÒ , äã^ÒââÒ ,ãâäÛflêÛfl âÜ~Þ ÝãÜ^ÒÜêÛëÒêâfl Ü âêÛßëÞÒ, ÑêÒß ëÚÒ ââÒÛ,Òêâfl äã ãêÜã?ÒÜÛ Ý ÜÒßë (ãê,ÞÒÝÒêâfl ãê ÜÒ,,ã). ùäÛâÜÛÒ äã^Òââ ÝãÜ^ÒÜê^ÛÛ ,ÜÛßÜÛfl ë,ÜÒÜÛÒß (2) ÝÚÒêâfl äãÇÞÒßêÛ~ÜÀß. ðÑ,ÒâêÜã, ~êã ãÇÒÜÛÒ ,ÒßÒÜÛ äëêÒß ÑßÒÜÀ t -t , êãß ë,ÜÒÜÛÛ äÛ,ãÛê Ý ÜÒÝãÒÝêÜãØ Ñ~Ò. ýÒß ÜÒ ßÒÜÒÒ , Çãêi [5, 6] äãÝÑÜã, ~êã äÒãÇÑã,ÜÛÒ ,ÒßÒÜÛ t t-1 , ë,ÜÒÜÛÛ (2) äÛ,ãÛê Ý ë,ÜÒÜÛ a0 I t = - ---- I , 2 t
2

ðâiãfl ÛÑ êÒÇã,ÜÛfl Ý~Òâê,ÒÜÜã-ä,ÛÞÈÜãØ Ñ,ÛâÛßãâêÛ äã^Òââ I(x, t) ãê ,ÒÞÛ~ÛÜÀ ÛÜêÒÜâÛ,ÜãâêÛ , ÝãééÛ^ÛÒÜê a0 ãÞÚÒÜ ëÇÀ,êÈ â ãâêãß ÛÜêÒÜâÛ,ÜãâêÛ (, êãß ßãÚÜã ëÇÒÛêÈâfl ÛÑ ÜÞÛÑ Ò?ÒÜÛfl Ñ~Û (5), (6)). ðÑ âããÇÚÒÜÛØ äãâêãêÀ ,ÀÇÒÒß Ò,,ã , ,ÛÒ a0 = -1 I I t = - --------2 + k ( ) t I . 2 t (7)

(3)

ùêßÒêÛß, ~êã ,ÀÇã ,êãã,,ã âÞ,,Òßã,,ã , ä,ãØ ~âêÛ äãäã^ÛãÜÞÈÜÀß t äãÛÑ,ãÛÞâfl , äã^ÒââÒ ÜÞÛÑ âããê,Òêâê,Ûfl ßãÒÞÛ ÝâäÒÛßÒÜêÞÈÜãßë ÑÝãÜë ûêÛ,ÒÜâ (êã äÒ,ÀØ ÝâäÒÛßÒÜê, â ÝãêãÀß â,ÜÛ,ÞâÈ ßãÒÞÈ Û Ü ãÇflâÜÒÜÛÒ Ýãêãã,,ã ãÜ ÇÀÞ ÛÑÜ~ÞÈÜã Üä,ÞÒÜ, âß. [10]), äãêãßë êÝãØ ,ÀÇã ÜÒÞÈÑfl â~ÛêêÈ ~Ûâêã êÒãÒêÛ~ÒâÝÛß (ÛÑ ëâÞã,Ûfl ,ãÑâêÜÛfl ÝãééÛ^ÛÒÜê Û äÛÜ^Ûä äãâêãêÀ). ÔÜÞÛÑ âããê,Òêâê,Ûfl äÒÞ,,ÒßãØ ßãÒÞÛ ÑÝãÜë ûêÛ,ÒÜâ äÛ,ÒÒÜ (ÛÑ âããÇÚÒÜÛØ Þã,,ÛÝÛ ÛÑÞãÚÒÜÛfl) , ÝãÜ^Ò ÜâêãflÒØ ÇãêÀ. ×ÀÇã ÚÒ a0 = -1, äã,ÛÛßãßë, ÜÒ ,ÞÛflÒê âëÒâê,ÒÜÜã Ü ãâÜã,ÜÀÒ ÒÑëÞÈêêÀ, äãÞë~ÒÜÜÀÒ , ßÝi ÜâêãflÒØ ÇãêÀ. ü,ÜÒÜÛÒ (7) ÑäÛâÜã , ÇÒÑÑßÒÜãß ,ÒßÒÜÛ. ?êãÇÀ äÒÒØêÛ Ý ÒÞÈÜãßë éÛÑÛ~ÒâÝãßë ,ÒßÒÜÛ, ,ÀäãÞÜÛß ÑßÒÜë äÒÒßÒÜÜãØ t Ç t, ,,Ò - äãâêãflÜÜÀØ äãÞãÚÛêÒÞÈÜÀØ ÝãééÛ^ÛÒÜê ÑßÒÜãâêÛ ,ÒßÒÜÛ (ßâ). × ÒÑëÞÈêêÒ äãÞë~Ûß ë,ÜÒÜÛÒ ÛÜßÛÝÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÒ?ÜÒ,,ã âêÛßëÞ [10] I -2 I t = - --------- + k ( ) t I . 22 t (8)

ÝãêããÒ äÛ ,ÀÇãÒ ãäãÞÜÛêÒÞÈÜã,,ã ëâÞã,Ûfl , ,ÛÒ I ( x, + ) = ( x ) (4) ((x) - éëÜÝ^Ûfl áÛÝ) ãäÛâÀ,Òê äã^Òââ ÝãÜ^ÒÜê^ÛÛ âëÇâêÜ^ÛÛ (, ÜÜãß âÞë~Ò - ,ÜÛßÜÛfl) , êã~ÝÒ x = 0. øÛ êãß Ñ~ (3),

ñÒâÈ t - ëÚÒ ÒÞÈÜãÒ ,Òßfl, ÛÑßÒflÒßãÒ , ßÛÞÞÛâÒÝëÜi. øßÒê ßãÒÞÛ ßãÚÒê Ñ,ÛâÒêÈ ãê ÛâäÀêëÒßã,,ã Û ëâÞã,ÛØ ÝâäÒÛßÒÜê. ôÝ ãäÒÒÞflÒêâfl ÝãééÛ^ÛÒÜê k(), ãäÛâÜã , ÑÒÞÒ 5.

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

743

ýÇÞÛ^ 1. áÛÜßÛÝ ,ãÑÇëÛßãâêÛ (B, 1/â) ÛâäÀêëÒßã,,ã ø.×. , ãÝÒâêÜãâêÛ äãÒÝ^ÛÛ âêÛßëÞ , äâÛiÛ~ÒâÝãß äãâêÜâê,Ò Table 1. The dynamics of the excitability (B, 1/s) of probationer P.V. in the neighbourhood of the projection of the stimulus in the psychical space t, ßâ R


140 2.36 2.25 2.19 2.20

170 2.76 2.42 2.32 2.22

200 2.85 2.55 2.34 2.29

250 2.99 2.61 2.45 2.41

300 3.06 2.67 2.51 2.42

350 3.19 2.68 - 2.45

400 3.24 2.63 - 2.47

500 3.28 2.78 - 2.45

600 3.28 - - -

700 3.28 2.65 - 2.35

900 3.00 2.79 - 2.56

1200 2.92 2.78 - 2.50

0 1 2 3

úÒ?ÒÜÛÒ ë,ÜÒÜÛfl ÛßÒÒê ,Û [5, 6, 10] 1 (9) , I ( r, t ) = ----------------- e 2D(t ) 2 -2 2 (10) D ( t ) = ------ + k ( ) t . 2 t ñÒâÈ ~ÒÒÑ r ãÇãÑÜ~ÒÜ ,ÒÞÛ~ÛÜ ãêÝÞãÜÒÜÛfl êÒÝëÒØ êã~ÝÛ x ãÇÞâêÛ S0 øø ãê äãÒÝ^ÛÛ O(0; 0) âêÛßëÞ , øø: r = ÁR, ,,Ò R = |x| - âããê,Òêâê,ëÒÒ ââêãflÜÛÒ. þëÜÝ^Ûfl D(t) âÜ~Þ ëÇÀ,Òê â êÒ~ÒÜÛÒß ,ÒßÒÜÛ, ~êã âããê,Òêâê,ëÒê ÝãÜ^ÒÜê^ÛÛ ,ÜÛßÜÛfl Ü âêÛßëÞÒ (ÜÑã,Òß êã äÒ,Àß êäãß äã^Òââ ,ãâäÛflêÛfl), ÑêÒß ,ãÑâêÒê, ~êã âããê,Òêâê,ëÒê ââÒflÜÛ ,ÜÛßÜÛfl (ÜÑã,Òß êã ,êãÀß êäãß). ÷ Ûâ. 1 äÒâê,ÞÒÜÀ ,,éÛÝÛ éëÜÝ^ÛÛ (9) , êÛ äãâÞÒã,êÒÞÈÜÀi ßãßÒÜê ,ÒßÒÜÛ äÒ,ã,,ã êä äã^Òââ ,ãâäÛflêÛfl: t1 < t2 < < t3, ÛÞÞâêÛëÛÒ ÝãÜ^ÒÜê^Û ,ÜÛßÜÛfl Ü âêÛßëÞÒ. úâäÒÒÞÒÜÛÒ ,ÜÛßÜÛfl , ÞÇãØ ßãßÒÜê ,ÒßÒÜÛ ^ÒÜêÞÈÜã-âÛßßÒêÛ~Üã (ê.Ò. Ñ,ÛâÛê êãÞÈÝã ãê ââêãflÜÛfl R, Üã ÜÒ ãê Üä,ÞÒÜÛfl âßÒÒÜÛfl ÛÑ êã~ÝÛ O). ùêßÒêÛß, ~êã äãÞë~ÒÜÜÀÒ âäÒÒÞÒÜÛfl ,ÜÛßÜÛfl Ý~Òâê,ÒÜÜã âããê,Òêâê,ëê ÝâäÒÛßÒÜêÞÈÜÀß ÒÑëÞÈêêß áÚ. õÜ,,ëÜ Û û. ÿÛÞÞÛ [28-30], ÛââÞÒã,,?Ûi ßÒêããß ×ø Ñ,ÛâÛßãâêÈ ,ÜÛßÜÛfl Ý ÑÛêÒÞÈÜÀß âêÛßëÞß (,âäÀ?Ýß) ãê ââêãflÜÛfl ã éãÝëâ ,ÜÛßÜÛfl, êÝÚÒ ÒÑëÞÈêêß ÷.ð. ?ëäÛÝã,ãØ [22], ÛââÞÒã,,?ÒØ ÛÜßÛÝë êÝãØ Ñ,ÛâÛßãâêÛ ßÒêããß ÛÑßÒÒÜÛfl ×ú. × âÞÒëÒß ÑÒÞÒ äã,ÒflÒêâfl ÝãÞÛ~Òâê,ÒÜÜãÒ âããê,Òêâê,ÛÒ äÒÞ,,ÒßãØ ßãÒÞÛ ÒÑëÞÈêêß ÇãêÀ [22]. 3. ôùóð?æûý×æ÷÷Ô? õæúÔ ×÷ðõÔ÷ð?: ×÷ðõÔ÷ðæ ð ×ùñÕüáðõùûý? × ÇãêÒ [22] ÛÑÞãÚÒÜÀ ÒÑëÞÈêêÀ ÝâäÒÛßÒÜêÞÈÜã,,ã ÛââÞÒã,ÜÛfl ÛÑßÒÜÒÜÛfl ,ãÑr - -------------2 D(t)
2

ÇëÛßãâêÛ ÑÞÛ~ÜÀi äëÜÝêã, ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã , äã^ÒââÒ ^ÒÞÒÜä,ÞÒÜÜã,,ã ,ãâäÛflêÛfl ÛâäÀêëÒßÀß ÑÛêÒÞÈÜã,,ã âêÛßëÞ. øãÝÑÜã, ~êã , Ü~ÞÒ äã^Òââ ,ãâäÛflêÛfl ÛßÒÒê ßÒâêã äã,À?ÒÜÛÒ ,ãÑÇëÛßãâêÛ ÜÒ êãÞÈÝã , äãÞãÚÛêÒÞÈÜãß äëÜÝêÒ ÜÞÛÑêã (ê.Ò. , êã~ÝÒ ù äãÒÝ^ÛÛ âêÛßëÞ , øø), Üã , â,ÜÛêÒÞÈÜã ?ÛãÝãØ ãÇÞâêÛ ÜÞÛÑêã (øø) ,ãÝë,, äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê. û êÒ~ÒÜÛÒß ,ÒßÒÜÛ äã,À?ÒÜÛÒ ,ãÑÇëÛßãâêÛ äãâêÒäÒÜÜã ÝãÜ^ÒÜêÛëÒêâfl , êã~ÝÒ O. øã^Òââ ÝãÜ^ÒÜê^ÛÛ ÑÜÛßÒê 250-600 ßâ. ÷ÒêëÜã ,ÛÒêÈ (âß. Ûâ. 1), ~êã êÝfl âÛêë^Ûfl âããê,Òêâê,ëÒê â,ãØâê,ß éëÜÝ^ÛÛ (9) Ü äÒ,ãß êäÒ äã^Òââ ,ãâäÛflêÛfl. × êÇÞ. 1 äÛ,ÒÒÜÀ ÝâäÒÛßÒÜêÞÈÜÀÒ ÑÜ~ÒÜÛfl ,ãÑÇëÛßãâêÛ ÝãÜÝÒêÜã,,ã ÛâäÀêëÒßã,,ã (ø.×.) Ü ÑÞÛ~ÜÀi ââêãflÜÛfli*R ãê äãÒÝ^ÛÛ âêÛßëÞ O , äãâÞÒã,êÒÞÈÜÀÒ ßãßÒÜêÀ ,ÒßÒÜÛ, ãêâ~ÛêÀ,ÒßÀÒ ãê ßãßÒÜê ÒØâê,Ûfl âêÛßëÞ. ×ãÑÇëÛßãâêÈ ,À~ÛâÞflÞâÈ äã éãßëÞÒ [23] 1 B = -- , (11)

,,Ò - ×ú Ü êÒâêÛëÛØ ÑÛêÒÞÈÜÀØ âêÛßëÞ. × Ý~Òâê,Ò ÛâäãÞÈÑã,ÞÛâÈ âÒÜÛÒ äã ÜÒâÝãÞÈÝÛß ÛÑßÒÒÜÛflß ÑÜ~ÒÜÛfl ×ú, ~âêÛ~Üã ,ÑflêÀÒ** ÛÑ êÇÞ. 3 ÇãêÀ [22, â. 168], ~âêÛ~Üã ÛÑßÒÒÜÜÀÒ äã Ûâ. 3, [22, â. 171]. úââêãflÜÛÒ R ÛÑßÒflÒêâfl , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i, äÛ~Òß Ñ ÒÛÜÛ^ë äÛÜÛßÒêâfl ââêãflÜÛÒ
* ðÜÒÝâ "" ãÑÜ~Òê - "ÝâäÒÛßÒÜêÞÈÜãÒ". **ùêßÒêÛß, ~êã , ÇãêÒ [22] ãäëÒÜ ãäÒ~êÝ

(äÒ,ÀØ ÞÒßÒÜê äãâÞÒÜÒØ âêãÝÛ êÇÞ. 3): âÒÜÒÒ ×ú , äãÞãÚÛêÒÞÈÜãß äëÜÝêÒ ÜÞÛÑêã , ßãßÒÜê ,ÒßÒÜÛ t = 300 ßâ ,ÒÜ = 327 ßâ, ÜÒ 335 ßâ, ÝÝ ëÝÑÜã , ÇãêÒ [22]. × êãß ßãÚÜã ëÇÒÛêÈâfl, ,À~ÛâÞÛ, âÒÜÒÒ ÛéßÒêÛ~ÒâÝãÒ ×ú, äãÞë~ÒÜÜÀi , ãêÒÞÈÜÀi ãäÀêi Û äÛ,ÒÒÜÜÀi , êãØ ÚÒ êÇÞ. 3 ÇãêÀ [22].

