\input amstex \magnification=1200 \font\cyr=wncyr10 \font\cyb=wncyb10 \font\cyi=wncyi10 \font\cyre=wncyr8 \font\cyie=wncyi8 \font\cyrf=wncyr6 at 5pt \font\cyrs=wncyr6 \documentstyle{amsppt} \NoRunningHeads \NoBlackBoxes \define\SU{\operatorname{\bold S\bold U}} \define\color{\operatorname{color}} \define\inp{\operatorname{ input}} \define\outp{\operatorname{ output}} \define\nom{no} \document\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \boxed{\boxed{\aligned &\text{\eightpoint"Thalassa Aitheria" Reports}\\ &\text{\eightpoint RCMPI-96/05}\endaligned}}\newline \ \newline \ \newline \topmatter \title\cyb K opisaniyu klassa fizicheskih interaktivnyh informatsionnyh sistem. \endtitle \author\cyb D.V.Yurp1ev$^{1)}$ \endauthor \address\newline\cyre Tsentr matematicheskoe0 fiziki i informatiki "Talassa E1teriya"\newline {\it E-mail address:\/} \rm denis\@juriev.msk.ru \endaddress \abstract\nofrills\cyre V dannoe0 rabote posledovatelp1no izlagaet\-sya printsipialp1naya storona te\-o\-re\-ti\-ches\-ko\-go podhoda k resheniyu aktualp1noe0, no pochti ne razrabotannoe0 zadachi matematicheskoe0 fiziki opisaniya estestvennyh interaktivnyh psihoinformatsionnyh (v tom chisle vizualp1nyh, inyh sensornyh, respiratornyh ili kompleksnyh) sistem. Klyuchevuyu rolp1 v konkretnoe0 me\-to\-di\-ke opisaniya igrayut apparat anomalp1nyh virtualp1nyh realp1nostee0 i vtorichnogo sinteza izobrazhenie0 v sovremennoe0 neklassicheskoe0 nachertatelp1noe0 (kompp1yuternoe0) geometrii, a takzhe ischislenie koe1ffitsientov Klebsha--Gordana i ego obobshcheniya. Vyyavleny svyazi obsuzhdaemoe0 metodiki i ee otdelp1nyh fragmentov s razlichnymi drugimi psi\-ho\-in\-for\-ma\-tsi\-on\-nymi (drae0vernymi ili interfee0snymi) komponentami "in\-for\-ma\-tsi\-on\-noe0 magistrali". \endabstract \endtopmatter \cyr V nastoyashchee vremya issledovaniya na styke e1ksperimentalp1noe0 ma\-te\-ma\-ti\-ki, psihofiziki i {\rm computer science} v {\cyi fizike informatsionnyh sred, struk\-tur i sistem\/} (kak estestvennyh, tak i iskusstvennyh ili smeshannyh) predstavlyayut pervostepennuyu znachimostp1 (cm. naprimer, [1]), yavlyayut\-sya aktualp1nymi, po ukazannoe0 tematike funktsioniruet tselye0 ryad kak na\-tsi\-o\-nalp1\-nyh (SShA i strany Zapadnoe0 Evropy), tak i mezhdunarodnyh (v ramkah Evropee0skogo Sodruzhestva) nauchnyh programm. Oni provodyat\-sya kak krypnymi kollektivami gosudarstvennyh nauchno--issledovatelp1skih institutov, chastnyh ili kommercheskih nauchnyh tsentrov, tak i ot\-delp1\-ny\-mi spetsialistami v perechislennyh stranah i vo vsem mire. V rabote avtora [2] ukazyvalosp1 na to, chto iskusstvennye in\-te\-raktiv\-nye psihoinformatsionnye videosistemy predstavlyayut interes kak yazyk matematicheskoe0 fiziki (cr.[3]) dlya opisaniya razlichnyh estestvennyh (v tom chisle vizualp1nyh i inyh sensornyh, respiratornyh ili kompleksnyh) interaktivnyh psihoinformatsionnyh sistem. Klyuchevuyu rolp1 v podobnom opisanii igraet sozdanie dinamicheskogo izobrazheniya protekayushchego v estestvennoe0 psihoinformatsionnoe0 sisteme interaktivnogo protsessa posredstvom intentsionalp1noe0 anomalp1noe0 virtualp1noe0 re\-alp1\-nos\-ti (IAVR) [4,5,6:Prilozh.1], realizovannoe0 (apparatno i prog\-ramm\-no) kompp1yuterograficheskim interfee0som nekotoroe0 iskusstvennoe0 interaktivnoe0 sis\-te\-my, kotorye0 v svoyu ocheredp1 ukazannaya IAVR geometricheski modeliruet. Pri e1tom izuchenie {\rm 2D} i {\rm 3D} {\cyi prostranstvenno--di\-na\-mi\-ches-kih osobennostee0 zritelp1nogo vospriyatiya\/} i {\cyi intentsionalp1nyh fe\-no\-me\-nov\/} v iskusstvennyh interaktivnyh psihoinformatsionnyh videosistemah [7,1,4,5] sleduet otnositp1 k {\cyi fizike\/} sootvet\-st\-vuyushchego {\cyi yazyka\/} (sr.[8]). {\cyi Operatornye metody\/} (vklyuchaya kvantovo--polevye i stohasticheskie) v te\-o\-rii interaktivnyh videosistem realp1nogo vremeni plodotvorno razvivalisp1 avtorom v serii rabot [7,1,2,4-6]. {\cyi Geometricheskie aspekty\/} in\-te\-rak\-tiv\-nyh sistem (v chastnosti, interpretatsionnaya i nealeksandrie0skaya geometrii) rassmatrivalisp1 v [4,5:\S 1,6:Prilozh.1], v to vremya kak v [5:\S2] vnimanie udelyalosp1 ih informatsionnym aspektam. Matematicheskaya teo\-riya anomalp1nyh virtualp1nyh realp1nostee0 (AVR), v tom chisle osnovnye protsedury naturalizatsii i transtsendirovaniya (a takzhe vizualizatsii -- sr.[9]), svyazyvayushchie AVR s abstraktnoe0 geometriee0, kak osobye0 razdel {\cyi sovremennoe0 neklassicheskoe0 nachertatelp1noe0 (kompp1yuternoe0) geometrii\/}, naryadu s primerami ee ispolp1zovaniya pri geometricheskom mo\-de\-li\-ro\-va\-nii konkretnyh kompp1yuternyh videosred, posledovatelp1no izlagalasp1 v rabotah [7,4,5:\S 1,6:Pri\-lozh.1]. Interpretatsiya sovokupnosti operatornyh (kvantovo--polevyh) metodov v teorii interaktivnyh videosistem re\-alp1\-no\-go vremeni kak nachertatelp1noe0 nekommutativnoe0 geometrii privedena v [1]. V dannoe0 nebolp1shoe0 chisto teoreticheskoe0 i v opredelennom smysle itogovoe0 rabote my ogranichivaemsya klassom estestvennyh interaktivnyh psihoinformatsionnyh sistem, kotorye dopuskayut vydelenie aktivnoe0 i passivnoe0 sostavlyayushchih: aktivnogo agenta -- "subp2ekta" i passivnogo agenta -- "obp2ekta". Takoe0 klass estestvennyh interaktivnyh psihoinformatsionnyh sistem naibolee blizok k sistemam, dopuskayushchim odnu iz klassicheskih form opisaniya (formulp1nogo ili graficheskogo, sta\-ti\-ches\-ko\-go ili dinamicheskogo, algoritmicheskogo, determinirovannogo ili veroyatnostnogo). Izlozhim printsipialp1nuyu storonu teoreticheskogo podhoda k resheniyu aktualp1noe0, no pochti ne razrabotannoe0 zadachi ma\-te\-ma\-ti\-ches\-koe0 fiziki opisaniya podobnyh sistem. Pri e1tom osnovnoe vnimanie budet udeleno, nesmotrya na nekotoruyu peregruzhennostp1 analiza chisto tehnicheskimi, no neobhodimymi s prakticheskoe0 tochki zreniya detalyami (bolp1shaya chastp1 kotoryh sobrana, odnako, v Prilozhenii i Primechaniyah), teoreticheskomu vyyavleniyu fundamentalp1noe0 roli {\cyi subp2ekt--obp2ektnyh otnoshenie0\/} v fizike informatsionnyh sred, struktur i sistem (vedp1, imenno neredutsiruemostp1 ukazannyh otnoshenie0 obuslovlivaet neobhodimostp1 ispolp1zovaniya nestandartnyh interaktivnyh yazykovyh sredstv dlya opi\-sa\-niya fizicheskih interaktivnyh informatsionnyh sistem). Otmetim, chto