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


744

,,ÞâÝã

ãê äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê ÜÞÛÑêã ã ÇÞÛÑÞÒÚÛi ÛÜÛééÒÒÜêÜÀi äëÜÝêã, (, êÒßÛÜãÞã,,ÛÛ ÇãêÀ [22]). áÞfl âÒÜÒëÞÒÜÜÀi äëÜÝêã, R = 2, Þfl ÞÒÝããêâê,ÞÒÜÜÀi R = 3, Þfl âßã,,ã äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê (äãÒÝ^ÛÛ âêÛßëÞ O) R = 0. úââêãflÜÛfl ãê ÛÜÛééÒÒÜêÜÀi äëÜÝêã, ÜÞÛÑêã ãÜãØ ,,ëääÀ ã äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê â~Ûêêâfl äÛßÒÜã ãÛÜÝã,ÀßÛ. ùÇãÑÜ~Ûß ~ÒÒÑ r ,ÒÞÛ~ÛÜë ãêÝÞãÜÒÜÛfl ÛÜÛééÒÒÜêÜã,,ã äëÜÝê ÜÞÛÑêã (âããê,Òêâê,ëÒØ êã~ÝÛ øø) ãê äãÞãÚÛêÒÞÈÜã,,ã (O): r = ÁR. ?êãÇÀ â,flÑêÈ ãêÜãâÛêÒÞÈÜãÒ ââêãflÜÛÒ r, éÛ,,ëÛëÒÒ , ë,ÜÒÜÛÛ ,ãâäÛflêÛfl (8), â ââêãflÜÛÒß r ,,ÒÒß ßâ?êÇÜÀØ ßÜãÚÛêÒÞÈ Mr r = M r r . ðÑßÒÒÜÛÒ ×ú Ü êÒâêÛëÛÒ âêÛßëÞÀ fl,ÞflÒêâfl ?ÛãÝã âäãâêÜÒÜÜÀß ßÒêããß ÛÑë~ÒÜÛfl ,ÜÛßÜÛfl. ûãÝÒÜÛÒ ×ú ëÝÑÀ,Òê Ü ëâÛÞÒÜÛÒ (äÛâëêâê,ÛÒ) ,ÜÛßÜÛfl [15]. ýÝ, , ßÜã,,ã~ÛâÞÒÜÜÀi ÝâäÒÛßÒÜêi ÇãêÀ [23] äãÝÑÜã, ~êã äÛ,ÞÒ~ÒÜÛÒ ,ÜÛßÜÛfl Ý âêÛßëÞë, ÜäÛßÒ â äãßãÈ âÞã,ÒâÜÀi ÛÜâêëÝ^ÛØ, ,ÒÒê Ý âãÝÒÜÛ ×ú. á. ó ÕÒ,, [27] , ÝâäÒÛßÒÜêi äã ãÇãâÜã,ÜÛ äãÚÒÝêãÜãØ êÒãÛÛ ,ÜÛßÜÛfl ?. ýÒØâßÜ êÝÚÒ ãäÛÞâfl Ü âãÝÒÜÛÒ ×ú Ü êÒâêÛëÛÒ ÑÛêÒÞÈÜÀÒ âêÛßëÞÀ. ø,, ,âÞÒâê,ÛÒ äÛÜ^Ûäã, äãÚÒÝêãÜãØ êÒãÛÛ, á. ó ÕÒ,, ÜÒ ÛÑßÒflÞ ,ÒÞÛ~ÛÜë ,ÜÛßÜÛfl êÝÛß ãÇÑãß, â~ÛêÞ, ~êã êß, ,,Ò ÒâêÈ ,ÜÛßÜÛÒ, ×ú ßÒÜÈ?Ò, êß, ,,Ò Ò,,ã ÜÒê, - ÇãÞÈ?Ò. áÚ. õÜ,,ëÜ Û û. ÿÛÞÞÛ [31] ÛâäãÞÈÑã,ÞÛ ×ú , Ý~Òâê,Ò ÛÜÛÝêã âêÒäÒÜÛ âäÒÒÞÒÜÛfl ÑÛêÒÞÈÜã,,ã ,ÜÛßÜÛfl ßÒÚë ÞÒ,Àß Û ä,Àß äãÞÒß ÑÒÜÛfl. × ÜâêãflÒØ ÇãêÒ äÒÞ,,Òêâfl â,flÑêÈ ÝãÞÛ~Òâê,ÒÜÜë ßÒë ,ÜÛßÜÛfl - äÞãêÜãâêÈ ,ÜÛßÜÛfl I(r, t) - ÝÝ éëÜÝ^Û äãâêÜâê, (øø) Û ,ÒßÒÜÛ â ×ú Ü âããê,Òêâê,ëÛØ êÒâêÛëÛØ âêÛßëÞ (,âäÀ?Ýë , âããê,Òêâê,ëÒØ êã~ÝÒ ÝÜ). ×ÜÛßÜÛÒ ÜiãÛêâfl , ãÇêÜãØ Ñ,ÛâÛßãâêÛ ãê ×ú Û, âÞÒã,êÒÞÈÜã, , äflßãØ Ñ,ÛâÛßãâêÛ ãê ,ãÑÇëÛßãâêÛ âããê,Òêâê,ëÒ,,ã äëÜÝê ÜÞÛÑêã. ùÜÝã ÜÒäãâÒâê,ÒÜÜã ãêãÚÒâê,ÛêÈ äÞãêÜãâêÈ ,ÜÛßÜÛfl I(r, t) â ,ãÑÇëÛßãâêÈ B(r, t) ÛÞÛ äãäã^ÛãÜÞÈÜãØ ÒØ ,ÒÞÛ~ÛÜãØ ÜÒÞÈÑfl. áÒØâê,ÛêÒÞÈÜã, ,ãÑÇëÛßãâêÈ ÜÒ ,Ü ÜëÞ ÜÛ , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ t = 0, ÜÛ Ü ÇãÞÈ?Ûi ââêãflÜÛfli ãê äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê ÜÞÛÑêã (,,Ò ,ÞÛflÜÛÒ âêÛßëÞ éÝêÛ~ÒâÝÛ ãêâëêâê,ëÒê). ûëÒâê,ëÒê ÜÒÝãêãÀØ "ÜãßÞÈÜÀØ" ("ÛÜÛééÒÒÜêÜÀØ") ëã,ÒÜÈ ,ãÑÇëÛßãâêÛ B0. × ÒÑëÞÈêêÒ ÒØâê,Ûfl âêÛ-

ßëÞ (,ÀÑ,ÜÜÀi êÛß ÒØâê,ÛÒß äâÛiãéÛÑÛãÞã,,Û~ÒâÝÛi äã^Òââã,) ,ãÑÇëÛßãâêÈ ãêÝÞãÜflÒêâfl ãê êã,,ã ëã,Üfl (, ÑÞÛ~ÜÀi êã~Ýi ÜÞÛÑêã Ü ÑÜë ,ÒÞÛ~ÛÜë). × ãêâëêâê,ÛÒ ÚÒ âêÛßëÞ ÛÞÛ Ü ÇãÞÈ?Ûi ââêãflÜÛfli ãê äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê ,ãÑÇëÛßãâêÈ ,Ü B0. × êã ÚÒ ,Òßfl äÞãêÜãâêÈ ,ÜÛßÜÛfl, ãäÒÒÞÒÜÜfl ,ÒÜâê,ãß (9), , Ü~ÞÈÜÀØ ßãßÒÜê ,ÒßÒÜÛ (t = 0) ,Ü ÜëÞ ,ã ,âÒß øø (â ßêÒßêÛ~ÒâÝãØ êã~ÝÛ ÑÒÜÛfl ÇãÞÒÒ êã~Üã âÝÑêÈ, ~êã ê éëÜÝ^Ûfl âêÒßÛêâfl Ý ÜëÞ äÛ t, âêÒßflÒßâfl Ý ÜëÞ). ýã~Üã êÝ ÚÒ éëÜÝ^Ûfl I(r, t) ÇëÒê (äÛßÒÜã) ,Ü ÜëÞ Ü ÇãÞÈ?Ûi ââêãflÜÛfli ãê êã~ÝÛ O. ùäÒÒÞÛß äÞãêÜãâêÈ ,ÜÛßÜÛfl , êã~ÝÒ x øø , ßãßÒÜê ,ÒßÒÜÛ t ÝÝ ,ÒÞÛ~ÛÜë, äãäã^ÛãÜÞÈÜë ÇâãÞêÜãØ ßÒÒ ãêÝÞãÜÒÜÛfl ,ãÑÇëÛßãâêÛ B(r) âããê,Òêâê,ëÒ,,ã äëÜÝê ÜÞÛÑêã , êãê ßãßÒÜê ,ÒßÒÜÛ ãê ÛÜÛééÒÒÜêÜã,,ã ëã,Üfl B0 [4] I ( r, t ) = M B ( B ( r , t ) - B 0 ) , (12) ,,Ò MB - ÑßÒÜÀØ äãâêãflÜÜÀØ ÝãééÛ^ÛÒÜê (ßâ?êÇÜÀØ ßÜãÚÛêÒÞÈ ,ãÑÇëÛßãâêÛ). × Ý~Òâê,Ò äÛÇÞÛÚÒÜÜã,,ã ÑÜ~ÒÜÛfl B0 äÛßÒß ,ãÑÇëÛßãâêÈ ÞÒÝããêâê,ÞÒÜÜÀi ÛÜÛééÒÒÜêÜÀi äëÜÝêã, ÜÞÛÑêã*. ûßë ÑÜãâêÈ ( r , t ) = B ( r , t ) - B
0

(12.1)

ÜÑã,Òß Þfl ÝêÝãâêÛ äÛÒÜÛÒß ,ãÑÇëÛßãâêÛ. ÷ Ûâ. 2 äÒâê,ÞÒÜÀ [4] ÒÑëÞÈêêÀ ääãÝâÛß^ÛÛ âäÒÒÞÒÜÛØ äÛÒÜÛfl ,ãÑÇëÛßãâêÛ (ÝëÚÝÛ) ,ÜëêÛ ãÇÞâêÛ ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã (R 3) , ÑÞÛ~ÜÀÒ ßãßÒÜêÀ ,ÒßÒÜÛ éëÜÝ^ÛflßÛ (âäÞã?ÜÀÒ ÝÛ,ÀÒ) 1 G ( r ) = ---------- e ~ 2 D
r - ------~ 2D
2

,

(13)

~ â ÑÞÛ~ÜÀßÛ ÑÜ~ÒÜÛflßÛ äßÒê D . øÛ êãß ÛâäãÞÈÑã,ÞÛâÈ âÞÒëÛÒ ÑÜ~ÒÜÛfl ßâ?êÇÜÀi ßÜãÚÛêÒÞÒØ: Mr 15.7, MB 75.2 â.
ðâÝÞ~ÒÜÛÒ ÇÀÞã âÒÞÜã Þfl ßãßÒÜê ,ÒßÒÜÛ t = 140 ßâ, Þfl Ýãêãã,,ã , Ý~Òâê,Ò B0 ÇÀÞã ,ÀÇÜã ÑÜ~ÒÜÛÒ ,ãÑÇëÛßãâêÛ , âÒÜÒëÞÒÜÜãß ÛÜÛééÒÒÜêÜãß äëÜÝêÒ ÜÞÛÑêã. ?êã ãÇëâÞã,ÞÒÜã êÒß, ~êã (äã-,ÛÛßãßë, ÛÑ-Ñ âÞë~ØÜãØ äã,,Ò?ÜãâêÛ ÛÑßÒÒÜÛØ) , êãê ßãßÒÜê ,ÒßÒÜÛ ,ãÑÇëÛßãâêÈ , ÞÒÝããêâê,ÞÒÜÜãß ÛÜÛééÒÒÜêÜãß äëÜÝêÒ ~ëêÈ ÇãÞÈ?Ò ,ãÑÇëÛßãâêÛ , âÒÜÒëÞÒÜÜãß (âß. êÇÞ. 2), êÝ ~êã ÛßÒÜÜã âÒÜÒëÞÒÜÜÀØ ÛÜÛééÒÒÜêÜÀØ äëÜÝê âÞÒëÒê ââßêÛ,êÈ , Ý~Òâê,Ò "ÜÛÇãÞÒÒ ÛÜÛééÒÒÜêÜã,,ã".
*

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5

745

-4 -3 -2 -1 0 1 2 3 4 5 Ç

-4 -3 -2 -1 0 1 2 3 4 5 Ò

-4 -3 -2 -1 0 1 2 3 4 5 ,

-4 -3 -2 -1 0 1 2 3 4 5 Ú

-4 -3 -2 -1 0 1 2 3 4 5 ,,

-4 -3 -2 -1 0 1 2 3 4 5 Ñ

-4 -3 -2 -1 0 1 2 3 4 5

-4 -3 -2 -1 0 1 2 3 4 5

úÛâ. 2. ÔääãÝâÛß^Ûfl âäÒÒÞÒÜÛØ äÛÒÜÛfl ,ãÑÇëÛßãâêÛ ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã , äãâÞÒã,êÒÞÈÜÀÒ ßãßÒÜêÀ ,ÒßÒÜÛ (t) âäÒÒÞÒÜÛflßÛ (13). - 140 ßâ; Ç - 170 ßâ; , - 200 ßâ; ,, - 250 ßâ; - 300 ßâ; Ò - 350 ßâ; Ú - 400 ßâ; Ñ - 500 ßâ; Û - 700 ßâ; Ý - 900 ßâ; Þ - 1200 ßâ. øã ãâÛ Çâ^Ûââ ãêÝÞÀ,Òêâfl ,ÒÞÛ~ÛÜ ãêÝÞãÜÒÜÛfl ãê äãÞãÚÛêÒÞÈÜã,,ã äëÜÝê ÜÞÛÑêã r (, ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i), äã ãâÛ ãÛÜê - äÛÒÜÛÒ ,ãÑÇëÛßãâêÛ , 1/â. úÛâëÜãÝ ÒßãÜâêÛëÒê âãiÜÒÜÛÒ ÝãÞÛ~Òâê, ,ÜÛßÜÛfl. Fig. 2. The approximation of the distributions of the change in the excitability of the visual analyzer in different moments of the time (t) by the distributions (13). - 140 ßâ; Ç - 170 ßâ; , - 200 ßâ; ,, - 250 ßâ; - 300 ßâ; Ò - 350 ßâ; Ú - 400 ßâ; Ñ - 500 ßâ; Û - 700 ßâ; Ý - 900 ßâ; Þ - 1200 ßâ. Axial of the abscissa lay off the magnitude of the deviation from the positive point of the analyzer re (in the relative unit), axial of the ordinate - the increment of the excitability , 1/s. The figure demonstrate of the conservation of the attention.
ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


746 Û 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 -4 -3 -2 -1 0 1 Ý 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 -4 -3 -2 -1 0 1 1.0 Þ 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -5 -4 -3 -2 -1 0 1

,,ÞâÝã

2

3

4

5

Ü. ùÜÝã, ÝÝ ÛÑ,ÒâêÜã, ÛÜêÒ,,Þ éëÜÝ^ÛÛ ~ (13) äã äãâêÜâê,ë ÜÒ Ñ,ÛâÛê ãê D . øãêãßë âÝÑÜÜãÒ ãÑÜ~Òê, ~êã ÛÜêÒ,,Þ äÛÒÜÛfl ,ãÑÇëÛßãâêÛ, ê.Ò. äÞãêÜãâêÛ ,ÜÛßÜÛfl I(r, t), äã ââßêÛ,ÒßãØ ãÇÞâêÛ ( êã ÜÒ ~êã ÛÜãÒ, ÝÝ ÝãÞÛ~Òâê,ã ,ÜÛßÜÛfl , ÜÜãØ ãÇÞâêÛ) ãÛÜÝã, , ÑÜÀÒ ßãßÒÜêÀ ,ÒßÒÜÛ, ê.Ò. ÝãÞÛ~Òâê,ÒÜÜã äãê,ÒÚÒê ,,ÛäãêÒÑë ã âãiÜÒÜÛÛ ,ÜÛßÜÛfl , ÞãÝÞÈÜãß âßÀâÞÒ (ê.Ò. , äÒÒÞi ãâêêã~Üã ßÞãØ ãÇÞâêÛ øø , êÒ~ÒÜÛÒ ãâêêã~Üã ßÞã,,ã äãßÒÚëêÝ ,ÒßÒÜÛ). ~ × êÇÞ. 2 äÛ,ÒÒÜ Ñ,ÛâÛßãâêÈ D (t), âããê,Òêâê,ëfl ääãÝâÛß^ÛÛ, äÒâê,ÞÒÜÜãØ Ü Ûâ. 2. ×ÛÜã, ~êã ê Ñ,ÛâÛßãâêÈ âããê,Òêâê,ëÒê ãäÛâÜÜãØ ÜÒÒ Ý~Òâê,ÒÜÜãØ ÑÝãÜã~ ßÒÜãâêÛ: âÜ~Þ éëÜÝ^Ûfl D (t) ëÇÀ,Òê (~êã âããê,Òêâê,ëÒê ÝãÜ^ÒÜê^ÛÛ ,ÜÛßÜÛfl), ÑêÒß Ü~ÛÜÒê ,ãÑâêêÈ (,ÜÛßÜÛÒ ââÒÛ,Òêâfl). ÷ Ûâ. 3 ê Ñ,ÛâÛßãâêÈ äÒâê,ÞÒÜ ,,éÛ~ÒâÝÛ (ÝëÚÝÛ). ûäÞã?Üfl ÞÛÜÛfl Ü Ûâ. 3 ãêÚÒê êÒãÒêÛ~ÒâÝë Ñ,ÛâÛßãâêÈ (10), âããê,Òêâê,ëë ÑÜ~ÒÜÛflß äßÒêã, = 16, 118 ßâ, '0 = 1.25 ç 10-3 (äßÒê '0 , iÝêÒÛÑëÛØ ßãÞÈÜãâêÈ ,ãâäÛflêÛfl, ãäÒÒÞÒÜ , ÑÒÞÒ 5). ù~Ò,ÛÜã, ~êã ê ÝÛ,fl ãâêêã~Üã ÜÒäÞãiã ääãÝâÛßÛëÒê ÝâäÒÛ~ ßÒÜêÞÈÜÀÒ ÑÜ~ÒÜÛfl D (t). øã äã,ãë ,ÀÇã ÑÜ~ÒÜÛfl äßÒê ãêßÒêÛß âÞÒëÒÒ. û ãÜãØ âêããÜÀ, , ÇãêÒ [22] ÛÜêÒÜâÛ,ÜãâêÈ ÜÒ ëÝÑÜ. û ë,,ãØ âêããÜÀ, äãâÝãÞÈÝë äßÒê , éÛ,,ëÛëÛØ , ë,ÜÒÜÛÛ (8), äÒâê,ÞflÒê ÛÜêÒÜâÛ,ÜãâêÈ , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i, êã ÑÜêÈ ÝâäÒÛßÒÜêÞÈÜë ,ÒÞÛ~ÛÜë ÛÜêÒÜâÛ,ÜãâêÛ ÜÒê ÜÒãÇiãÛßãâêÛ. ýÝÛß ãÇÑãß, ãÝÑÀ,Òêâfl â,ãÇãÜÀß äßÒêãß ßãÒÞÛ. ñÜ~ÒÜÛÒ ÚÒ äßÒê '0 (ÝâêêÛ, ÑßÒêÜã ,ÞÛflÒÒ Ü éãßë êÒãÒêÛ~ÒâÝãØ ÝÛ,ãØ D(t)) âããê,Òêâê,ëÒê ,ãâäÛflêÛ flÝãâêÛ â,Òê êã~Ò~Üã,,ã Ûâêã~ÜÛÝ , ëâÞã,Ûfli êÒßÜã,ãØ äê^ÛÛ (âß. ÑÒÞ 5).

2

3

4

5

2

3

4

5

úÛâ. 2. ùÝãÜ~ÜÛÒ.

õÜãÚÛêÒÞÛ M r Û M B ,ÀÇÛÞÛâÈ êÝ, ~êãÇÀ äãÞë~ÛêÈ ÝÝ ßãÚÜã Þë~?ë ääãÝâÛß^Û âäÒÒÞÒÜÛfl (r) , ßãßÒÜê ,ÒßÒÜÛ t = 300 ßâ (Ûâ. 2, ). ù~Ò,ÛÜã, ~êã , ^ÒÞãß ääãÝâÛß^Ûfl Ûâ. 2 ãâêêã~Üã ëÇÒÛêÒÞÈ-

~ ýÇÞÛ^ 2. ñ,ÛâÛßãâêÈ D (t), âããê,Òêâê,ëfl ääãÝâÛß^ÛÛ ÝâäÒÛßÒÜêÞÈÜÀi âäÒÒÞÒÜÛØ äÛÒÜÛfl ,ãÑÇëÛßãâêÛ Ü Ûâ. 2 ~ Table 2. The dependence D (t), correspondents to the approximation of experimental distributions of the change in the excitability on the fig. 2 t, ßâ ~ D 140 0.0170 170 0.0039 200 0.0038 250 0.0037 300 0.0033 350 0.0029 400 0.0028 500 0.0026 700 0.0023 900 0.0047 1200 0.0050

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

747

× ÇãêÒ [13] äã,ÒÒÜã â,ÜÒÜÛÒ äÒâÝÑÜÛØ äÒÞ,,ÒßãØ ßãÒÞÛ â ÛÜßÛÝãØ ,ãÑÇëÛßãâêÛ ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã Þfl ,âÒi ë,,Ûi ÛâäÀêëÒßÀi ÇãêÀ [22]. × ^ÒÞãß ÒÑëÞÈêêÀ â,ÜÒÜÛfl ,,ã,ãflê , äãÞÈÑë ÒÝ,êÜãâêÛ ßãÒÞÛ. ùêßÒêÛß, ~êã äßÒêÀ ßãÒÞÛ , MB Û Mr ÑÞÛ~ÜÀ Þfl ÑÜÀi ÛâäÀêëÒßÀi Û iÝêÒÛÑëê Ûi ÛÜÛ,ÛëÞÈÜÀÒ ãâãÇÒÜÜãâêÛ. 4. ×÷ðõÔ÷ðæ ð ×?ñ×Ô÷÷?ò øùýæ÷åðÔó ÿãã?ã ÛÑ,ÒâêÒÜ ßÒêã ÛÑë~ÒÜÛfl ,ÜÛßÜÛfl, ãâÜã,ÜÜÀØ Ü ÛÑßÒÒÜÛÛ ßäÞÛêë ÑÞÛ~ÜÀi ÝãÞÒÇÜÛØ ×ø [15] N1, P1, N2 Û ê.. øÛ êãß ,ÜÛßÜÛÒ â,flÑÀ,Òêâfl â ãêÒÞÈÜÀßÛ ÝãßäãÜÒÜêßÛ ×ø, êÝÛßÛ ÝÝ ÜÒ,,êÛ,ÜãâêÈ ââã,,Þâã,ÜÛfl (÷ú) Û äã^ÒââÜfl ÜÒ,,êÛ,ÜãâêÈ (ø÷). ×ãÞÜ ÷ú âããê,Òêâê,ëÒê ÜÒäãÛÑ,ãÞÈÜãßë ,ÜÛßÜÛ, ,ãÞÜ ø÷ - äãÛÑ,ãÞÈÜãßë. øÛ êãß ÜÒäãÛÑ,ãÞÈÜãÒ ,ÜÛßÜÛÒ â,flÑÀ,Òêâfl â ÒÝ^ÛÒØ Ü Üã,ÛÑÜë âêÛßëÞ. × ÜâêãflÒØ ÇãêÒ äÒÞ,,Òêâfl ââßêÛ,êÈ ,ÜÛßÜÛÒ ÝÝ éëÜßÒÜêÞÈÜë éëÜÝ^Û, iÝêÒÛÑëë ÞÇãØ äã^Òââ ,ãâäÛflêÛfl. ôÚÀØ ,ãâäÛÜÛßÒßÀØ (âãÑÜêÒÞÈÜã ÛÞÛ ÇÒââãÑÜêÒÞÈÜã) âêÛßëÞ äÛ,ÞÒÝÒê Ý âÒÇÒ ,ÜÛßÜÛÒ (ÇãÞÈ?ÒÒ ÛÞÛ ßÒÜÈ?ÒÒ). ûêÛßëÞ, ÜÒ äÛ,ÞÒÝÛØ ,ÜÛßÜÛfl, ÜÒ ,ãâäÛÜÛßÒêâfl (ÜÒ ,ÀÑÀ,Òê ÜÛÝÝÛi äâÛiãéÛÑÛãÞã,,Û~ÒâÝÛi äã^Òââã, ,ããÇÒ). × ÞÇãØ ßãßÒÜê ,ÒßÒÜÛ ,ÜÛßÜÛÒ âäÒÒÞÒÜã äã ,âÒßë ßÜãÚÒâê,ë âêÛßëÞã,, ãâêëäÜÀi ,ãâäÛflêÛ ( êÝÚÒ äã ßÜãÚÒâê,ë ",ÜëêÒÜÜÛi" âêÛßëÞã,, ,,ÒÜÒÛëÒßÀi âßÛß ßãÑ,,ãß). ×ÜÛßÜÛÒ ÝÝ ^ÒÞãÒ (,ÝÞ~fl äãÛÑ,ãÞÈÜãÒ Û ÜÒäãÛÑ,ãÞÈÜãÒ), ãäÛâÀ,Òêâfl ãÜãØ éëÜÝ^ÛÒØ I(x, t) Û ê éëÜÝ^Ûfl â,flÑÀ,Òêâfl â ßäÞÛêëãØ ×ø ÝÝ éëÜÝ^ÛÒØ ,ÒßÒÜÛ. æâêÒâê,ÒÜÜã, ê éëÜÝ^Ûfl âãÒÚÛê ,ÝÞÀ ÑÞÛ~ÜÀi äã^Òââã,, , ~âêÜãâêÛ ÷ú Û ø÷. û,ÜÒÜÛÒ Ò?ÒÜÛfl ë,ÜÒÜÛfl (8) â ÝâäÒÛßÒÜêÞÈÜÀßÛ ÜÜÀßÛ ÒßãÜâêÛëÒê äãëÝêÛ,ÜãâêÈ êÝã,,ã äãiã. × âããê,Òêâê,ÛÛ â éãßëÞßÛ (9), (10), , äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÒ?ÜÒ,,ã âêÛßëÞ ,ÜÛßÜÛÒ ÛâäÀêëÒßã,,ã âÜ~Þ ÝãÜ^ÒÜêÛëÒêâfl Ü âêÛßëÞÒ, ÑêÒß ââÒÛ,Òêâfl (äã ãêÜã?ÒÜÛ Ý ÜÒßë). ôÝ âÞÒâê,ÛÒ, ,ÜÛßÜÛÒ, ëÒÞflÒßãÒ âêÛßëÞë, âÜ~Þ ,ãÑâêÒê, ÑêÒß ãâêÛ,,Òê ßÝâÛßëß Û Ü~ÛÜÒê ëÇÀ,êÈ t 1 I ( 0, t ) = ----- ------------------------------------ . 2 2 3 + 2 k ( ) t3
2 2