razvernutaya postanovka zadachi izucheniya subp2ekt--obp2ektnyh otnoshenie0 kak fundamentalp1noe0 problemy teoreticheskoe0 fiziki prinadlezhit, po--vidimomu, E1rnstu Mahu, chp1i vzglyady, v svoyu ocheredp1, bazirovalisp1 na predshestvovavshih kontseptsiyah G.T.Fehnera i G.L.F.Gelp1mgolp1tsa. Kiberneticheskie aspekty ukazannoe0 problemy otmechalisp1 Norbertom Vi\-ne\-rom. Podcherknem, chto integrirovannostp1 subp2ekta v fizicheskuyu kartinu mira yav\-lya\-et\-sya neotemlemym harakternym svoe0stvom fiziki in\-for\-ma\-tsi\-on\-nyh sred, struktur i sistem. \subhead\cyb 1. Virtualizatsiya fizicheskih interaktivnyh informatsionnyh sis\-tem \endsubhead \definition{\cyb Opredelenie} {\cyi Izobrazheniem estestvennoe0 interaktivnoe0 psi\-ho\-in\-for\-ma\-tsi\-on\-noe0 sistemy s pomoshchp1yu iskusstvennoe0 interaktivnoe0 psi\-ho\-in\-for\-ma\-tsi\-on\-noe0 videosistemy\/} \cyr budem nazyvatp1 zadanie algoritma postroeniya dinamicheskogo izobrazheniya proizvolp1nogo protekayushchego v estestvennoe0 sisteme interaktivnogo protsessa posredstvom intentsionalp1noe0 ano\-malp1\-noe0 virtualp1noe0 realp1nosti, realizuemoe0 kompp1yuterograficheskim interfee0som iskusstvennoe0 interaktivnoe0 videosistemy. {\cyi Virtualizatsiee0 estestvennoe0 interaktivnoe0 psihoinformatsionnoe0 sistemy\/} budem nazyvatp1 sopostavlenie ee0 ee izobrazheniya s pomoshchp1yu iskusstvennoe0 in\-te\-rak\-tiv\-noe0 psihoinformatsionnoe0 videosistemy po opredelennoe0 sovokupnosti e1ksperimentalp1nyh dannyh o sisteme v ustanovivshemsya avtokolebatelp1nom rezhime. V svoyu ocheredp1 is\-hod\-nuyu interaktivnuyu sistemu budem nazyvatp1 {\cyi realizatsiee0 iskusstvennoe0 interaktivnoe0 sistemy}. \enddefinition \cyr Inymi slovami, virtualizatsiya estestvennoe0 interaktivnoe0 psi\-ho\-in\-for\-ma\-tsi\-on\-noe0 sistemy posvolyaet po harakteristikam nekotorogo og\-ra\-ni\-chen\-no\-go mnozhestva avtokolebatelp1nyh interaktivnyh protsessov for\-mi\-ro\-vatp1 dinamicheskoe izobrazhenie proizvolp1nogo (ne obyazatelp1no avtokolebatelp1nogo) interaktivnogo protsessa posredstvom nekotoroe0 is\-kus\-st\-ven\-noe0 interaktivnoe0 psihoinformatsionnoe0 sistemy. Vybor termina "virtualizatsiya" svyazan s tem, chto dinamicheskoe izobrazhenie interaktivnogo protsessa predstavlyaet soboe0 anomalp1nuyu virtualp1nuyu re\-alp1\-nostp1 v shirokom smysle e1togo ponyatiya (sm.[4,5,6:Prilozh.1]). Vvidu deleniya interesuyushchih nas estestvennyh interaktivnyh psi\-ho\-in\-for\-ma\-tsi\-on\-nyh sistem na aktivnuyu i passivnuyu sostavlyayushchie (aktivnogo i passivnogo agenta) harakteristiki ustanovivshegosya avtokolebatelp1nogo protsessa podrazdelyayut\-sya na graficheskie dannye o di\-na\-mi\-ches\-kom sostoyanii passivnogo agenta i chastotnye harakteristiki ak\-tiv\-no\-go agenta. Virtualizatsiya estestvennoe0 interaktivnoe0 psi\-ho\-in\-for\-ma\-tsi\-on\-noe0 sistemy takim obrazom zaklyuchaet\-sya v zadanii algoritma {\cyi vto\-rich\-nogo sinteza\/} (sm.~Prilozhenie) graficheskih dannyh o dinamicheskom so\-sto\-ya\-nii passivnogo agenta pri lyubom interaktivnom protsesse po za\-dan\-noe0 sovokupnosti ukazannyh dannyh pri ustanovivshihsya av\-to\-ko\-le\-ba\-telp1\-nyh protsessah iz nekotogo mnozhestva, a takzhe sootvetstvuyushchih chastotnyh harakteristik aktivnogo agenta v e1tih protsessah. Tem samym, prin\-tsi\-pi\-alp1\-naya strukturno--algoritmicheskaya s\-hema virtualizatsii estestvennyh interaktivnyh psihoinformatsionnyh sistem, osnovannoe0 na is\-polp1\-zo\-va\-nii vtorichnogo sinteza izobrazhenie0, imeet vid: \boxed{\boxed{{\aligned &\foldedtext\foldedwidth{0.9in}{\cyrf Estestvennaya inter- \newline aktivnaya psihoinfor-\newline matsionnaya sistema}\\ &\boxed{\foldedtext\foldedwidth{0.7in}{\cyrf Passivinye0\newline agent ("obp2ekt")}}\\ &\boxed{\foldedtext\foldedwidth{0.7in}{\cyrf Aktivnye0\newline agent ("subp2ekt")}}\endaligned}\ \boxed{\aligned &\foldedtext\foldedwidth{1.2in}{\cyrf Interaktivnye0 protsess v avto-\newline kolebatelp1nom rezhime}\\&\to\boxed{\foldedtext \foldedwidth{0.63in}{\cyrf Graficheskie\newline dannye}}\to\\&\to\boxed{\foldedtext\foldedwidth{0.63in}{\cyrf Chastotnye\newline harakteristiki}}\nearrow\endaligned}} \aligned&\\&\Rightarrow \boxed{\foldedtext\foldedwidth{0.45in}{\cyrf Algoritm\newline vtorichnogo\newline sinteza}} \Rightarrow\endaligned \boxed{\aligned &\foldedtext\foldedwidth{1.4in}{\cyrf Iskusstvennaya interaktivnaya psi-\newline hoinformatsionnaya videosistema}\\& \boxed{\foldedtext\foldedwidth{1.4in}{\cyrf Dinamicheskoe izobrazhenie proiz-\newline volp1nogo (ne obyazatelp1no avtokole-\newline batelp1nogo) interaktivnogo protses-\newline sa v intentsionalp1noe0 anomalp1noe0\newline virtualp1noe0 realp1nosti}}\endaligned}} Opisannaya protsedura virtualizatsii lezhit v osnove primeneniya apparata anomalp1nyh virtualp1nyh realp1nostee0 kak razdela sovremennoe0 neklassicheskoe0 nachertatelp1noe0 (kompp1yuternoe0) geometrii dlya gra\-fi\-ches\-ko\-go predstavleniya i opisaniya e1ksperimentalp1nyh dannyh (sr.[9]) v fizike informatsionnyh sred, struktur i sistem. \subhead\cyb 2. Kriterie0 korrektnosti virtualizatsii \endsubhead \remark{\cyi\ Kriterie0 adekvatnosti izobrazheniya i korrektnosti virtualizatsii}\linebreak\cyr Virtualizatsiya estestvennoe0 interaktivnoe0 sistemy yavlyaet\-sya kor\-rek\-t\-noe0, esli poluchayushcheesya v rezulp1tate nee izobrazhenie e1toe0 sistemy po\-sred\-st\-vom nekotoroe0 iskusstvennoe0 interaktivnoe0 psihoinformatsionnoe0 videosistemy adekvatno is\-hodnoe0 sisteme, to estp1 pri odnovremennom funktsionirovanii kak iskusstvennoe0, tak i estestvennoe0 interaktivnyh sistem s odnim i tem zhe aktivnym agentom vosproizvedenie izobrazheniya zadannogo interaktivnogo protsessa pozvolyaet (pri opredelennom so\-sto\-ya\-nii i reshenii aktivnogo agenta) vyzvatp1 ego upravlyaemoe protekanie v estestvennoe0 interaktivnoe0 psihoinformatsionnoe0 sisteme. \endremark \cyr Razumeet\-sya, izobrazhenie mozhet bytp1 odnokratno postroeno na osnovanii e1ksperimentalp1nyh dannyh o funktsionirovanii estestvennoe0 interaktivnoe0 sistemy s drugim aktivnym agentom nezheli tot, kotorye0 uchastvuet v vosproizvedenii izobrazheniya (chto yavlyaet\-sya harakternoe0 osobennostp1yu metodiki pochti "po opredeleniyu", poskolp1ku issleduet\-sya sama interaktivnostp1 kak takovaya, a