D 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0 500 1200 t, ßâ

úÛâ. 3. û,ÜÒÜÛÒ êÒãÒêÛ~ÒâÝãØ Û ÝâäÒÛßÒÜêÞÈÜãØ Ñ,ÛâÛßãâêÒØ D(t). ôëÚÝÛ äÒ~ âê,Þflê ÑÜ~ÒÜÛfl D (t), âããê,Òêâê,ëÛÒ ÝÛ,Àß Ü Ûâ. 2 (êã ÝâäÒÛßÒÜêÞÈÜÀÒ ÑÜ~ÒÜÛfl), âäÞã?Üfl ÞÛÜÛfl äÒâê,ÞflÒê êÒãÒêÛ~ÒâÝë Ñ,ÛâÛßãâêÈ (10). Fig. 3. The compare of the theoretical dependence D(t) and the experimental it. The small circles repre~ sent values of the function D (t), correspondent to curves on the fig. 2 (that is experimental values). The firm line represent the theoretical dependence (10).

øããÇÜfl ÛÜßÛÝ iÝêÒÜ Û Þfl ßäÞÛêëÀ ×ø. øÛ,ÒÒß ÜÒâÝãÞÈÝã äÛßÒã,. ÷ Ûâ. 4, Û Ç (âÞÒ,) äÒâê,ÞÒÜÀ âÞëiã,ÀÒ ×ø, ,ÑflêÀÒ ÛÑ Çãê [18] Û [25] âããê,Òêâê,ÒÜÜã. ÷ Ûâ. 4, , (âÞÒ,) äÒâê,ÞÒÜ ×ø , ãê,Òê Ü âãßêãâÒÜâãÜÀØ âêÛßëÞ, ,ÑflêÀØ ÛÑ ÇãêÀ [17]. ùêßÒêÛß, ~êã ,ã ,âÒi äÛ,ÒÒÜÜÀi äÛßÒi ÇãÞÒÒ ÛÞÛ ßÒÜÒÒ ~ÒêÝã ,ÀäãÞÜflÒêâfl ÒÒ ãÜ ÑÝãÜãßÒÜãâêÈ: ~âêãê ÝãÞÒÇÜÛØ ßãÜãêãÜÜã ëÇÀ,Òê, ê.Ò. ,ÒßÒÜÜ ÀÒ ÛÜêÒ,Ä ÞÀ ßÒÚë äÛÝßÛ âêëê. æâêÒâê,ÒÜÜã äÒäãÞãÚÛêÈ, ~êã ãâê ßäÞÛêëÀ ×ø , Ü~ÞÒ äã^Òââ ,ãâäÛflêÛfl ãÇflâÜflÒêâfl ëâÛÞÒÜÛÒß ,ÜÛßÜÛfl Ý âêÛßëÞë Ü äÒ,ãß êäÒ êã,,ã äã^Òââ, äãâÞÒëÛØ âä ßäÞÛêëÀ - ãâÞÇÞÒÜÛÒß ,ÜÛßÜÛfl Ý ÜÒßë Ü ,êããß êäÒ. ðÑ âããÇÚÒÜÛØ äãâêãêÀ äÒäãÞãÚÛß, ~êã ßäÞÛêë ×ø a(t) äãäã^ÛãÜÞÈÜ äÞãêÜãâêÛ ,ÜÛßÜÛfl , êã~ÝÒ äãÒÝ^ÛÛ âêÛßëÞ , øø t a ( t ) = I ( 0, t ) = ----- ------------------------------------ , (15) 3 2 2 + 2 k ( ) t3
2 2

(14)

,,Ò - äãâêãflÜÜÀØ ÝãééÛ^ÛÒÜê (ÛÑßÒflÒßÀØ , ßÛÝã,ãÞÈêi). øÛ êãß Ò~È ßãÚÒê

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


748

,,ÞâÝã
50 ßÝ× P1 25 P0 0 -25 -50 ßÝ× N2 Ç N2 25 ßÝ× N1 P1 P3 P2 1â N3 -3 N1 1â N3 P2 , ßÝ× 90 80 70 60 50 40 30 20 10 0 , ßÝ× 80 70 60 50 40 30 20 10 0 1000 , ãêÜ. Ò. 7 6 5 4 3 2 1 500 500 ßâ 0 500 1000 1500 2000 t, ßâ 2000 3000 t, ßâ 1000 2000 3000 t, ßâ

,

úÛâ. 4. áÛÜßÛÝ ßäÞÛêëÀ ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ. ûÞÒ,: ëâÒÜÒÜÜÀØ ×ø. - âÞëiã,ãØ ×ø ÛÑ ÇãêÀ [18] (âêÛßëÞ - êãÜã,fl äãâÀÞÝ); Ç - âÞëiã,ãØ ×ø ÛÑ ÇãêÀ [25] (cêÛßëÞ - ÒÞ~ãÝ); , - âãßêãâÒÜâãÜÀØ ×ø ÛÑ ÇãêÀ [17]. ûä,: ÛÑßÒÜÒÜÛÒ ßäÞÛêëÀ ×ø â êÒ~ÒÜÛÒß ,ÒßÒÜÛ. ûäÞã?Üfl ÞÛÜÛfl - êÒãÒêÛ~ÒâÝfl ÝÛ,fl, ÝëÚÝÛ - ÝâäÒÛßÒÜêÞÈÜÀÒ ÑÜ~ÒÜÛfl. Fig. 4. The dynamics of the amplitude of the evoked potential. Left: the averaged evoked potential. a - auditory evoked potential from [18] (stimulus - the tone burst); Ç - auditory evoked potential from [25] (stimulus - the click); , - somatosensory evoked potential from [17]. Right: evolution of the amplitude of the evoked potential. The firm line - the theoretical curve, the small circles - experimental values.

ÛêÛ ÝÝ ã ×ø, ÜÒäãâÒâê,ÒÜÜã ÛÜÛ^ÛÛã,ÜÜãß ÒØâê,ÛÒß âêÛßëÞ, êÝ Û ã ×ø , ââã^ÛêÛ,ÜÀi ãÇÞâêfli ÝãÀ. × äãâÞÒÜÒß âÞë~Ò - êã, ,ãÑßãÚÜã, ëÚÒ ÜÒ ÛÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ (âß. ÑÒÞ 2), x = 0 - êã~Ý äãÒÝ^ÛÛ ",ÜëêÒÜÜÒ,,ã" âêÛßëÞ , øø. û ë~Òêãß âÝÑÜÜã,,ã ÜÒÒ ,,ÛäãêÒÑ (15) ,ÜãâÛÞÈÜ äÒäãÞãÚÒÜÛ ã â,flÑÛ ßÒÚë ßäÞÛêëãØ ×ø Û ,ãÑ-

ÇëÛßãâêÈ (,ÒãflêÜã, ,ãÑÇëÛßãâêÈ ,ÞÛflÒê Ü ×ø). û ë,,ãØ âêããÜÀ, éãßëÞë (15) ßãÚÜã äãÜÛßêÈ Û ÝÝ ãäÒÒÞÒÜÛÒ ÞãÝÞÈÜãØ ßÒÀ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl, ÞÈêÒÜêÛ,ÜãÒ ÒÒ ãäÒÒÞÒÜÛ ~ÒÒÑ ,ãÑÇëÛßãâêÈ (äÛ êãß Ñ,ÛâÛßãâêÈ ,ÜÛßÜÛfl ãê x ßãÚÜã ÛââÞÒã,êÈ Ü ãâÜã,Ò ßÒêãÛÝÛ, ÛâäãÞÈÑëÒßãØ áÚ. õÜ,,ëÜãß Û û. ÿÛÞÞÛãß [30]). ùê-

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

749

ßÒêÛß, ~êã éãßëÞ (15) âããê,Òêâê,ëÒê ÒÑëÞÈêêß ÝâäÒÛßÒÜêÞÈÜÀi ÛââÞÒã,ÜÛØ Ñ,ÛâÛßãâêÛ ßäÞÛêëÀ ×ø ãê ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ . ýÝ, ÛÑ,ÒâêÜã, ~êã ëßÒÜÈ?ÒÜÛÒ ÛÜêÒÜâÛ,ÜãâêÛ Ñ,ëÝã,ã,,ã âêÛßëÞ ,ÒÒê Ý âÜÛÚÒÜÛ ßäÞÛêëÀ Û ãâêë ÞêÒÜ^ÛÛ âÒÜÒÞêÒÜêÜÀi ãê,Òêã, [15, 32, 34]. ?ê éãßëÞ âããê,Òêâê,ëÒê êÝÚÒ ÒÑëÞÈêêß ÛââÞÒã,ÜÛfl ,ÞÛflÜÛfl äãÛÑ,ãÞÈÜã,,ã ,ÜÛßÜÛfl Ü ×ø. ýÝ, iãã?ã ÛÑ,ÒâêÜã [15], ~êã äãÛÑ,ãÞÈÜãÒ ,ÜÛßÜÛÒ äÛ ÑÛêÒÞÈÜãß ,ãâäÛflêÛÛ ,ÒÒê Ý ãâêë ßäÞÛêë ÝãÞÒÇÜÛØ P1, N1 Û N2. × ~âêÜãâêÛ, áÚ. õÜ,,ëÜ Û û. ÿÛÞÞÛ [30], Ò,,ÛâêÛã,,?ÛÒ ×ø , ãê,Òê Ü ÑÛêÒÞÈÜÀÒ âêÛßëÞÀ, äã~ÒÝÛ,ê, ~êã ééÒÝê äãÛÑ,ãÞÈÜã,,ã ,ÜÛßÜÛfl äãfl,ÞflÒêâfl ÝÝ ßäÞÛêëÜfl ßãëÞfl^Ûfl êÛi ÝãÞÒÇÜÛØ ÇÒÑ ÛÑßÒÜÒÜÛfl Ûi ÞêÒÜ^ÛØ, äãÞflÜãâêÛ ÛÞÛ éãßÀ ,ãÞÜÀ. øßÒêÀ Û ßã,,ëê Ñ,ÛâÒêÈ ãê ÛÜÛ,ÛëÞÈÜÀi ãâãÇÒÜÜãâêÒØ âëÇÒÝê ,ãâäÛflêÛfl. ÕëÒß ,ÀÇÛêÈ Ûi ÛÑ ëâÞã,Ûfl ãäêÛßÞÈÜãØ ääãÝâÛß^ÛÛ ÝâäÒÛßÒÜêÞÈÜã ÛÑßÒÒÜÜãØ ßäÞÛêëÀ ×ø êÒãÒêÛ~ÒâÝãØ ÝÛ,ãØ. × äãâêÒØ?Òß âÞë~Ò Þfl äãÞë~ÒÜÛfl iãã?ÒØ ääãÝâÛß^ÛÛ ãâêêã~Üã äãêÒÇã,êÈ âã,äÒÜÛfl êÒãÒêÛ~ÒâÝÛi Û ÝâäÒÛßÒÜêÞÈÜÀi ÑÜ~ÒÜÛØ tmax Û amax, ,,Ò amax - ÜÛÇãÞÈ?ÒÒ ÑÜ~ÒÜÛÒ ßäÞÛêëÀ ×ø , äã^ÒââÒ ,ãâäÛflêÛfl, tmax - ßãßÒÜê ,ÒßÒÜÛ, , ÝãêãÀØ êã ÑÜ~ÒÜÛÒ ãâêÛ,,Òêâfl a
êÒã max

=a

Ýâä max

,

t

êÒã max

=t

Ýâä max

.

(16)

× ãÇÒß âÞë~Ò éãßëÞÀ (16) ßãÚÜã ÛâäãÞÈÑã,êÈ Þfl äãÞë~ÒÜÛfl Ü~ÞÈÜã,,ã äÛÇÞÛÚÒÜÛfl Ý ßâ?êÇÜÀß ßÜãÚÛêÒÞflß Û . úÒÑëÞÈêêÀ â,ÜÒÜÛfl êÒãÒêÛ~ÒâÝÛi äÒâÝÑÜÛØ â ÝâäÒÛßÒÜêÞÈÜÀßÛ ÜÜÀßÛ äãÝÑÞÛ [9, 13, 14], ~êã éãßëÞ (15) ÒÝ,êÜã ãäÛâÀ,Òê ÛÜßÛÝë ßäÞÛêëÀ ×ø, äã ÝØÜÒØ ßÒÒ , âÞë~fli, Ýã,, ×ø âããê,Òêâê,ëÒê ÞÒßÒÜêÜãßë âêÛßëÞë Û ßãÜãäãÞflÜã ÛÑßÒÒÜ , ãÇÞâêÛ ÝãÀ ßãÑ,,, ÒÝãßÒÜëÒßãØ Þfl ÜÜãØ ßãÞÈÜãâêÛ (, ~âêÜãâêÛ, , äãÒÝ^ÛãÜÜãØ ÑãÜÒ). ×âÒ,,ã ÇÀÞã ãÇÇãêÜã ãÝãÞã 45 ×ø âÞëiã,ãØ, ÑÛêÒÞÈÜãØ Û âãßêãâÒÜâãÜãØ ßãÞÈÜãâêÒØ. øÛ êãß äÛßÒÜã , 70% âÞë~Ò, ÇÀÞã ãÇÜëÚÒÜã ãê~ÒêÞÛ,ãÒ âããê,Òêâê,ÛÒ êÒãÛÛ Û ÝâäÒÛßÒÜê, , 20% âÞë~Ò, âããê,Òêâê,ÛÒ ãÝÑÞãâÈ ßÒÜÒÒ ãê~ÒêÞÛ,Àß, Üã äÛÒßÞÒßÀß, , 10% âÞë~Ò, äãÞë~ÛÞâÈ äÞãifl ääãÝâÛß^Ûfl. øÞãifl ÛÞÛ âÒÜflfl ääãÝâÛß^Ûfl ãêÜãâÛêâfl, ÝÝ ä,ÛÞã, Ý âÞë~flß, Ýã,, ×ø Ò,,ÛâêÛã,ÞÛ ÇÛäãÞflÜã ÛÞÛ ëâÒÜflÞÛ äã ,,ëääÒ ÛâäÀêëÒßÀi. øãâÞÒÜÒÒ ÒâêÒâê,ÒÜÜã , êãß âÞë~Ò, ÒâÞÛ ÑÜÀÒ ÛâäÀêëÒßÀÒ ,ÜëêÛ ,,ëääÀ ÛßÒê ÑÞÛ~ÜÀÒ ä-

ßÒêÀ Û . × âÞë~fli ÚÒ, Ýã,, ×ø Ü ÞÒßÒÜêÜÀØ éÛÑÛ~ÒâÝÛØ âêÛßëÞ Ò,,ÛâêÛã,ÞÛ ßãÜãäãÞflÜã, ë ãÜã,,ã ÛâäÀêëÒßã,,ã, , ãÇÞâêÛ, ÒÝãßÒÜã,ÜÜãØ Þfl âããê,Òêâê,ëÒØ ßãÞÈÜãâêÛ (, ~âêÜãâêÛ, , äãÒÝ^ÛãÜÜãØ ÑãÜÒ Û ãÇÞâêÛ ,ÒêÒÝâ Þfl âÞëiã,Ài âêÛßëÞã,), ÝÝ ä,ÛÞã, ÜÇÞÞãâÈ ãê~ÒêÞÛ,ãÒ âããê,Òêâê,ÛÒ ßÒÚë êÒãÛÒØ Û ÝâäÒÛßÒÜêãß. ùê~ÒêÞÛ,ãÒ âããê,Òêâê,ÛÒ ã~ÒÜÈ ~âêã ÜÇÞÞãâÈ Û Þfl ,,ëääÀ ÛâäÀêëÒßÀi (äã-,ÛÛßãßë, , âÞë~fli, Ýã,, ÑÞÛ~ÜÀÒ ÛâäÀêëÒßÀÒ iÝêÒÛÑëêâfl ÇÞÛÑÝÛßÛ ÑÜ~ÒÜÛflßÛ äßÒêã, Û ). øãâÝãÞÈÝë , ÇãÞÈ?ÛÜâê,Ò âÞë~Ò, Ü ÝâäÒÛßÒÜêÞÈÜãØ ÝÛ,ãØ ×ø ãêâëêâê,ëÒê ÞÛÜÛfl ÜëÞÒ,ã,,ã äãêÒÜ^ÛÞ, ßäÞÛêë, ÝÝ ä,ÛÞã, ÛÑßÒflÞâÈ ßÒÚë äÛÝßÛ âãâÒÜÛi ÝãÞÒÇÜÛØ* [17] Û âê,ÛÞâÈ , âããê,Òêâê,ÛÒ ßãßÒÜêë ,ÒßÒÜÛ, âÒÜÒßë ßÒÚë ÞêÒÜêÜÀßÛ äÒÛãßÛ êÛi ÝãÞÒÇÜÛØ. ×ÒÞÛ~ÛÜ éÛÝâÛã,ÞâÈ äãÛÑ,ãÞÈÜÀß ãÇÑãß: Ñ,ÛâÛßãâêÈ ßäÞÛêëÀ ×ø ãê ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ ÜÒ äã,ÒflÞâÈ (,ã ßÜã,,Ûi ÝâäÒÛßÒÜêÞÈÜÀi Çãêi ÛÜêÒÜâÛ,ÜãâêÈ ÜÒ ëÝÑÀ,Òêâfl, , ßãÒÞÛ - êã ÛÜêÒÜâÛ,ÜãâêÈ , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i). øÛ éÛÝâÛã,ÜÜãß äßÒêÀ Û ,ÀÇÛÞÛâÈ ÛÑ ëâÞã,Ûfl ãäêÛßÞÈÜãØ ääãÝâÛß^ÛÛ. øÛ,ÒÒß ÜÒâÝãÞÈÝã äÛßÒã, [9]. 1. ôÛ,fl Ü Ûâ. 4, (âÞÒ,), ,Ñflêãß ÛÑ ÇãêÀ [18] (â. 16, Ûâ. 1, âÒÜÛØ, êãÜÝfl ÞÛÜÛfl), äÒâê,ÞflÒê ÝâäÒÛßÒÜêÞÈÜã ÛÑßÒÒÜÜÀØ äãâÒâê,ãß ÞÒÝêã, ,ÚÛ,ÞÒÜÜã,,ã , ßãÑ,,, âÞëiã,ãØ ×ø , ãê,Òê Ü ÇÛÜëÞÈÜã ,ãâäÛÜÛßÒßë (äÒfl,ÞflÒßë â äãßãÈ ,,ãßÝã,,ã,ãÛêÒÞfl, âäãÞãÚÒÜÜã,,ã äÒÒ ÛâäÀêëÒßÀß) êãÜã,ë äãâÀÞÝë ÞÛêÒÞÈÜãâêÈ 50 ßâ. ùÇãÑÜ~ÒÜÛfl ÝãÞÒÇÜÛØ ~âêÛ~Üã ,ÜÒâÒÜÀ ,êããß ÜâêãflÒØ ÇãêÀ. ?ÒÒÑ P0 ãÇãÑÜ~ÒÜã äãÞãÚÛêÒÞÈÜãÒ ÝãÞÒÇÜÛÒ ÜÒäãâÒâê,ÒÜÜã äÒÒ ßãßÒÜêãß ÒØâê,Ûfl âêÛßëÞ (ãÜã ÛâäãÞÈÑëÒêâfl , ÞÈÜÒØ?Òß). õÒêã ÛÑßÒÒÜÛfl (ÛßäÞÜêÛã,ÜÜÀØ , ßãÑ,, ÞÒÝêã), ã~Ò,ÛÜã, ãÞÚÒÜ ãÇÒâäÒ~Û,êÈ âëÒâê,ÒÜÜã Ç?ÞÈ?ë êã~ÜãâêÈ, ~Òß äÛ Ò,,Ûâê^ÛÛ â äã,ÒiÜãâêÛ ,,ãÞã,À. ÿãêfl ÛââÞÒã,ÜÛfl äã,ãÛÞÛâÈ â ÇãÞÈÜÀßÛ äÝÛÜâãÜÛÑßãß, ,êããß ÇãêÀ [18] äã~ÒÝÛ,Òêâfl, ~êã ë ÛâäÀêëÒßÀi ÜÒ ÇÀÞã âäÒ^ÛéÛ~ÒâÝÛi Üë?ÒÜÛØ ,ãâäÛflêÛfl. × êÇÞ. 3, äÛ,ÒÒÜÀ ÑÜ~ÒÜÛfl ßäÞÛêëÀ ×ø Û âããê,Òêâê,ëÛÒ ÞêÒÜêÜÀÒ äÒÛãÀ, ÛÑßÒÒÜÜÀÒ äã Ûâ. 4, (âÞÒ,). ÔßäÞÛêë Ýã*× êÒßÛÜãÞã,,ÛÛ, äÛÜflêãØ äÛ ÜÞÛÑÒ ÝãÞÒÇÜÛØ, ê ,ÒÞÛ~ÛÜ ÜÑÀ,Òêâfl Ñßiãß ÝãÞÒÇÜÛØ.

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


750

,,ÞâÝã

ýÇÞÛ^ 3. ñ,ÛâÛßãâêÈ ßäÞÛêëÀ ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ ãê ,ÒßÒÜÛ, ÛÑßÒÒÜÜfl äã Ûâ. 4, , Ç, , (âÞÒ,) âããê,Òêâê,ÒÜÜã Table 3. The time dependence of the evoked potential amplitude, measured on fig. 4, a, Ç, , (left) correspondent ôãÞÒÇÜÛÒ P0-N1 N1-P1 P1-N2 N2-P2 P2-N3 t, ßâ a, ßÝ× 37 9.7 137 36.1 Ç ôãÞÒÇÜÛÒ P1-N1 N1-P2 P2-N2 N2-P3 P3-N3 t, ßâ a, ßÝ× 70.8 14.39 142 258 608 1200 30.30 75.00 65.15 24.24 , t, ßâ 12 a, ãêÜ. Ò. 0.7 24 1.5 42 1.3 68 110 175 301 2.5 4.3 6.9 6.4 269 78.4 489 79.8 857 46.5

ÞÒÇÜÛfl N1 ÛÑßÒflÞâÈ ãê äÛÝ êã,,ã ÝãÞÒÇÜÛfl ã äÒ?Òâê,ëÒ,,ã Òßë äãÞãÚÛêÒÞÈÜã,,ã äÛÝ P0. ÷ Ûâ. 4, (âä,) äÒâê,ÞÒÜ êÒãÒêÛ~ÒâÝfl Ñ,ÛâÛßãâêÈ ßäÞÛêëÀ ×ø ãê ,ÒßÒÜÛ (âäÞã?Üfl ÞÛÜÛfl) Û ÝâäÒÛßÒÜêÞÈÜÀÒ ÑÜ~ÒÜÛfl ßäÞÛêëÀ (ÝëÚÝÛ). ù~Ò,ÛÜã, ~êã êãê ÛâëÜãÝ ÒßãÜâêÛëÒê ÇÞÒâêflÒÒ âããê,Òêâê,ÛÒ ßÒÚë êÒãÛÒØ Û ÝâäÒÛßÒÜêãß. 2. ôÛ,fl Ü Ûâ. 4, Ç (âÞÒ,), ,Ñflêfl ÛÑ ÇãêÀ [25] (â. 139, Ûâ. 65), äÒâê,ÞflÒê âÞëiã,ãØ ×ø , ãê,Òê Ü ÒÞ~ãÝ ,ã ,êããØ éÑÒ âÜ. ùÇãÑÜ~ÒÜÛÒ N3 ,ÜÒâÒÜã , ÛâëÜãÝ ,êããß ÜâêãflÒØ ÇãêÀ. û,ÜÒÜÛÒ äÒâÝÑÜÛØ äÒÞ,,ÒßãØ ßãÒÞÛ â ×ø ,ã ,Òßfl âÜ ÛÜêÒÒâÜã êÒß, ~êã ,ã âÜÒ ,ÜÛßÜÛÒ ÛâäÀêëÒßã,,ã ßÝâÛßÞÈÜã ââÒflÜã. þÝêÛ~ÒâÝÛ ãêâëêâê,ëê ë,,ÛÒ âêÛßëÞÀ (äÒÚÒ ,âÒ,,ã ,ÜëêÛßãÑ,,ã,ã,,ã äãÛâiãÚÒÜÛfl), "ÝãÜÝëÛëÛÒ" â ÛââÞÒëÒßÀß. ðÜ~Ò ,,ã,ãfl, ëâÞã,Ûfl ÝâäÒÛßÒÜê ßãÚÜã â~ÛêêÈ ÜÛÇãÞÒÒ "~ÛâêÀßÛ" , âßÀâÞÒ ÛÑãÞÛã,ÜÜãâêÛ ãê ÜÒÝãÜêãÞÛëÒßÀi ,ÜÒ?ÜÛi éÝêãã,. × êÇÞ. 3, Ç äÛ,ÒÒÜ Ñ,ÛâÛßãâêÈ ßäÞÛêëÀ ×ø ãê ,ÒßÒÜÛ, ÛÑßÒÒÜÜfl äã Ûâ. 4, Ç (âÞÒ,). ù~Ò,ÛÜã, amax = 75 ßÝ×, tmax = 258 ßâ. ùÜÝã âããê,Òêâê,ëÛÒ ÑÜ~ÒÜÛfl äßÒêã, Û ÛâäãÞÈÑã,ÞÛâÈ êãÞÈÝã , Ý~Òâê,Ò Ü~ÞÈÜã,,ã äÛÇÞÛÚÒÜÛfl. ðÑ ëâÞã,Ûfl ãäêÛßÞÈÜãØ ääãÝâÛß^ÛÛ ÇÀÞÛ ,ÀÇÜÀ âÞÒëÛÒ ÑÜ~ÒÜÛfl äßÒêã,: = 3.4 ç 103 ßâ, = = 228 ßÝ×. û,ÜÒÜÛÒ êÒãÒêÛ~ÒâÝãØ (âäÞã?Üfl ÞÛÜÛfl) Û ÝâäÒÛßÒÜêÞÈÜãØ (ÝëÚÝÛ) Ñ-