ne reaktsii konkretnogo aktivnogo agenta; v prikladnom aspekte e1ta osobennostp1 obespechivaet vozmozhnostp1 sozdaniya obuchayushchih sistem). Otmetim takzhe, chto pri vosproizvedenii izobrazheniya predusmatrivaet\-sya sovmestnoe odnovremennoe fun\-k\-tsi\-o\-ni\-ro\-va\-nie dvyh razlichnyh interaktivnyh sistem (iskusstvennoe0 i es\-tes\-t\-ven\-noe0) s odnim subp2ektom. Takim obrazom, osnovnoe otlichie vir\-tu\-a\-li\-za\-tsii ot matematicheskoe0 modeli zaklyuchaet\-sya v tom, chto poslednyaya yavlyaet\-sya {\cyi chistym deskriptorom\/} fizicheskogo protsessa, v to vremya kak pervaya -- {\cyi deskriptorom--konstruktorom}, chto predstavlyaet\-sya sushchestvennym s prikladnoe0 tochki zreniya. Vopros o tom, kak vozmozhna korrektnaya virtualizatsiya (t.e. teo\-re\-ti\-ches\-kie0 vyvod samoe0 vozmozhnosti iz nekotoryh pervyh printsipov), hotya i yavlyaet\-sya vesp1ma vazhnym, sushchestvennym i interesnym, ne stavit\-sya v dannoe0 rabote kak ne vpolne otnosyashchie0sya k matematicheskoe0 fizike (od\-na\-ko, odin iz svoih gipoteticheskih otvetov na e1tot vopros avtor rass\-chityvaet izlozhitp1 v drugoe0 rabote): predpolagaet\-sya, chto korrektnostp1 kazhdoe0 virtualizatsii i adekvatnostp1 kazhdogo izobrazheniya mogut bytp1 provereny lishp1 e1ksperimentalp1no. Tem ne menee, imeet smysl sformulirovatp1 ryad fenomenologicheskih printsipov, vypolnenie kotoryh, po-vidimomu, neobhodimo dlya korrektnosti virtualizatsii. \subhead\cyb 3. Fenomenologicheskie printsipy virtualizatsii \endsubhead \remark{\cyi\ Printsip izostrukturnoe0 ideografichnosti virtualizatsii} \cyr Vir\-tu\-a\-li\-za\-tsiya estestvennoe0 interaktivnoe0 psihoinformatsionnoe0 sistemy dolzhna bytp1 postroena tak, chto poluchayushcheesya posredstvom nee izobrazhenie ime\-la tu zhe vnutrennyuyu algebraicheskuyu strukturu, chto i is\-hodnaya sistema. \endremark \cyr Ispolp1zovanie sformulirovannogo vyshe printsipa predpolagaet zna\-nie algebraicheskoe0 struktury, lezhashchee0 v osnove fizicheskoe0 interaktivnoe0 sistemy. V silu opredleniya virtualizatsii dannaya struktura dolzhna bytp1 vosstanavlivaema po dannym o sisteme v avtokolebatelp1nyh (ustanovivshihsya) rezhimah. V kachestve takovyh imeet smysl ras\-smat\-ri\-vatp1 sostoyanie sistemy do "vklyucheniya" vzaimodee0stviya i posle ustanovleniya statsionarnyh avtokolebanie0. E1ksperimentalp1nye dannye o perehodnyh protsessah ne ispolp1zuyut\-sya. Takim obrazom, dlya opredeleniya algebraicheskoe0 struktury fizicheskoe0 interaktivnoe0 sistemy ne\-ob\-ho\-di\-mo reshitp1 obratnuyu zadachu rasseyaniya. \definition{\cyb Opredelenie} \cyr Vzaimnoe rasseyanie sostoyanie0 aktivnogo i passivnogo\linebreak agentov fizicheskoe0 interaktivnoe0 sistemy v protsesse ee fun\-k\-tsi\-o\-ni\-ro\-va\-niya budem nazyvatp1 {\cyi interaktivnym subp2ekt--obp2ektnym rasseyaniem}. \enddefinition \cyr Otmetim, chto interaktivnoe subp2ekt--obp2ektnoe rasseyanie, kak pravilo, neuprugo. tem samym, dlya vosstanovleniya algebraicheskoe0 struktury tselesoobrazno ispolp1zovatp1 matematicheskie0 apparat {\cyi analiza ne\-ga\-milp1\-to\-no\-va vzaimodee0stviya sistem}, fragment kotorogo soderzhit\-sya v serii rabot [10] i predvaritelp1noe0 versii obzora [11]. Otmetim, chto postanovka negamilp1tonovoe0 obratnoe0 zadachi rasseyaniya predpolagaet nahozhdenie po dannym rasseyaniya ne tolp1ko analiticheskih harakteristik vzaimodee0stviya tipa potentsialov, no i algebraicheskoe0 struktury, upravlyayushchee0 vzaimodee0stviem [10,11]. Tem samym, negamilp1tonova obratnaya zadacha rasseyaniya vklyuchaet naryadu s obratnoe0 zadachee0 po\-ten\-tsi\-alp1\-no\-go rasseyaniya [12] obratnye zadachi teorii potentsiala (sr.[13]) i teorii predstavlenie0 [14]. Virtualizatsiya fizicheskoe0 interaktivnoe0 sistemy stroit\-sya putem na\-tu\-ra\-li\-za\-tsii [7,1,4,5,6:Prilozh.1] poluchennyh pri reshenii obratnoe0 za\-da\-chi interaktivnogo subp2ekt--obp2ektnogo rasseyaniya algebraicheskih\linebreak struktur, opisyvayushchih simmetrii (v obobshchennom smysle) subp2\-ekt--obp2\-ekt\-no\-go vzaimodee0stviya. kak by to ni bylo, naturalizatsiya abstraktnoe0 kvantovoe0 modeli opredelena neodnoznachno. Konechno zhe, ee vybor nosit bolee ili menee e1vristicheskie0 harakter (sr.[7,1,4-5]). Odnako, razumno pri e1tom inogda prinimatp1 vo vnimanie nekotorye0 fenomenologicheskie0 printsip, dopolnyayushchie0 sformulirovannye0 vyshe printsip izostrukturnoe0 ideografichnosti. \remark{\cyi\ Printsip dinamicheskoe0 e1kvivalentnosti intentsie0} \cyr Virtualizatsiya estestvennoe0 interaktivnoe0 psihoinformatsionnoe0 sistemy dolzhna bytp1 postroena tak, chtoby parametry, harakterizuyushchie intensivnostp1 intentsii subp2ekta na obp2ekt, dlya nee i ee izobrazheniya sovpadali v pro\-tses\-se dinamicheskogo subp2ekt--obp2ektnogo vzaimodee0stviya. V kachestve podobnogo parametra mozhno rassmatrivatp1 korrelyatsiyu povedencheskih reaktsie0 subp2ekta i dinamicheskih harakteristik obp2ekta. \endremark \cyr Ispolp1zovanie fenomenologicheskih printsipov virtualizatsii, a takzhe e1vristicheskie soobrazheniya, spetsificheskie dlya kazhdoe0 konkretnoe0 za\-da\-chi, dolzhny obespechivatp1 korrektnostp1 virtualizatsii. Takim obrazom, sformulirovannuyu v rabote [2] zadachu ob opisanii klassa fizicheskih interaktivnyh informatsionnyh sistem mozhno s\-chitatp1 teoreticheski re\-shen\-noe0 v printsipe. Predlozhennaya metodika mozhet, s odnoe0 storony, posledovatelp1no primenyatp1sya k imeyushchimsya mnogochislennym konkretnym zadacham fiziki informatsionnyh sred, struktur i sistem, s drugoe0 zhe, chto ne menee vazhno, predostavlyaet vozmozhnostp1 ispolp1zovaniya obshchih teoreticheskih i matematicheskih metodov dlya vyyavleniya svyazee0 mezhdu nimi$^{2)}$. \head\cyb Prilozhenie: vtorichnye0 sintez izobrazhenie0\endhead \cyr Klyuchevaya rolp1 apparata anomalp1nyh virtualp1nyh realp1nostee0 i vto\-rich\-no\-go sinteza izobrazhenie0 (VSI) v rassmotrennoe0 metodike za\-klyu\-cha\-et\-sya v obespechenii dostatochnoe0 strukturirovannosti i, sledovatelp1no, potentsialp1noe0 yazykovoe0 nasyshchennosti (sr.