,ÛâÛßãâêÒØ ßäÞÛêëÀ ×ø ãê ,ÒßÒÜÛ äÒâê,ÞÒÜã Ü Ûâ. 4, Ç (âä,). ù~Ò,ÛÜã, êãê ÛâëÜãÝ ÒßãÜâêÛëÒê äÒ,ãâiãÜãÒ âããê,Òêâê,ÛÒ ßÒÚë êÒãÛÒØ Û ÝâäÒÛßÒÜêãß. 3. ôÛ,fl Ü Ûâ. 4, , (âÞÒ,), ,Ñflêfl ÛÑ ÇãêÀ [17], äÒâê,ÞflÒê âãßêãâÒÜâãÜÀØ ×ø. úÒÑëÞÈêêÀ ÛÑßÒÒÜÛfl Ñ,ÛâÛßãâêÛ a(t) äã êãßë ÛâëÜÝë äÒâê,ÞÒÜÀ , êÇÞ. 3, ,. øãâÝãÞÈÝë Ü Ûâ. 4, , (âÞÒ,) ãêâëêâê,ëÒê ßâ?êÇ äã ãâÛ ãÛÜê, ÑÜ~ÒÜÛfl ßäÞÛêëÀ , êÇÞ. 3, , ëÝÑÜÀ , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i. ÕÀÞÛ ,ÀÇÜÀ âÞÒëÛÒ ÑÜ~ÒÜÛfl äßÒêã,: = 2 ç 103 ßâ, = 20 ãêÜ. Ò. þãßëÞÀ(16) ÛâäãÞÈÑã,ÞÛâÈ Þfl ,ÀÇã Ü~ÞÈÜã,,ã äÛÇÞÛÚÒÜÛfl. úÒÑëÞÈêêÀ â,ÜÒÜÛfl äÒâê,ÞÒÜÀ Ü Ûâ. 4, , (âä,) Û, ã~Ò,ÛÜã, ãâêêã~Üã ëÇÒÛêÒÞÈÜÀ. × âÞë~Ò, Ýã,, Ü ÝâäÒÛßÒÜêÞÈÜãØ ÝÛ,ãØ ×ø äÛâëêâê,ëÒê ÞÛÜÛfl ÜëÞÒ,ã,,ã äãêÒÜ^ÛÞ, ßäÞÛêëë ×ø ,ãÑßãÚÜã ÛÑßÒflêÈ ÜÒ ßÒÚë äÛÝßÛ âãâÒÜÛi ÝãÞÒÇÜÛØ, ãê ÞÛÜÛÛ ÜëÞÒ,ã,,ã äãêÒÜ^ÛÞ ã äÛÝ ÝãÞÒÇÜÛfl Û âê,ÛêÈ , âããê,Òêâê,ÛÒ ÞêÒÜêÜãßë äÒÛãë ÝãÞÒÇÜÛfl. × êãß âÞë~Ò ÜÒêëÜã ,ãââêÜã,ÛêÈ êÝÚÒ âß ×ø. ×ø p(t) äÒâê,ÞflÒê âãÇãØ ,,ßãÜÛ~ÒâÝÛÒ ÝãÞÒÇÜÛfl â äÒÒßÒÜÜãØ ßäÞÛêëãØ a(t) Û ~âêãêãØ (t) p ( t ) = a ( t ) sin ( ( t ) t + ) . ?âêãê ×ø ßãÜãêãÜÜã ëÇÀ,Òê â êÒ~ÒÜÛÒß ,ÒßÒÜÛ Û âêÒßÛêâfl Ý ÜëÞ äÛ t, âêÒßflÒßâfl Ý ÇÒâÝãÜÒ~ÜãâêÛ. æâêÒâê,ÒÜÜã ÛâÝêÈ ÒÒ , ,ÛÒ ( t ) = 0 e .
- st

øßÒêÀ 0, s Û ,ÀÇÒÒß ÛÑ ëâÞã,Ûfl ãäêÛßÞÈÜãØ ääãÝâÛß^ÛÛ. ÷ Ûâ. 5 äÒâê,ÞÒÜÀ ÒÑëÞÈêêÀ ääãÝâÛß^ÛÛ ×ø, ÛÑãÇÚÒÜÜã,,ã Ü Ûâ. 4, (âÞÒ,). áë,,ãØ äÛßÒ äããÇÜãØ ääãÝâÛß^ÛÛ äÛ,ÒÒÜ , ÇãêÒ [13]. ñ,ÛâÛßãâêÈ (t), ,ÒãflêÜã, ÜÒ â,flÑÜ â ÛÜßÛÝãØ ,ÜÛßÜÛfl: ,ÜÛßÜÛÒ ,ÞÛflÒê êãÞÈÝã Ü ßäÞÛêëë ÝãÞÒÇêÒÞÈÜã,,ã äã^Òââ. 5. ñÔôù÷ ø?æúù÷Ô ð ñÔôù÷ ûýð×æ÷ûÔ ùäÒÒÞÛß ×ú ÝÝ ÞÛêÒÞÈÜãâêÈ äã^Òââ I(0, t). ÿãêfl êãê äã^Òââ , ßÝi ÇâêÝ^ÛÛ (äÛÇÞÛÚÒÜÛfl) ë,ÜÒÜÛfl (8) ÇÒâÝãÜÒ~ÒÜ, I(0, t) âêÒßÛêâfl Ý ÜëÞ äÛ âêÒßÞÒÜÛÛ t Ý ÇÒâÝãÜÒ~ÜãâêÛ, ßãÚÜã â~ÛêêÈ Ò,,ã Ñ,Ò?ÒÜÜÀß,

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

751

Ýã,, ,ÜÛßÜÛÒ Ý âêÛßëÞë âêÜã,Ûêâfl ãâêêã~Üã ßÞÀß I ( 0, ) = I 0 , (17) ,,Ò I0 Imax (Imax - ÜÛÇãÞÈ?ÒÒ ÑÜ~ÒÜÛÒ éëÜÝ^ÛÛ I(0, t)). úÑÞÛ~ÜÀÒ ,êãÀ â,flÑÀ,ê ÛÜêÒÜâÛ,ÜãâêÈ ãëÒÜÛfl (ÒÝ^Û) â ßäÞÛêëãØ ÑÞÛ~ÜÀi ãêÒÞÈÜÀi ÝãÞÒÇÜÛØ ×ø [17]. ñÒâÈ äÒÞ,,Òêâfl â,ãÒãÇÑÜfl ÞÈêÒÜêÛ, êÝãßë äãiãë. ùäÒÒÞÛß ÛÜêÒÜâÛ,ÜãâêÈ ãëÒÜÛfl ÝÝ âÒÜÒÒ ÑÜ~ÒÜÛÒ ßäÞÛêëÀ ×ø (ê.Ò. äÞãêÜãâêÛ ,ÜÛßÜÛfl , êã~ÝÒ x = 0) Ñ ×ú 0 = ----- I ( 0, t ) dt .
0

p, ßÝ× 50 25 0 -25 -50 ßÝ×

0



t

(18)

øßÒê 0 ÜÑã,Òß ßâ?êÇãß ßãÞÈÜãâêÛ: ãÜ ßãÚÒê ÇÀêÈ ÑÞÛ~ÜÀß Þfl ÑÜÀi ßãÞÈÜãâêÒØ. ùêßÒêÛß, ~êã ,,Ûë âiãÛßãâêÛ ÛÜêÒ,,Þ (18), ,ÀÇã I0 âëÒâê,ÒÜÜãØ ãÞÛ Þfl ÞÈÜÒØ?Ò,,ã ÜÒ Û,,Òê. ÙÞ,ÜãÒ, ~êãÇÀ êãê äßÒê ÇÀÞ ãâêêã~Üã ßÞ. øÒÒØÒß êÒäÒÈ Ý ãäÒÒÞÒÜÛ ÝãééÛ^ÛÒÜê k() , ë,ÜÒÜÛÛ (8). ù~Ò,ÛÜã, ~êã ~Òß ÇãÞÈ?Ò ÛÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ, êÒß ÇÀâêÒÒ ãÜ äÛ,ÞÒ~Òê Ý âÒÇÒ ,ÜÛßÜÛÒ Û êÒß ÇãÞÈ?ÒÒ ,ÜÛßÜÛÒ ãÜ Ý âÒÇÒ äÛ,ÞÒ~Òê (âß. ÑÒÞ 1). áë,,ÛßÛ âÞã,ßÛ, â ãâêãß ÛÜêÒÜâÛ,ÜãâêÛ "äÛÝ" Ü Ûâ. 4 (âä,), ê.Ò. ,,éÛÝ éëÜÝ^ÛÛ I(0, t), ãÞÚÒÜ ,Àêfl,,Û,êÈâfl ,,Òi Û âëÚêÈâfl, âÚÛßflâÈ Ý ãâÛ ãÛÜê (ê.Ò. äãâÞÒã,êÒÞÈÜãâêÈ éëÜÝ^ÛØ I(0, t) äããÇÜ -ãÇÑÜãØ äãâÞÒã,êÒÞÈÜãâêÛ). áÞfl êã,,ã ãâêêã~Üã äãêÒÇã,êÈ ÜãßÛã,ÝÛ éëÜÝ^ÛÛ I(0, t)


úÛâ. 5. û,ÜÒÜÛÒ ÝâäÒÛßÒÜêÞÈÜã,,ã ×ø, äÒâê,ÞÒÜÜã,,ã Ü Ûâ. 4, (âÞÒ,), â êÒãÒêÛ~ÒâÝÛß. Fig. 5. The compare of the experimental evoked potential, represent on the fig. 4, a (left), with the theoretical it.

Þã,,ÛéßÛ~ÒâÝãß ßâ?êÇÒ (äã ãâÛ Çâ^Ûââ ãêÝÞÀ,Òêâfl x = ln, äã ãâÛ ãÛÜê - y = = ln) äÒâê,ÞÒÜÀ ,,éÛÝÛ êãØ Ñ,ÛâÛßãâêÛ Þfl I0 = 0.01 Û êÒi ÑÞÛ~ÜÀi ÑÜ~ÒÜÛØ äßÒê '0 = 0/L. ù~Ò,ÛÜã, ~êã ,ã ,âÒi êÒi âÞë~fli äãÞë~ÒÜÜfl Ñ,ÛâÛßãâêÈ , ?ÛãÝãß ÛäÑãÜÒ ÛÑßÒÜÒÜÛfl ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ ãâêêã~Üã êã~Üã âããê,Òêâê,ëÒê äâÛiãéÛÑÛ~ÒâÝãßë ÑÝãÜë ûêÛ,ÒÜâ = c , ê.Ò. ÝÛ,ÀÒ Ü ÛâëÜÝÒ ÇÞÛÑÝÛ Ý äflßÀß y = x + + b, ,,Ò b = lnc. ñ,ÛâÛßãâêÈ Ü Ûâ. 6, âããê,Òêâê,ëÒê ÑÜ~ÒÜÛ äßÒê '0 = 0.1. ðÜêÒÜâÛ,ÜãâêÈ ßÒÜflÒêâfl , 50 Ñ. øãÝÑêÒÞÈ ÑÝãÜ ûêÛ,ÒÜâ äÛ êãß ,ÒÜ 0.53 (ãÜ ÛÑßÒflÒêâfl ÝÝ êÜ,,ÒÜâ ë,,Þ ÜÝÞãÜ äflßãØ), ~êã âããê,Òêâê,ëÒê ,ãâäÛflêÛ ,,ãßÝãâêÛ Ñ,ëÝ äÛ ßãÜãëÞÈÜãß ÑÚÒÜÛÛ [20]. úÛâ. 6, Ç ãê,Ò~Òê ÑÜ~ÒÜÛ '0 = 10. ðÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ êÝÚÒ ßÒÜflÒêâfl , 50 Ñ. øÛ êãß 0.6, ~êã âããê,Òêâê,ëÒê ,ãâäÛflêÛ ,,ãßÝãâêÛ Ñ,ëÝ äÛ ÇÛÜëÞÈÜãß ÑÚÒÜÛÛ [20]. ÷ÝãÜÒ^, Ü Ûâ. 6, , äÒâê,ÞÒÜ Ñ,ÛâÛßãâêÈ Þfl âÞë~fl '0 = 1.25 ç 10-3. ðÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ ßÒÜflÒêâfl , 200 Ñ. ûããê,Òêâê,ëÒÒ ÑÜ~ÒÜÛÒ 0.5, ~êã ãê,Ò~Òê ,ãâäÛflêÛ flÝãâêÛ â,Òê êã~Ò~Üã,,ã Ûâêã~ÜÛÝ , ëâÞã,Ûfli êÒßÜã,ãØ äê^ÛÛ [20].



0

I ( 0, t ) dt = C .