[5]) videoinformatsii, ot\-sut\-stvie kotoryh do nastoyashchego vremeni yavlyalosp1 osnovnym nedostatkom, tormozyashchim razvitie podhoda, orientirovannogo na videosistemy, i sti\-mu\-li\-ro\-vav\-shim razrabotku alp1ternativnyh metodik, ispolp1zuyushchih audiosistemy (kotorye, odnako, v silu svoee0 ritmomelodicheskoe0 prirody okazyvayut\-sya prisposoblennymi skoree dlya realizatsii "zhestkoe0 na\-st\-roe0\-ki", nezheli vysokoskorostnoe0 interaktivnosti v realp1nom vremeni). S teoreticheskoe0 tochki zreniya VSI nesomnenno, nesmotrya na svoe chisto tehnicheskoe proishozhdenie (v e1lektronnoe0 kompp1yuternoe0 fotografii,\linebreak E1KF), yavlyaet\-sya fundamentalp1noe0 protseduroe0 {\cyi sovremennoe0 neklassicheskoe0 nachertatelp1noe0 (kompp1yuternoe0) geometrii\/} kak samoe0 po sebe, tak i kak graficheskoe0 formy predstavleniya fizicheskih e1ksperimentalp1nyh dannyh. Klassicheskimi analogami VSI yavlyayut\-sya razlichnye preobrazovaniya chertezha tipa sinteza aksonometrii po trem proektsiyam ili se\-che\-ni\-yam (v tom chisle nestandartnogo, tipa "nevozmozhnyh figur" E1shera [15]), a takzhe zameny tsentra perspektivy [16]. Poskolp1ku primenenie VSI (naryadu s raspoznavaniem obrazov) vskryvaet novye aspekty zadach {\cyi identifikatsii obp2ekta v kontekste psi\-ho\-fi\-zi\-ches\-koe0\/} (tochnee, {\cyi fenomenologicheskoe0\/}) {\cyi problemy}, imeet smysl udelitp1 vnimanie konkretnoe0, naibolee prostoe0 i harakternoe0, forme VSI, vtorichnomu sintezu izobrazhenie0 v E1KF. Osnovnaya ideya VSI v E1KF, predlozhennogo avtorom v 1992 godu, sostoit v preobrazovanii raznorodnyh, no prosto organizovannyh vhodnyh vizualp1nyh dannyh (poluchennyh v razlichnye momenty vremeni v razlichnyh rakursah i podvergnutyh "standartnomu" pervichnomu sintezu [17]) v odnorodnye vyhodnye dannye {\cyi bolee slozhnoe0\/} struktury v {\cyi nestandartnoe0\/} tsvetoperspektivnoe0 sisteme (TsPS) [18]. Ispolp1zovanie nestandartnyh TsPS i, v chastnosti, anomalp1nyh tsvetovyh prostranstv, soderzhashchih naryadu s tremya osnovnymi bazisnymi tsvetami dostatochnoe kolichestvo obertsvetov, pozvolyaet polnostp1yu sohranitp1 vhodnuyu informatsiyu pri ukazannom preobrazovanii. Prin\-tsi\-pi\-alp1\-naya s\-hema E1KF, osnovannoe0 na VSI, imeet vid: \boxed{\text{\cyre Videokompp1yuter}}\leftarrow \boxed{\text{\cyre Kompp1yuternye0 anomalae0zer}}\leftarrow \boxed{\aligned &\text{\cyre Detektory [prinimayushchie}\\ &\text{\cyre ustroe0stva, fotokamery]}\endaligned} Ispolp1zovanie neskolp1kih detektorov (prinimayushchih ustroe0stv) poz\-vo\-lya\-et uchestp1 stereoe1ffekty, v to vremya kak sp2emka v razlichnye momenty vremeni -- dvizhenie snimaemogo obp2ekta. Kompp1yuternye anomalae0zery ({\rm computer anomalizers}) preobrazuyut po opredelennomu pravilu vhodnye dannye, predstavlennye v tsifrovoe0 forme, v vyhodnye dannye, vos\-pro\-iz\-vo\-di\-mye na monitore videokompp1yutera. Vhodnaya tsifrovaya informatsiya mozhet podvergatp1sya VSI kak v moment sp2emki, tak i v moment vosproizvedeniya. V zavisimosti ot vybora s\-hemy kompp1yuternye0 anomalae0zer yav\-lya\-et\-sya libo pristavkoe0 k tsifrovoe0 fotokamere, libo sostavnoe0 chastp1yu programmnogo obespecheniya videokompp1yutera. Razberem protsess VSI v E1KF na modelp1nom, dostatochno harakternom primere TsPS "podvizhnogo videniya" ({\rm mobilevision, MV}) [18], raz\-ra\-bo\-tan\-no\-go avtorom v 1991 godu. {\rm MV} predstavlyaet soboe0 intentsionalp1nuyu anomalp1nuyu virtualp1nuyu realp1nostp1, naturalizuyushchuyu kvantovuyu pro\-ek\-tiv\-nuyu teoriyu polya (KPTP) [4-6] (sm. takzhe raboty [19,2,20,1], v kotoryh issledovalisp1 razlichnye algebraicheskie struktury KPTP), ili v inyh terminah, interaktivnuyu psihoinformatsionnuyu videosistemu s proektivno--invariantnoe0 obratnoe0 svyazp1yu$^{3)}$, osnovyvayushchee0sya na geometricheskih harakteristikah dvizhenie0 glaz (polozhenii tochki vzora i skorosti ee smeshcheniya)$^{4)}$[6]. Interaktivnye psihoinformatsionnye videosistemy s biologicheskoe0 obratnoe0 svyazp1yu, yavlyayushchiesya uproshchennymi analogami {\rm MV}, intensivno izuchayut\-sya v nastoyashchee vremya (nachinaya s 1993 goda) v Laboratorii po izucheniyu interaktivnyh sistem "che\-lo\-vek-kom\-pp1yu\-ter" (Vashington)[21]; biologicheskaya obratnaya svyazp1 v e1tih sistemah, buduchi opredelyaemoe0 parametrami dvizheniya glaz, ne yavlyaet\-sya, odnako, ni proektivno, ni $\SU(3)_{\color}$-invariantnoe0, tem ne menee otdelp1nye raz\-ra\-bot\-ki laboratorii (otnosyashchiesya k inym versiyam {\cyi interpretatsionnyh geo\-met\-rie0\/} [4,5,6:Prilozh.1]$^{5)}$ predstavlyayut opredelennye0 interes v rakurse dannoe0 statp1i. Otmetim takzhe otechestvennye issledovaniya osobennostee0 zritelp1nogo vospriyatiya v optikomehanicheskih interaktivnyh sistemah (sm. raboty [22] i ssylki v nih). Vhodnye dannye v sluchae {\rm MV} opisyvayut\-sya linee0nym prostranstvom $V_{\inp}=\oplus_{a\in A}V_a$, gde $V_a$ -- linee0nye prostranstva, izomorfnye obychnomu globalp1nomu tsvetovomu prostranstvu $V$, indeks $a$ harakterizuet prinimayushchee ustroe0stvo i moment sp2emki. E1lementy globalp1nogo tsvetovogo prostranstva $V$ -- funktsii tochki $z$ e1krana monitora so znacheniyami v standartnom potochechnom trehmernom tsvetovom prostranstve $V^{\circ}$. Vyhodnye dannye opisyvayut\-sya anomalp1nym tsvetovym prostranstvom $V_{\outp}$, predstavlyayushchim soboe0 proektivnye0 $\SU(3)$-gipermulp1tiplet [1,4-6]; struktura proektivnogo $\SU(3)$-gipermulp1tipleta v anomalp1nom tsvetovom prostranstve realizuet dinamicheskie simmetrii (sr.[23]) v nem. Takim obrazom, kompp1yuternye0 anomalae0zer osushchestvlyaet potochechnoe otobrazhenie $D$ (voobshche govorya, nelinee0noe) iz $V_{\inp}$ v $V_{\outp}$. E1tomu otobrazheniyu sootvet\-stvuet linee0nye0 operator $\hat D$ iz $S(V_{\inp}^{\circ})$, summy simmetricheskih stepenee0 prostranstva $V_{\inp}^{\circ}=\oplus_{a\in A} V_a^{\circ}$ ($V_a^{\circ}\simeq V^{\circ}$ ($V^{\circ}$ -- standartnoe potochechnoe trehmernoe tsvetovoe prostranstvo) v linee0noe prostranstvo $V_{\outp}^{\circ}$, summu mulp1tipletov proektivnogo $\SU(3)$-gipermulp1tipleta $V_{\outp}$. Dlay togo chtoby nae0ti dopustimoe mnozhestvo otobrazhenie0 $D$ iz $V_{\inp}$ v $V_{\outp}$ (ili, chto to zhe samoe, linee0nyh operatorov $\hat D$ iz $S(V_{\inp}^{\circ})$ v $V_{\outp}^{\circ}$), osushchestvlyayushchih VSI, neobhodimo uchestp1 vnutrennie simmetrii $V_{\inp}^{\circ}$ i $V_{\outp}^{\circ}$. Estestvenno predpolagatp1, chto $\hat D$ yavlyaet\-sya $\SU(3)$-spletayushchim operatorom [24]; tem samym, otobrazhenie $D$ stroit\-sya na baze ko\-e1f\-fi\-tsi\-en\-tov Klebsha-Gordana gruppy $\SU(3)$ [25]. Rassmotrim sluchae0 $\operatorname{^t\!