(19)

ðÑ (18), (19), äãÞë~Ûß = L = const, (20) ,,Ò L = 0C. ?êã iãã?ã ÛÑ,ÒâêÜÀØ [11, 12] ÝâäÒÛßÒÜêÞÈÜÀØ ÑÝãÜ øÈÒãÜ-óÒÇÒÒ,-ñÇãÛÜ: äãÛÑ,ÒÒÜÛÒ ÛÜêÒÜâÛ,ÜãâêÛ ãëÒÜÛfl Ü ×ú ÒâêÈ ,ÒÞÛ~ÛÜ äãâêãflÜÜfl, ÜÒ Ñ,Ûâflfl ãê ,ÒÞÛ~ÛÜÀ (, ÜÜãß âÞë~Ò - ÛÜêÒÜâÛ,ÜãâêÛ) ÒØâê,ëÒ,,ã âêÛßëÞ. øãâÞÒ ,À~ÛâÞÒÜÛfl ÛÜêÒ,,Þ ë,ÜÒÜÛÒ (19) äÒãÇÑëÒêâfl , (ã,ãÞÈÜã ,,ãßãÑÝãÒ) êÜâ^ÒÜÒÜêÜãÒ ë,ÜÒÜÛÒ Þfl éëÜÝ^ÛÛ k(). úÒ?Û, Ò,,ã (~ÛâÞÒÜÜã), ÜØÒß ÛÑ (14) Û (17) Ñ,ÛâÛßãâêÈ (), ÑêÒß ÛÑ (20) - Ñ,ÛâÛßãâêÈ (). × Ý~Òâê,Ò äÛßÒ Ü Ûâ. 6 , ,ãØÜãß

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


752 ln - 4.0 - 4.5 - 5.0 - 5.5 - 6.0 - 2.5 - 2.0 - 1.5 - 1.0 - 0.5 ln - 0.5 - 1.0 - 1.5 - 2.0 - 2.5 - 3.0 - 2.5 - 2.0 - 1.5 - 1.0 - 0.5 ln , - 6.5 - 7.0 - 7.5 - 8.0 - 8.5 - 9.0 - 9.5 -3 -2 -1 0 1 2 0 Ç

,,ÞâÝã úÛâ. 6. ýÒãÒêÛ~ÒâÝfl Ñ,ÛâÛßãâêÈ ,ÒÞÛ~ÛÜÀ ÒÝ^ÛÛ ãê ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ , ,ãØÜãß Þã,,ÛéßÛ~ÒâÝãß ßâ?êÇÒ Þfl ÑÞÛ~' ÜÀi ÑÜ~ÒÜÛØ äßÒê 0 . ðÜêÒÜâÛ,ÜãâêÈ âêÛßëÞ Û ÒÝ^Ûfl ,ÀÚÒÜÀ , ãêÜãâÛêÒÞÈÜÀi ÒÛÜÛ^i. ×ÛÜã, ~êã ,âÒ ÝÛ,ÀÒ Ü ÛâëÜÝÒ ÇÞÛÑÝÛ Ý äflßÀß. øãâÞÒÜÒÒ ãÑÜ~Òê, ~êã êÒãÒêÛ~ÒâÝfl Ñ,ÛâÛßãâêÈ () âããê,Òêâê,ëÒê ÝâäÒÛßÒÜêÞÈÜãßë ÑÝãÜë ûêÛ,ÒÜâ. - äßÒê ßãÒÞÛ '0 = 0.1. øÛ êãß äãÝÑêÒÞÈ ÑÝãÜ ûêÛ,ÒÜâ (ÛÑßÒflÒßÀØ ÝÝ êÜ,,ÒÜâ ë,,Þ ÜÝÞãÜ äflßãØ Ü ÛâëÜÝÒ) 0.53, ~êã âããê,Òêâê,ëÒê ,ãâäÛflêÛ ,,ãßÝãâêÛ Ñ,ëÝ äÛ ßãÜãëÞÈÜãß ÑÚÒÜÛÛ; Ç - äßÒê '0 = 10. øÛ êãß 0.6, ~êã âããê,Òêâê,ëÒê ,ãâäÛflêÛ ,,ãßÝãâêÛ Ñ,ëÝ äÛ ÇÛÜëÞÈÜãß ÑÚÒÜÛÛ; , - äßÒê '0 = 1.2 ç 10-3. øÛ êãß 0.5, ~êã âããê,Òêâê,ëÒê ,ãâäÛflêÛ flÝãâêÛ â,Òê êã~Ò~Üã,,ã Ûâêã~ÜÛÝ , ëâÞã,Ûfli êÒßÜã,ãØ äê^ÛÛ. Fig. 6. The theoretical plot of the reaction from the stimulus for several values of '0 . It is used log- log scale. The stimulus and the reaction are represent in relative unit. One can see, that all curves are related to straight lines. That mean, that the theoretical dependence () correspondent to the Stivens'es law. - the parameter of the model '0 = 0.1. At that exponent of the Stivens'es law (equal slope ratio of the straight line in the figure) 0.53, that correspondent to perception of the sound volume by monaural listening; Ç - the parameter '0 = 10. At that 0.6, that correspondent to perception of the sound volume by binaural hearing; , - the parameter '0 = 1.25 ç 10-3. At that 0.5, that correspondent to perception of the luminosity of a point source by conditions of dark adaptation.

0

0.5 1.0 1.5 ln

0.5 1.0 1.5 ln

ln

ñÔôó??æ÷ðæ × ÜâêãflÒØ ÇãêÒ äÒÞãÚÒÜã ÝãÞÛ~Òâê,ÒÜÜãÒ ãäÒÒÞÒÜÛÒ (äÞãêÜãâêÛ) ,ÜÛßÜÛfl ÝÝ éëÜÝ^ÛÛ , äâÛiÛ~ÒâÝãß äãâêÜâê,Ò (øø) Û ,ÒßÒÜÛ, ãâÜã,ÜÜãÒ Ü â,flÑÛ ,ÜÛßÜÛfl Û ,ÒßÒÜÛ ÒÝ^ÛÛ (×ú) Ü êÒâêÛëÛÒ âêÛßëÞÀ. ÷ ãâÜã,Ò Ý~Òâê,ÒÜÜÀi ÑÝãÜãßÒÜãâêÒØ ÛÜßÛÝÛ ,ÜÛßÜÛfl äãâêãÒÜã ÛÜßÛ~Ò-

âÝãÒ ë,ÜÒÜÛÒ (8) Þfl äÞãêÜãâêÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl ÞÒßÒÜêÜã,,ã ,ÜÒ?ÜÒ,,ã âêÛßëÞ â ÝãééÛ^ÛÒÜêãß k(), ãäÒÒÞflÒßÀß ,ÒÜâê,ãß (19). ÷ ÇÑÒ êã,,ã ë,ÜÒÜÛfl äãâêãÒÜ ßêÒßêÛ~ÒâÝfl ßãÒÞÈ äã^Òââ ,ãâäÛflêÛfl, , ßÝi ÝãêããØ ÑÞÛ~ÜÀÒ äâÛiãéÛÑÛãÞã,,Û~ÒâÝÛÒ ,ÒÞÛ~ÛÜÀ (ßäÞÛêë ×ø, ÛÜêÒÜâÛ,ÜãâêÈ ãëÒÜÛfl, ×ú) ,ÀÚêâfl ~ÒÒÑ äÞãêÜãâêÈ ,ÜÛßÜÛfl. øÒâÝÑÜÛfl ßãÒÞÛ âããê,Òêâê,ëê ÇãÞÈ?ãßë ãÇÒßë ÝâäÒÛßÒÜêÞÈÜÀi ÜÜÀi. ýÝ, Ò?ÒÜÛÒ ë,ÜÒÜÛfl (8) ,äãÞÜÒ ëã,ÞÒê,ãÛêÒÞÈÜã ãäÛâÀ,Òê ÝâäÒÛßÒÜêÞÈÜë ÛÜßÛÝë ,ãÑÇëÛßãâêÛ ÑÛêÒÞÈÜã,,ã ÜÞÛÑêã , äã^ÒââÒ ^ÒÞÒÜä,ÞÒÜÜã,,ã ,ãâäÛflêÛfl. × ~âêÜãâêÛ, äãê,ÒÚÒêâfl ,,ÛäãêÒÑ ã âãiÜÒÜÛÛ ,ÜÛßÜÛfl (Üã,fl ÛÜêÒäÒê^Ûfl âÒÞÒÝêÛ,ÜãâêÛ). ×ÀêÒÝfl ÛÑ ßãÒÞÛ éãßëÞ (15) Þfl ÛÜßÛÝÛ ßäÞÛêëÀ ×ø äãê,ÒÚÒêâfl â,ÜÒÜÛÒß â

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008


õùáæó? áð÷Ôõðôð ×÷ðõÔ÷ð? × øúùåæûûæ ×ùûøúð?ýð?

753

ßÜãÚÒâê,ãß ÝâäÒÛßÒÜêÞÈÜÀi ÛÑßÒÒÜÛØ ×ø. ðÑ ßãÒÞÛ âÞÒëÒê ÑÝãÜ øÈÒãÜ. ýÒãÒêÛ~ÒâÝfl Ñ,ÛâÛßãâêÈ ÒÝ^ÛÛ (ÛÜêÒÜâÛ,ÜãâêÛ ãëÒÜÛfl) ãê ÛÜêÒÜâÛ,ÜãâêÛ âêÛßëÞ, ,À~ÛâÞÒÜÜfl Þfl ÜÒâÝãÞÈÝÛi ßãÞÈÜãâêÒØ, âããê,Òêâê,ëÒê ÝâäÒÛßÒÜêÞÈÜãßë ÑÝãÜë ûêÛ,ÒÜâ. ×ãÑßãÚÜÀ âÞÒëÛÒ ÜÒØãéÛÑÛãÞã,,Û~ÒâÝÛÒ ÛÜêÒäÒê^ÛÛ äÒÞ,,ÒßãØ ßãÒÞÛ. 1. øÒ,fl ,ãÑßãÚÜfl ÛÜêÒäÒê^Ûfl ãâÜã,Ü Ü âÞÒëÛi âããÇÚÒÜÛfli. ûÒÞÒÝêÛ,ÜãâêÈ ,ÜÛßÜÛfl ãÇëâÞã,ÞÒÜ ÇãÈÇãØ Ñ ÒâëâÀ. ×âÒ âêÛßëÞÀ, ãâêëäÜÀÒ , êÒÝëÛØ ßãßÒÜê ,ÒßÒÜÛ ,ãâäÛflêÛ, ÜÒ ßã,,ëê , ãÛÜÝã,ãØ âêÒäÒÜÛ ãê~ÒêÞÛ,ã Û äãÞÜã ,ãâäÛÜÛßêÈâfl (äã,Ò,,êÈâfl ÛÜéãß^ÛãÜÜãØ ãÇÇãêÝÒ), äãâÝãÞÈÝë ,ãâäÛflêÛÒ ÝÚã,,ã ÛÑ âêÛßëÞã, êÒÇëÒê ãäÒÒÞÒÜÜÀi Ñêê Òâëâã, ã,,ÜÛÑß, êÛi Òâëâã, ÛßÒÒêâfl ã,,ÜÛ~ÒÜÜãÒ ÝãÞÛ~Òâê,ã. úãÞÈ Òâëâã, ßã,,ëê Û,,êÈ ÑÞÛ~ÜÀÒ iÛßÛ~ÒâÝÛÒ ,ÒÒâê,, âãÒÚÛÒâfl , ÚÛÝãâêfli, ãÝëÚÛi ÜÒ,ÜÀÒ ÝÞÒêÝÛ, , ~âêÜãâêÛ , Ýã,Û* (ÜäÛßÒ, , Ý~Òâê,Ò êÝã,Ài ßãÚÜã ââßêÛ,êÈ K+, Na+, Ca2+ Û ÛÑ,ÒâêÜÀÒ ãêÛ^êÒÞÈÜÀÒ ÛãÜÀ ÞÛÇã äÛêêÒÞÈÜÀÒ ,ÒÒâê,). æâêÒâê,ÒÜÜã â,flÑêÈ äÞãêÜãâêÈ ,ÜÛßÜÛfl â äÞãêÜãâêÈ êÛi iÛßÛ~ÒâÝÛi ,ÒÒâê, , ÜÜãØ êã~ÝÒ ÝãÀ ,,ãÞã,Üã,,ã ßãÑ,,, êã,, âÒÞÒÝêÛ,ÜãâêÈ (âãiÜÒÜÛÒ) ãÇÒêÒê äãâêãØ éÛÑÛ~ÒâÝÛØ âßÀâÞ: ãÜ ãÇëâÞã,ÞÒÜ ÛééëÑÛÒØ ,ÒÒâê, , ÚÛÝãØ âÒÒ (ÛÞÛ ÛééëÑÛÒØ âßãØ ÚÛÝãâêÛ) äã ÝãÒ. ýÝfl ÛÜêÒäÒê^Ûfl ãÇflâÜflÒê ãäÛâÜÛÒ äã^Òââ ,ãâäÛflêÛfl Ü ãâÜã,Ò ë,ÜÒÜÛfl äÇãÞÛ~ÒâÝã,,ã êÛä (ë,ÜÒÜÛfl ÛééëÑÛÛ). × äãÞÈÑë êãØ ÛÜêÒäÒê^ÛÛ ,,ã,ãÛê êãê éÝê [15], ~êã âÒÞÒÝêÛ,ÜãÒ ,ÜÛßÜÛÒ ëâÛÞÛ,Òê ÞãÝÞÈÜÀØ ßãÑ,,ã,ãØ Ýã,ãêãÝ , ßãÞÈÜã-âäÒ^ÛéÛ~ÒâÝÛi ãÇÞâêfli ßãÑ,,, ê.Ò. Ýã,È äÒÒâäÒÒÞflÒêâfl ßÒÚë ãÇÞâêflßÛ ÝãÀ , äã^ÒââÒ âÒÞÒÝ^ÛÛ. æâêÒâê,ÒÜÜã äÒäãÞãÚÛêÈ, ~êã êÝãÒ äÒÒâäÒÒÞÒÜÛÒ äãÛâiãÛê Û , ßÒÜÈ?Ûi ßâ?êÇi: , äÒÒÞi ãÜãØ ßãÞÈÜã-âäÒ^ÛéÛ~ÒâÝãØ ãÇÞâêÛ. øã äÒäãÞãÚÒÜÛ ø. úãÞÜ [33], äÒÒâäÒÒÞÒÜÛÒ Ýã,ãêãÝ â,flÑÜã â ,ÀÑ,ÜÜÀß ,ÜÛßÜÛÒß ë,ÒÞÛ~ÒÜÛÒß ,ãÑÇëÛßãâêÛ , âããê,Òêâê,ëÒØ ãÇÞâêÛ ÝãÀ. æâÞÛ â,flÑêÈ äÞãêÜãâêÈ ,ÜÛßÜÛfl â äÞãêÜãâêÈ Ýã,Û (ÛÞÛ ,ÞÛflÛi Ü ,ãÑÇëÛßãâêÈ iÛßÛ~ÒâÝÛi ,ÒÒâê,, , ÜÒØ âãÒÚÛiâfl), äÛÒß Ý âÞÒëÒØ ÛÜêÒäÒê^ÛÛ: ,ÜÛßÜÛÒ ,ÞÛflÒê Ü ,ãÑÇëÛßãâêÈ, ,ãÑÇëÛßãâêÈ ,ÞÛflÒê Ü ,ãÑÇëÚÒÜÛÒ, ê.Ò. Ü ×ø.
*