\SU(3)\text{\rm-WZNW}}$-tsvetovogo prostranstva [18] v ka\-ches\-t\-ve primera. V e1tom sluchae, kak pravilo, opredelena estestvennaya proektsiya $D_0:T(V^{\circ})\mapsto V_{\outp}^{\circ}$, gde $T(V^{\circ})$ -- summa tenzornyh stepenee0 prostranstva $V^{\circ}$. Operator $D_0$ neposredstvenno vyrazhaet\-sya cherez ko\-e1f\-fi\-tsi\-en\-ty Klebsha-Gordana gruppy $\SU(3)$, v to vremya kak otobrazhenie $D$ op\-re\-de\-lya\-et\-sya polinomom $P(x_1,\ldots,x_N)$ ot $N$ nekommutiruyushchih peremennyh $x_a$, otvechayushchih vhodnym prostranstvam $V_a$ ($N=\#A$), a imenno, esli $v_a$ -- sovokupnostp1 e1lementov iz $V_a$, to $D(v_1,\ldots,v_n)(z)=D_0(P(v_1(z),\ldots,v_N(z)))$ dlya proizvolp1noe0 tochki $z$ e1krana. Prostranstvennye simmetrii opredelyayut\-sya konfiguratsiee0 pri\-ni\-ma\-yu\-shchih ustroe0stv. Naprimer, v binokulyarnom sluchae imeet\-sya $\Bbb Z_2$-sim\-met\-riya, a v die1dralp1nom geksagonalp1nom sluchae $D_6$-simmetriya, takim obrazom, v naibolee interesnyh sluchayah geometricheskie konfiguratsii detektorov opisyvayut\-sya konechnymi gruppami [26]. Vremennye simmetrii mogut bytp1 rassmotreny analogichno. esli simmetrii obrazuyut gruppu $G$, to e1ta gruppa obyazana dee0stvovatp1 v proektivnom $\SU(3)$-gi\-per\-mulp1\-ti\-ple\-te $V_{\outp}$ avtomorfizmami. Ukazannoe trebovanie suzhaet krug dopustimyh anomalp1nyh tsvetovyh prostranstv, a takzhe nakladyvaet na operator $D$ dopolnitelp1noe uslovie: on dolzhen bytp1 ne tolp1ko $\SU(3)$-spletayushchim, no i $G$-spletayushchim operatorom; kak sledstvie, pri po\-st\-ro\-e\-nii mnogochlena $P(x_1,\ldots,x_N)$ ispolp1zuyut\-sya koe1ffitsienty Klebsha-Gordana konechnoe0 gruppy $G$. Issledovanie vozmozhnyh skrytyh simmetrie0 (osobenno, pri obrabotke razlichnyh fizicheskih e1ks\-pe\-ri\-men\-talp1\-nyh dannyh slozhnoe0 netsvetovoe0 struktury, chto tipichno dlya obshchih, ne obya\-za\-telp1\-no chisto vizualp1nyh, estestvennyh interaktivnyh in\-for\-ma\-tsi\-on\-nyh sistem) predstavlyaet soboe0 vesp1ma interesnuyu zadachu (na vazhnostp1 izucheniya skrytyh simmetrie0 i svyazannyh s nimi dinamik ukazyvalosp1 v rabote avtora [1], tekushchee sostoyanie del otrazheno v obzore [14] i ssylkah v nem). V svyazi s tem, chto algebraicheskie obp2ekty, opisyvayushchie skrytye simmetrii, mogut imetp1 vesp1ma slozhnye0 harakter, izu\-che\-nie vozmozhnyh obobshchenie0 (v osobennosti, nehopfovyh) is\-chisleniya ko\-e1f\-fi\-tsi\-en\-tov Klebsha-Gordana i svyazannyh kombinatornyh struktur predstavlyaet osobye0 interes. Otmetim takzhe v zaklyuchenie, chto {\cyi sistemy vtorichnogo sinteza izobrazhenie0 v e1lektronnoe0 kompp1yuternoe0 fotografii\/} predstavlyayut interes i kak obp2ekt samostoyatelp1nyh issledovanie0$^{6)}$. Naibolee perspektivnym yavlyaet\-sya, po-vidimomu, izuchenie intellektualp1nyh sistem VSI s dinamicheskoe0 interaktivnoe0 nastroe0koe0 (a takzhe razrabotka portativnyh videosistem sinhronnogo BSI i kompleksnyh mnogopolp1zovatelp1skih sistem, sr.[5]$^{7)}$, poslednie imeyut nesomnennoe znachenie v kontekste statp1i [2] i dannoe0 raboty). Krome togo, sistemy VSI s dinamicheskoe0 in\-te\-rak\-tiv\-noe0 nastroe0koe0 (v tom chisle mnogopolp1zovatelp1skie) mogut rassmatrivatp1sya kak sistemy "avtomaticheskoe0 aranzhirovki vospriyatiya" v rakurse deyatelp1nosti, svyazannoe0 s kompp1yuternymi sistemami interaktivnogo "avtomaticheskogo pisp1ma", a takzhe issledovanie0 sinteticheskoe0 pertseptsii. Imeet smysl i izuchenie oktonionnogo anomalp1nogo {\rm 3D} stereosinteza [4]$^{8)}$ (nekotorye simmetrie0nye aspekty obychnogo stereosinteza v ramkah psihologii vospriyatiya i teorii mashinnogo zreniya is\-sle\-do\-va\-lisp1, naprimer, v [27]), kiralp1noe0 dissimmetrii zritelp1nogo analizatora v interaktivnyh protsessah i ee vliyaniya na stereosintez, tak zhe kak i prilozheniya VSI v E1KF k problemam tsifrovogo, v tom chisle interaktivnogo, viseo$^{9)}$ i interaktivnogo kompp1yuternogo zreniya [28]. Predstavlyaet\-sya takzhe osobo vazhnym izuchenie sovmestnogo fun\-k\-tsi\-o\-ni\-ro\-va\-niya estestvennyh interaktivnyh sistem i ih virtualizatsie0 (i v dannom sluchae umestno govoritp1 ob urovnyah realp1nosti) pri razrabotke spetsificheski kompleksnyh estestvenno-iskusstvennyh (in\-teg\-ri\-ro\-van\-nyh) interaktivnyh sistem (realizuyushchih {\cyi "integrirovannuyu realp1nostp1"\/}), v tom chisle sistem uskorennoe0 neverbalp1noe0 kognitivnoe0 kommunikatsii, odna iz komponent kotoryh izuchalasp1 v [5:\S 2]. Podhod k razrabotke integrirovannyh sistem uskorennoe0 neverbalp1noe0 kognitivnoe0 kom\-mu\-ni\-ka\-tsii, baziruyushchihsya na ispolp1zovanii IAVR-telestezii v kachestve apparata predvaritelp1nogo raspoznavaniya i interaktivnoe0 {\cyi samonastroe0ki\/} kommunikatsionnyh "klyuchee0" subp2ektov, a takzhe ih dinamicheskoe0 sin\-hro\-ni\-za\-tsii, prizvan obespechitp1 pokanalp1nuyu interaktivnuyu op\-re\-de\-lya\-e\-mostp1 "klyuchee0" svyazi i, tem samym, printsipialp1nuyu neinterpretiruemostp1 (nedeshifruemostp1) soobshcheniya izvne. K integrirovannym sis\-te\-mam, vklyuchayushchim v sebya iskusstvennye interaktivnye videopodsistemy avtomaticheskoe0 aranzhirovki vospriyatiya (sm.vyshe), otnosyat\-sya in\-teg\-ri\-ro\-van\-nye videosensornye sistemy interaktivnogo zreniya (sr.[6]) s estestvennoe0 sensornoe0 podsistemoe0 i integrirovannye vi\-de\-o\-res\-pi\-ra\-tor\-nye interaktivnye sistemy (t.e. interaktivnye videosistemy s respiratornoe0 modulyatsiee0 ili, v bolee obshchem sluchae, tran\-s\-for\-ma\-tsi\-ee0 vi\-zu\-alp1\-nyh interaktivnyh protsessov) psihofiziologicheskogo au\-to\-tre\-nin\-ga (kak passivno-relaksatsionnogo, tak i aktivno-dinamicheskogo). V to zhe samoe vremya sami iskusstvennye interaktivnye psihoinformatsionnye videosistemy interesny s tochki zreniya zadach organizatsii i intensifikatsii cheloveko-nashinnogo interfee0sa (sm.napr.[29]), raboty sistem upravleniya v poluavtomaticheskom rezhime i peredachi informatsii cherez kompp1yuternye seti, pri e1tom operatornye (kvantovo-polevye) aspekty teorii interaktivnyh videosistem mogut okazatp1sya poleznymi dlya adaptatsii metodov kvantovoe0 kriptografii [30] k poslednemu iz upomyanutyh krugu voprosov. S drugoe0 storony, vozmozhny interesnye prilozheniya kvantovoe0 teorii upravleniya i idempotentnogo analiza [31] k interaktivnym videosistemam upravleniya v poluavtomaticheskom rezhime v ram\-kah operatornogo (kvantovo-polevogo i stohasticheskogo) podhoda. Vazhnoe0 zadachee0 yavlyaet\-sya opredelenie spektra kvazichastits v abstraktnyh kvantovo-polevyh modelyah interaktivnyh videosistem realp1nogo vremeni$^{10))}$, v chastnosti, informatsionnyh kvazichastits, sposobnyh k sa\-mo\-or\-ga\-ni\-za\-tsii i samovosproizvedeniyu v interaktivnyh protsessah, ({\cyi vi\-ne\-ro\-nov\/}), i nenablyudaemyh informatsionnyh kvazichastits, struk\-tu\-ri\-ru\-yu\-shchih vospriyatie ostalp1nyh obp2ektov, ({\cyi paulionov}, sr. prim. 9), a takzhe vyyavlenie svyazi kvantovo-poleogo "odevaniya" subp2ekta v ukazannyh mo\-de\-lyah i virtualp1nyh nablyudatelee0 v interaktivnyh videosistemah [5:\S 2]. Opredelennye0 interes dlya teorii interaktivnyh videosistem predstavlyayut i strunno-polevye modeli [32], i, kak sledstvie, obp2ekty bes\-ko\-nech\-no\-mer\-noe0 geometrii, lezhashchie v ih osnove [33,32; i ssylki v nih]. Aktualp1noe0 zadachee0 yavlyaet\-sya razrabotka sistem filp1tratsii v di\-na\-mi\-ches\-kih interaktivnyh videosistemah (a takzhe smeshannyh i in\-teg\-ri\-ro\-van\-nyh sistemah), ispolp1zuyushchih alghoritmy vtorichnogosinteza, chto s teoreticheskoe0 tochki zreniya predpolagaet analiz izobrazhenie0, obratnye0 opisannomu vyshe vtorichnomu sintezu. Sovmestnoe ispolp1zovanie me\-to\-dov analiza i vtorichnogo sinteza pozvolyaet proizvoditp1 resintez vto\-rich\-no\-sin\-te\-zi\-ro\-van\-nyh izobrazhenie0 (matematicheskie aspekty resinteza zatragivalisp1 v obzore [14]). Otmetim, chto v kontekste sozdaniya integrirovannyh interaktivnyh sistem nebezynteresno izuchenie spektra vozmozhnyh realizatsie0 fiksirovannoe0 iskusstvennoe0 interaktivnoe0 sis\-temy. V zaklyuchenie, avtor rad vyrazitp1 priznatelp1nostp1 prof.E1.E1.Godiku za besedy v 1993 godu, zalozhivshie osnovu izlozhennogo vyshe avtorskogo podhoda k opisaniyu fizicheskih interaktivnyh sistem (a v prikladnom aspekte obuslovivshie orientatsiyu na vozmozhnostp1 ego ispolp1zovaniya dlya sozdaniya obuchayushchih sistem). Avtor blagodaren akad.I.V.Smirnovu za obsuzhdenie kak kontseptualp1nyh (teoreticheskih i prakticheskih) aspektov temy, tak i konkretnyh prilozhenie0; prof.A.Yu.Morozovu i uchastnikam ego seminara v ITE1F, sposobstvovavshim kristallizatsii ob\-shche\-fi\-zi\-ches\-ko\-go i informatsionno-fizicheskogo ponimaniya predmeta avtorom; prof.V.N.Kolokolp1tsovu, blagodarya besedam s kotorym okazalosp1 vozmozhnym istolkovanie syuzheta v terminah interaktivogo upravleniya i interaktivnyh igr i, sledovatelp1no, kak razdela teorii upravlyaemyh sistem i metematicheskoe0 teorii igr, a takzhe mnogim drugim kollegam, chp1e vliyanie na formirovanie fragmentov i otdelp1nyh detalee0 obshchee0 kar\-ti\-ny nesomnenno. \ \tenpoint \subhead{\cyb Primechaniya}\endsubhead \eightpoint\ \newline 1. {\cyre Predvaritelp1nye e1lektronnye versii osnovnogo teksta i Prilozheniya ras\-po\-la\-ga\-yut\-sya v e1lek\-t\-ron\-nom arhive Natsionalp1nyh Laboratorie0 v Los Alamose (SShA) po adaptatsii i sa\-mo\-or\-ga\-ni\-za\-tsii pod nomerami {\rm "adap-org/9409003"} i {\rm "adap-org/9409002"}.} \newline 2. {\cyre Izlozhennaya metodika opisaniya klassa fizicheskih interaktivnyh in\-for\-ma\-tsi\-on\-nyh sistem ne predpolagaet reduktsiyu matematiki, lezhashchee0 v osnove pro\-iz\-volp1\-nyh sensornyh vospiyatie0, k toe0 ili inoe0 geometrii. Predpolagaya, sleduya T.Sa\-a\-ti [8], nalichie osoboe0, eshche matematicheski ne vyyavlennoe0, ne\-prostranstvennoe0, negeometricheskoe0 intuitsii inyh, otlichnyh ot zritelp1nyh, sensornyh vos\-pri\-ya\-tie0, ona namechaet e1ksperimentalp1nye0 putp1 k raskrytiyu sushchestvennyh svyazee0 mezhdu so\-ot\-vet\-st\-vu\-yu\-shchee0 matematikoe0 i geometriee0, podobnyh vzaimootnosheniyu mezhdu po\-sled\-nee0 i algebroe0, raskrytomu v kontse {\rm XIX} stoletiya.} \newline 3. {\cyre Invariantnoe0 takzhe otnositelp1no priblizhennyh tsvetovyh $\SU(3)_{\color}$--sim\-met\-rie0 [4-6] (sm. takzhe [34]).} \newline 4. {\cyre Takim obrazom, prostee0shie demonstratsionnye versii {\rm MV} mogut bytp1 realizovany naryadu so mnogimi drugimi interaktivnymi videosistemami v "domashnih us\-lo\-vi\-yah" na standartnom PK s sistemoe0 tsifrovoe0 obrabotki biosignalov. Bazisnye svedeniya o napisanii drae0verov dlya podobnyh sistem, vvedenie v osnovy or\-ga\-ni\-za\-tsii videosistem PK i ih programmirovanie, a takzhe e1lementy programmirovaniya v re\-alp1\-nom vremeni i animatsii v srede {\rm Windows} soderzhat\-sya v knigah [35,36].} \newline 5. {\cyre Otmetim, chto konstruktivno zadavaemye metodami e1ksperimentalp1noe0 ma\-te\-ma\-ti\-ki razlichnye interpretatsionnye figury formalizuyut\-sya ne aksiomaticheski, no opi\-sy\-va\-yu\-t\-sya dinamicheskimi simulyakrami ponyatie0, t.e. interaktivnymi ponyatie0ny\-mi obp2ektami s dinamicheskim (intentsionalp1nym) smyslovym soderzhaniem. Takim ob\-ra\-zom, ispolp1zovanie dinamicheskih simulyakrov yavlyaet\-sya estestvennym dlya e1kspe\-ri\-men\-talp1\-noe0 matematiki, operiruyushchee0 s yavno postroennymi obp2ektami, ne do\-pus\-ka\-yu\-shchi\-mi vydeleniya bazisnoe0 konechnoe0, schetnoe0 ili konstruktivno opisuemoe0 sis\-te\-my svoe0stv, iz kotoryh vse ostalp1nye svoe0stva vyvodyat\-sya formalp1nymi me\-to\-da\-mi.} \newline 6. {\cyre Avtor raspolagaet e1ksperimentalp1noe0 versiee0 programmnogo paketa {\rm "Ma\~nju\v sri"} vtorichnogo sinteza {\rm TrueColor Bitmap} izobrazhenie0 v srede {\rm Windows}, razrabotannoe0 v TsMFI "Talassa E1teriya".} \newline 7. {\cyre Otmetim, chto odin iz rezulp1tatov poslednee0 raboty sostoit v vydelenii klassa geometricheskih obp2ektov e1ksperimentalp1noe0 matematiki (sm.prim.5), nablyudaemyh tolp1ko v mnogopolp1zovatelp1skom rezhime (potae0nyh figur), chto predstavlyaet\-sya vesp1\-ma sushchestvennym dlya ponimaniya haraktera subp2ekt--obp2ektnyh otnoshenie0 v tse\-lom i v kontekste problemy polisubp2ektnosti, v chastnosti. Mnogie interaktivnye pro\-tses\-sy v mnogopolp1zovatelp1skom rezhime imeet smysl rassmatrivatp1 kak {\cyie in\-ter\-ak\-tiv\-nye igry\/} v ramkah obshchee0 matematicheskoe0 teorii igr [37], pri e1tom, mozhno go\-vo\-ritp1 o virtualizatsii i realizatsii interaktivnyh igr. Formalp1no pod {\cyie in\-ter\-ak\-tiv\-nym upravleniem}, kotoroe i realizuet\-sya igrokami v interaktivnyh igrah, po\-ni\-ma\-et\-sya upravlenie, sparennoe s neupravlyaemoe0 i ne izvestnoe0 polnostp1yu obratnoe0 svyazp1yu. S e1toe0 formalp1noe0 tochki zreniya matematicheskie0 interes predstavlyaet raz\-lo\-zhe\-nie slozhnogo interaktivnogo upravleniya po prostym bazisnym ili inoe pre\-ob\-ra\-zo\-va\-nie k nim vvidu sushchestvennoe0 neredutsiruemosti interaktivnosti kak takovoe0.