2. ×ãÑßãÚÜ, ãÜÝã, Û ë,,fl ÛÜêÒäÒê^Ûfl , ßâ?êÇi ÜÒØãÜÜãØ âÒêÛ. øããÇÜã êãßë ÝÝ êÒäÞã , ê,Òãß êÒÞÒ âäãâêÜflÒêâfl äëêÒß äÒÒ~Û ,ãÑÇëÚÒÜÛØ (éãÜãÜã,) ßÒÚë êãßßÛ ÝÛâêÞÞÛ~ÒâÝãØ Ò?ÒêÝÛ, ,ãÑÇëÚÒÜÛÒ , ÝãÒ ,,ãÞã,Üã,,ã ßãÑ,, âäãâêÜflÒêâfl äëêÒß äÒÒ~Û äãêÒÜ^ÛÞã, ÒØâê,Ûfl ßÒÚë ÜÒØãÜßÛ âÒêÛ. þãÜãÜ (Ý,Üê êÒäÞã,ãØ ÜÒ,,ÛÛ), äÒÒ,flâÈ ãê êãß A Ý âãâÒÜÒßë êãßë B, äãÝÛÒê êãß A. ÔÜÞã,,Û~Üã, ÒâÞÛ ÜÒØãÜ A ,ãÑÇëÚÒê (âÛÜäêÛ~ÒâÝÛß äëêÒß) âãâÒÜÛØ ÜÒØãÜ B, êã ÜÒØãÜ B ßãÚÒê ãÝÑÀ,êÈ êãßãÑflÒÒ ÒØâê,ÛÒ Ü ÜÒØãÜ A (,ãÑ,êÜãÒ êãßãÚÒÜÛÒ). × ÒÑëÞÈêêÒ ,ãÑÇëÚÒÜÛÒ, äÒÒ,flâÈ ÜÒØãÜë B, "äãÝÛÒê" ÜÒØãÜ A, ê.Ò. "äÒÒßÒÒêâfl" ãê ÜÒØãÜ Ý ÜÒØãÜë. ýÝ ÚÒ ÝÝ âããê,Òêâê,ÛÒ ßÒÚë ãÚÒÜÛÒß Û ëÜÛ~êãÚÒÜÛÒß éãÜãÜã, ãÇëâÞã,ÞÛ,Òê âãiÜÒÜÛÒ êÒäÞãêÀ, âããê,Òêâê,ÛÒ ßÒÚë ,ãÑÇëÚÒÜÛÒß Û êãßãÚÒÜÛÒß ÜÒØãÜã, ãÇëâÞã,ÞÛ,Òê âãiÜÒÜÛÒ ,ÜÛßÜÛfl (âÒÞÒÝêÛ,ÜãâêÈ). øããÇÛÒ äã^Òââã, Ü ßÛÝãâÝãäÛ~ÒâÝãß ëã,ÜÒ äÛ,ãÛê Ý äããÇÛ ÛÜßÛ~ÒâÝÛi ë,ÜÒÜÛØ Ü ßÝãâÝãäÛ~ÒâÝãß ëã,ÜÒ. øÛ êÝãØ ÛÜêÒäÒê^ÛÛ äÞãêÜãâêÈ ,ÜÛßÜÛfl iÝêÒÛÑëÒê ÜÒäãâÒâê,ÒÜÜã ,ãÑÇëÚÒÜÛÒ ÜÒØãÜã, Û ~ÒÒÑ ÜÒ,,ã ãäÒÒÞflÒê ßäÞÛêëë ×ø. × ÑÝÞ~ÒÜÛÒ ãêßÒêÛß, ~êã Þfl ÞÈÜÒØ?ÒØ äã,ÒÝÛ ,,ÛäãêÒÑÀ ã âãiÜÒÜÛÛ ,ÜÛßÜÛfl Û ÒÝ,êÜãâêÛ äÒÞ,,ÒßãØ ßãÒÞÛ äã^Òââ ,ãâäÛflêÛfl ÇÀÞã ÇÀ iãã?ã äã,êãÛêÈ ÝâäÒÛßÒÜê äã ßÒêãÛÝÒ ÇãêÀ [22] , ÇãÞÒÒ Ñ,ÒÜëêãß ,ÛÜêÒ (ê.Ò. äã,ÒâêÛ ÛÑßÒÒÜÛfl , ÇãÞÈ?Òß ~ÛâÞÒ êã~ÒÝ). × ~âêÜãâêÛ, ÚÒÞêÒÞÈÜã ë,ÒÞÛ~ÛêÈ ~ÛâÞã ÛÑë~ÒßÀi ÛÜÛééÒÒÜêÜÀi äëÜÝêã, Û ÛââÞÒã,êÈ ÛÜÛééÒÒÜêÜÀÒ äëÜÝêÀ, ÒÒ ÇãÞÒÒ ëÞÒÜÜÀÒ ãê äãÞãÚÛêÒÞÈÜã,,ã. ðÜêÒÒâÜã êÝÚÒ ÇãÞÒÒ äããÇÜã ÛÑë~ÛêÈ äã^Òââ ââÒflÜÛfl ,ÜÛßÜÛfl (,ãÑÇëÛßãâêÛ). ûøðûùô óðýæúÔýüú?
1. ÕÜã,-ôÀÞã, ð.÷. øâÛiãéÛÑÛãÞã,,Û~ÒâÝÛÒ ßÒiÜÛÑßÀ äãÛÑ,ãÞÈÜã,,ã Û ÜÒäãÛÑ,ãÞÈÜã,,ã ,ÜÛßÜÛfl ë ~ÒÞã,ÒÝ: Ô,êãÒé. Ûâ. ... ãÝê. ÇÛãÞ. ÜëÝ. ûøÇ.: ðÜ-ê éÛÑÛãÞã,,ÛÛ Ûß. ð.ø. ø,Þã, úÔ÷, 1999. 34 â. 2. ÕÞãÝ ×. üã,ÜÛ Çãâê,ã,ÜÛfl Û ,ÜÛßÜÛÒ. ?ÝâäÒÛßÒÜêÞÈÜfl äâÛiãÞã,,Ûfl. øã Ò. þÒââ ø., øÛÚÒ ì. õ.: øã,,Òââ, 1970(5): 97-146. 3. ÕãØÝã æ.ð. õÒiÜÛÑßÀ ëßâê,ÒÜÜãØ ÒflêÒÞÈÜãâêÛ. ðÑÇÜÜÀÒ äâÛiãÞã,,Û~ÒâÝÛÒ êëÀ. øã Ò. Õë?ÞÛÜâÝã,,ã Ô.×., ü?Ýã,ãØ ý.÷. õ.: õãâÝã,âÝÛØ äâÛiãÞã,,ã-âã^ÛÞÈÜÀØ ÛÜ-ê. ×ããÜÒÚ: ÷øù "õùá?ô", 2002. 688 â.

ûß. êÝÚÒ [10].

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4. ÙÞâÝã Ô.×. ×ÜÛßÜÛÒ ÝÝ ÛÜßÛ~ÒâÝÛØ ÛÜ,ÛÜê. ùÇãÑ. äÛÝÞ. Û äãßÀ?Þ. ßêÒß. 2006. 13(4): 624-625. 5. ÙÞâÝã Ô.×. ðÜ,ÒâÜÀØ äãiã Ý äãÇÞÒßÒ ãÇÒÜÛfl ,ÒßÒÜÛ , ë,ÜÒÜÛÛ êÒäÞãäã,ãÜãâêÛ. ûÇãÜÛÝ Üë~ÜÀi êëã, ýÒêÈÒØ ×âÒãââÛØâÝãØ ÝãÜéÒÒÜ^ÛÛ "÷ÒãÇêÛßÀÒ äã^ÒââÀ , äÛãÒ Û êÒiÜÛÝÒ". õ.: õÙýü Ûß. ÷.?. ÕëßÜ, 2005(1): 46-55. 6. ÙÞâÝã Ô.×. ô ,ãäãâë ãÇ ãÇÒÜÛÛ ,ÒßÒÜÛ , ë,ÜÒÜÛÛ êÒäÞãäã,ãÜãâêÛ. ÷ÒãÇêÛßÀÒ äã^ÒââÀ , äÛãÒ Û êÒiÜÛÝÒ. ýÒÑ. ãÝÞã, ýÒêÈÒØ ×âÒãââÛØâÝãØ ÝãÜéÒÒÜ^ÛÛ. õ.: õ Ù ýü Ûß. ÷.?. ÕëßÜ, 2005: 130-131. 7. ÙÞâÝã Ô.×. ù ,ãâäÛflêÛÛ ßëÑÀÝÞÈÜãØ ßÒÞãÛÛ. ùÇãÑ. äÛÝÞ. Û äãßÀ?Þ. ßêÒß. 2008. 15(2): 278-279. 8. ÙÞâÝã Ô.×. ù ,ãâäÛflêÛÛ iëãÚÒâê,ÒÜÜãØ ÝãßäãÑÛ^ÛÛ. ùÇãÑ. äÛÝÞ. Û äãßÀ?Þ. ßêÒß. 2008. 15(2): 279-280. 9. ÙÞâÝã Ô.×. øâÛiãéÛÑÛ~ÒâÝÛØ ÑÝãÜ ûêÛ,ÒÜâ, ßäÞÛêë ,ÀÑ,ÜÜã,,ã äãêÒÜ^ÛÞ Û ÛÜßÛÝ ,ÜÛßÜÛfl. øâÛiãéÛÑÛÝ âÒ,,ãÜfl. øã Ò. ÷ãâëÞÒÜÝã ×.÷., ûÝãêÜÛÝã,ãØ ð.Ù. õ.: ðø úÔ÷, 2007: 136-143. 10. ÙÞâÝã Ô.×. ûÛÜêÒÑ ÑÝãÜ ÛÜëÝ^ÛÛ ø,Þã, Û äâÛiãéÛÑÛ~ÒâÝã,,ã ÑÝãÜ ûêÛ,ÒÜâ , ÛÜßÛ~ÒâÝãß ë,ÜÒÜÛÛ äã^Òââ ,ãâäÛflêÛfl. AIS'05, CAD-2005, "ðÜêÒÞÞÒÝêëÞÈÜÀÒ âÛâêÒßÀ", "ðÜêÒÞÞÒÝêëÞÈÜÀÒ ûÔøú". ýëÀ ÝãÜéÒÒÜ^ÛØ. õ.: þÛÑßêÞÛê, 2005. 2: 166-174. 11. ñÇãÛÜ ?.õ. ùâÜã,À äâÛiãéÛÑÛ~ÒâÝãØ êÒãÛÛ âÒÜâãÜÀi äã^Òââã, (ýÒãÒêÛ~ÒâÝfl Û ÝâäÒÛßÒÜêÞÈÜfl äâÛiãéÛÑÛÝ): Ô,êãÒé. Ûâ. ... ãÝê. äâÛiãÞ. ÜëÝ. ó.: óÒÜÛÜ,,. ëÜ-ê Ûß. Ô.Ô. ìÜã,, 1977. 46 â. 12. ñÇãÛÜ ?.õ., óÒÇÒÒ, Ô.÷. øâÛiãéÛÑÛãÞã,,Ûfl Û äâÛiãéÛÑÛÝ. õ.: "÷ëÝ", 1977. 286 â. 13. ôã,ÞÝÛÜ û.û. ô ÝâäÒÛßÒÜêÞÈÜãßë ãÇãâÜã,ÜÛ ÜÒÝãêããØ ßãÒÞÛ ,ãâäÛflêÛfl. áÛäÞãßÜfl Çãê. õ.: õÙýü Ûß. ÷.?. ÕëßÜ, 2007. 104 â. 14. õÛÑflÝ ×.Ù. áÛÜßÛÝ ßäÞÛêëÀ âÞëiã,Ài Û ÑÛêÒÞÈÜÀi ,ÀÑ,ÜÜÀi äãêÒÜ^ÛÞã, ÝÝ âÞÒâê,ÛÒ ÛÜßÛÝÛ ,ÜÛßÜÛfl , äã^ÒââÒ ,ãâäÛflêÛfl ,ÜÒ?ÜÒ,,ã âêÛßëÞ. áÛäÞãßÜfl Çãê. õ.: õÙýü Ûß. ÷.?. ÕëßÜ, 2007. 102 â. 15. ÷êÜÒÜ ú. ×ÜÛßÜÛÒ Û éëÜÝ^ÛÛ ßãÑ,,. õ.: ðÑ-,ã õÙü, 1998. 600 â. 16. øã,,ÜÛ~ÜÀÒ äãÇÞÒßÀ äâÛiãÞã,,ÛÛ Û éÛÑÛãÞã,,ÛÛ. øã Ò. ÕãØÝã æ.ð. õ.: ðÑ-,ã Ôø÷ úûþûú, 1961. 212 â. 17. úëêßÜ ?.õ. ×ãÑßãÚÜãâêÛ äÛßÒÜÒÜÛfl ëâÒÜÒÜÜÀi ,ÀÑ,ÜÜÀi äãêÒÜ^ÛÞã, , äâÛiãéÛÑÛÝÒ. øãÇÞÒßÀ äâÛiãéÛÑÛÝÛ. õ.: "÷ëÝ", 1974. 251 â. 18. ûÒ,ãâêÈflÜã, Ô.×. ðÜê^ÒÒÇÞÈÜÀÒ ,ÀÑ,ÜÜÀÒ äãêÒÜ^ÛÞÀ Û ÛßäëÞÈâÜfl ÝêÛ,ÜãâêÈ ÜÒØãÜã, ,,ãÞã,Üã,,ã ßãÑ,, ~ÒÞã,ÒÝ , êÒâêi Ü ,ÜÛßÜÛÒ: Ô,êãÒé. Ûâ. ... ÝÜ. ÇÛãÞ. ÜëÝ. ûøÇ.: ðÜ-ê ßãÑ,, ~ÒÞã,ÒÝ, 1995. 20 â. 19. ûãÝãÞã, E.H. ýÒãÒêÛ~ÒâÝfl äâÛiãéÛÑÛãÞã,,Ûfl. õ.: ðÑ-,ã õÙü, 1986. 107 â.

ìüú÷Ôó ×?û?æò ÷æú×÷ùò áæ?ýæó?÷ùûýð êãß 58 < 6 2008