} \newline 8. {\cyre Nekotorye momenty, otchasti napominayushchie stereosintez v {\rm MV}, vstrechayut\-sya i v {\cyie neinteraktivnyh\/} stereosistemah e1mulyatsii trehmernoe0 vir\-tu\-alp1\-noe0 realp1nosti, postroennyh na printsipah dinamicheskogo (neinteraktivnogo) e1kranirovaniya. Ispolp1zovanie dinamicheskogo interaktivnogo e1kranirovaniya (kotoroe mozhet bytp1 osu\-shches\-tv\-le\-no kak programmno, tak i na analogovom ili tsifrovom apparatnom urovne) vmeste s mehanizmami, opisannymi v rabotah [5,1,4-6], predostavlyaet optimalp1noe reshenie problemy nerazrusheniya izobrazheniya (sm.[6]) v "podvizhnom videnii". Imeet smysl rassmatrivatp1 i funktsionalp1noe (ispolp1zuyushchee predystoriyu) di\-na\-mi\-ches\-koe e1kranirovanie (e1kranirovanie s pamyatp1yu), v kvantovoe0 teorii izmereniya analogichnaya neinteraktivnaya protsedura byla nedavno predlozhena D.A.Slavnovym [38]. V modeli D.A.Slavnova, vne zavisimosti ot ee adekvatnosti kvantovoe0 realp1nosti, zaklyucheny vazhnye resursy s tochki zreniya fiziki informatsionnyh sred, struktur i sistem. Analogovoe interaktivnoe dinamicheskoe e1kranirovanie mozhet osnovyvatp1sya kak na sravnitelp1no prostyh (interaktivnyh) integratorah signalov tsvetnosti, tak i na obp2emnyh vektor--matrichnyh peremnozhitelyah, vklyuchayushchih mnogochastotnye0 akustoopticheskie0 modulyator [39]. Otmetim takzhe, chto integrirovannye0 vysokochastotnye0 tsifrovoe0 displee0 s optoe1lektronnym nee0roprotsessorom [40,39] predstavlyaet soboe0 idealp1nuyu sredu dlya realizatsii {\rm MV} i stohasticheskogo {\rm MV} [6], kak, vprochem, i osnovyvayushchee0sya na nih interaktivnoe0 vychislitelp1noe0 {\rm MISD}--arhitektury [5:\S 2]. Kak otmechalosp1 v [6], interaktivnaya {\rm MISD}--arhitektura predstavlyaet interes dlya uskoreniya obrabotki sensornoe0 informatsii v sistemah {\rm VR(AVR)--}telekommunikatsie0.} \newline 9. {\cyre V nastoyashchee vremya vtorichnye0 sintez obp2emnyh ({\rm 3D}) stereoizobrazhenie0 e1f\-fek\-tiv\-no ispolp1zuet\-sya dlya generatsii {\cyie obobshchennogo\/} (v tom chisle dinamicheskogo interak\-tiv\-no\-go, naprimer, "dopplerovskogo", t.e. opredelyayushchego zavisimostp1 tsveta e1lemen\-ta poverhnosti kak ot polozheniya, tak i ot skorosti nablyudatelya) {\cyie osveshcheniya\/} (vve\-de\-nie v metody generatsii "standartnogo" osveshcheniya soderzhit\-sya v knige [17]) v e1k\-s\-pe\-ri\-men\-talp1\-noe0 sisteme {\rm 3D} stereoanimatsii {\rm "M\B ay\B a"}, razrabotannoe0 v TsMFI "Talassa E1teriya" (anonsirovana na {\rm AIHENP'96}). Na neslozhnom primere realizuemoe0 po\-sred\-s\-t\-vom e1toe0 sistemy anomalp1noe0 virtualp1noe0 realp1nosti dostatochno yasno raskryvaet\-sya netrivialp1nostp1 zadach (esli tak mozhno vyrazitp1sya, {\cyie matematicheskoe0 fe\-no\-me\-no\-lo\-gii\/}) identifikatsii obp2ektov (naprimer, nevidimyh istochnikov obobshchennogo osveshcheniya). Otmetim takzhe, chto videosistemy obobshchennogo os\-ve\-shche\-niya predstavlyayut uni\-ver\-salp1\-noe sredstvo dlya vizualizatsii fizicheskih vzaimodee0stvie0 i protsessov iz\-me\-re\-niya (pri e1tom vtorichnye0 sintez izobrazhenie0 reshaet vizualizirovannuyu obratnuyu za\-da\-chu rasseyaniya).} \newline 10. {\cyre Analogom "korpuskulyarnogo" podhoda v kvantovoe0 teorii polya i reshetochnyh mo\-de\-lyah yavlyaet\-sya animatsiya sprae0tov v kompp1yuternoe0 grafike, kotoraya mozhet is\-polp1\-zo\-vatp1\-sya pri vizualizatsii lokalizovannyh kvazichastits.} \tenpoint \head\bf Список литературы\endhead \eightpoint \roster \widestnumber\item{} \item"[1]" {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1994. T.98, \nom.2. \cyre S.220-240}. \item"[2]" {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1994. T.101, \nom.3. \cyre S.331-348}. \item"[3]" {\cyie Manin Yu.I.}, {\cyre Matematika i fizika. M., Znanie, 1979}. \item"[4]" {\cyie Yurp1ev D.V.} /\!/ {\cyre FPM, v pechati} [preliminary e-version: hep-th/9401047 (1994)]; {\it Juriev D.}, Octonionic binocular mobilevision. An overview: Report RCMPI-95/05 (1995) [e-version: adap-org/9511002 (1995)]. \item"[5]" {\it Juriev D.}, Visualizing 2D quantum field theory: geometry and informatics of mobilevision: Report RCMPI-96/02 (1996) [e-version: hep-th/9401067+9404137 (1994)]. \item"[6]" {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1996. T.106, \nom.2. \cyre S.333-352.} \item"[7]" {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1992. T.92, \nom.1. \cyre S.172-176.} \item"[8]" {\it Saaty T.L.} /\!/ Lett.Appl.Math. 1988. V.1, \nom.2. P.79-82. \item"[9]" {\it Visualized\/} flow. Ed.Y.Nakayama, Pergamon, Oxford, 1988; {\it Visualization\/} in human--com\-pu\-ter interaction. Eds.P.Gorny and M.J.Taubes, Springer, 1990; {\it Scientific\/} visualization of physical phenomena. Ed.N.M.Patrikalakis, Springer, 1991; {\it Scientific\/} visualization: techniques and applications. Ed.K.W.Brodlie, Springer, 1992; {\it Focus\/} on scientific visualization. Eds.H.Hagen, H.M\"uller and G.M.Nielson, Springer, 1993; {\it Visualization\/} in scientific computing. Eds.M.Grave, Y.Le Lous and W.T.Hewitt, Springer, 1994. \item"[10]" {\it Juriev D.} /\!/ Russian J.Math.Phys. 1995. V.3, \nom.4. P.453-460; Topics in nonhamiltonian (magnetic--type) interaction of classical Hamiltonian dynamical systems. II. Generalized Euler--Am\-p\`ere equations and Biot--Savart operators: Report RCMPI-96/02 [e-version: mp\_arc/95-538 (1995)]; {\cyie Yurp1ev D.V.}/\!/ {\cyre TMF. 1995. T.105, \nom.1. \cyre S.18-28}; {\cyre TMF, v pechati} [e-version: q-alg/9511012 (1995)]; {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1996. T.109, \nom.00. \cyre S.00-00}; {\it Juriev D.}, Symmetric designs on Lie algebras and interactions of Hamiltonian systems: Preprint ESI 170 (1994) [e-version: solv-int/9503003 (1995)]; {\cyie Yurp1ev D.V.} /\!/ {\cyre Mat.zametki, v pechati} [preliminary e-version: mp\_arc/95-519 (1995)]; {\it Juriev D.}/\!/ Russian J.Math.Phys., to appear [e-version: funct-an/9409003 (1994)]; On the dynamics of noncanonically coupled oscillators and its hidden superstructure: Preprint ESI 167 (1994) [e-version: solv-int/9503003 (1995)]. \item"[11]" {\cyie Yurp1ev D.V.}, {\cyre Klassicheskaya i kvantovaya dinamika negamilp1tonovo vza\-i\-mo\-dee0\-st\-vu\-yu\-shchih gamilp1tonovyh sistem}: Report RCMPI-96/03 (1996). \item"[12]" {\cyie De Alp1faro V., Redzhe T.}, {\cyre Potentsialp1noe rasseyanie. M., Mir, 1966}; {\cyie Np1yuton R.}, {\cyre Teoriya rasseyaniya voln i chastits. M., Mir, 1969}; {\cyie Rid M., Sae0mon B.}, {\cyre Me\-to\-dy so\-vre\-men\-noe0 matematicheskoe0 fiziki. T.3. Teoriya rasseyaniya. M., Mir, 1982}; {\cyie Mer\-kurp1\-ev S.P., Faddeev L.D.}, {\cyre Kvantovaya teoriya rasseyaniya dlya sistem ne\-s\-kolp1\-kih chastits. M., Nauka, 1985}. \item"[13]" {\cyie Sretenskie0 L.N.}, {\cyre Teoriya np1yutonovskogo potentsiala. M.-L., 1946}; {\cyie Prilepko A.I.} /\!/ {\cyre Diff. ur-niya. 1966. T.2, \nom.1. \cyre S.107-124}. \item"[14]" {\cyie Yurp1ev D.V.}, {\cyre E1kskurs v obratnuyu zadachu teorii predstavlenie0}: Report RCMPI-95/04 (1995) ({\cyre sm.takzhe:} {\it Juriev D.}/\!/ J.Math.Phys. 1994. V.35. P.5021-5024; {\it Ju\-ri\-ev D.}, Topics in hidden symmetries: E-print, hep-th/9405050 (1994); {\cyie Yurp1ev D.V.}/\!/ {\cyre FPM, v pechati} [e-version: funct-an/9411007 (1994)]; {\cyre FPM, v pechati} [e-version: funct-an/9507001 (1995)]). \item"[15]" {\it Escher M.C.}, The graphic work of M.C.Escher. Ballantine, New York, 1971; {\it Penrose R.} /\!/ Struct.Topology. 1991. V.17. P.11-16. \item"[16]" {\cyie Monzh G.}, {\cyre Nachertatelp1naya geometriya. M., Izd-vo AN SSSR, 1947}; {\cyie Russkevich N.L.}, {\cyre Nachertatelp1naya geometriya, Kiev, Budi1velp1nik, 1970}; {\cyie Bubennikov A.V., Gromov M.Ya.}, {\cyre Nachertatelp1naya geometriya, M., Vysshaya shkola, 1973}. \item"[17]" {\cyie Martines F.}, {\cyre Sintez izobrazhenie0. Printsipy, apparatnoe i programmnoe obe\-spe\-che\-nie. M., Radio i svyazp1, 1990}. \item"[18]" {\it Juriev D.} /\!/ The Visual Computer. 1994. V.11. \nom.2. P.113-120. \item"[19]" {\it Juriev D.} /\!/ Lett.Math.Phys. 1991. V.21. P.113-115, V.22. P.141-144; {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1991. T.86, \nom.3. \cyre S.338-343; Algebra i anal. 1991. T.3, \nom.3. \cyre S.197-205}; {\it Ju\-ri\-ev D.} /\!/ J.Math.Phys. 1992. V.33. P.492-496; Commun.Math.Phys. 1991. V.138. P.569-581, 1992. V.146. P.427; J.Funct.Anal. 1991. V.101. P.1-9; J.Math.Phys. 1991. V.32. P.2034-2038; {\cyie Yurp1ev D.V.} /\!/ {\cyre UMN. 1991. T.46, \nom.4. \cyre S.115-138}. \item"[20]" {\it Juriev D.} /\!/ J.Math.Phys. 1992. V.33. P.3112-3116; {\cyie Yurp1ev D.V.} /\!/ {\cyre TMF. 1992. T.93, \nom.1. \cyre S.32-38}; {\it Juriev D.} /\!/ J.Math.Phys. 1992. V.33. P.1153-1157; P.2819-2822; 1993. V.34. P.1615; 1994. V.35. P.3368-3379; {\cyie Bychkov S.A., Yurp1ev D.V.}/\!/ {\cyre UMN. T.46, \nom.5. \cyre S.161-162}; {\cyie Bychkov S.A.} /\!/ {\cyre UMN. T.47, \nom.4. \cyre S.187-188}; {\cyie Bychkov S.A., Plotnikov S.V., Yurp1ev D.V.} /\!/ {\cyre UMN. 1993. T.48, \nom.3. \cyre S.153}; {\cyie Bychkov S.A., Yurp1ev D.V.} /\!/ {\cyre TMF. 1993. T.97, \nom.3. \cyre S.336-347}. \item"[21]" {\it Jacob R.J.K.} /\!/ ACM Trans. on Inform. Systems. V.11. April 1993. P.152-169; Advances in Human--Computer Interaction. V.4. Eds. H.R.Harston and D.Hix. Norwood, NJ, Ab\-lex Publ. Co. 1993. P.151-190; Human--Machine Communication for Education Systems Design. Eds. M.D.Brouwer-Jause and T.L.Harrington (NATO ASI Series. F: Computer and Systems Sciences. V.129) Springer, 1994, P.131-138. \item"[22]" {\cyie Dvizheniya\/} {\cyre glaz i zritelp1noe vospriyatie.} II. {\cyre Issledovanie mehanizmov re\-gu\-lya\-tsii dvizhenie0 glaz v usloviyah transformatsii zritelp1noe0 obratnoe0 svyazi.} {\cyre M., Nauka, 1978. S.71-170}; {\cyie Barabanshchikov V.A., Belopolp1skie0 V.I., Vergiles N.Yu.} /\!/ {\cyre Psihol.zhurn. 1980. T.1, \nom.3. \cyre S.85-94}; {\cyie Barabanshchikov V.A.}, {\cyre Dinamika zri\-telp1\-no\-go vospriyatiya. M., Nauka, 1990}; {\cyie Barabanshchikov V.A.} /\!/ {\cyre Psihol.zhurn. 1995. T.16, \nom.5. \cyre S.67-86}. \item"[23]" {\it Lenz R.}, Group theoretical methods in image processing. Springer, 1990. {\it Kanatani K.I.}, Group theoretical methods in image understanding. Sprin\-ger, 1991. \item"[24]" {\cyie Barut A., Ronchka R.}, {\cyre Teoriya predstavlenie0 grupp i ee prilozheniya. M., Nauka, 1980}; {\cyie Bazp1 A.I., Zelp1dovich Ya.B., Perelomov A.M.}, {\cyre Rasseyanie, reaktsii i raspady v nerelyativist\-skoe0 kvantovoe0 mehanike. M., Nauka, 1971}; {\cyie Malkin I.A., Manp1ko V.I.}, {\cyre Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovyh sistem. M., Nauka, 1979}; {\cyie Perelomov A.M.}, {\cyre Obobshchennye kogerentnye so\-sto\-ya\-niya i ih primenenie. M., Nauka, 1987}; {\cyie Zhelobenko D.P.}, {\cyre Predstavleniya re\-duk\-tiv\-nyh algebr Li. M., Nauka, 1994}; {\it Symmetries\/} in science. VII. Spectrum--ge\-ne\-ra\-ting al\-geb\-ras and dynamic symmetries in physics. Eds.B.Gruber, T.Otsake, Plenum Publ., 1995. \item"[25]" {\cyie Klimyk A.U.}, {\cyre Matrichnye e1lementy i koe1ffitsienty Klebsha--Gordana pred\-s\-tav\-le\-nie0 grupp. M., Nauka, 1979.} \item"[26]" {\cyie Kovalev O.V.}, {\cyre Neprivodimye i indutsirovannye predstavleniya i ko\-pred\-stav\-le\-niya fedorovskih grupp. M., Nauka, 1986.} \item"[27]" {\cyie Nikolaev P.P.} /\!/ {\cyre Sensornye sistemy. 1990. T.4, \nom.4. \cyre S.421-442, 1991. T.5, \nom.1. \cyre S.89-104, \nom.2. \cyre S.85-98, \nom.3. \cyre S.70-80}; {\it Computer\/} vision. Proceedings ECCV-90, Springer, 1990; {\cyie Nikolaev P.P.} /\!/ {\cyre Sensornye sistemy. 1995. T.9, \nom.2-3. \cyre S.109-131}; {\cyie Rozhkova G.I., Podugolp1nikova T.A., Sisengalieva G.Zh., Matveev S.G.} /\!/ {\cyre Sensornye sistemy. 1996. T.10, \nom.1. \cyre S.46-76.} \item"[28]" {\it Batchelor B., Waltz F.}, Interactive image processing for machine vision. Springer, 1993. \item"[29]" {\it Rheingold H.}, Virtual reality. Summit, New York, Tokyo, 1991; {\it Virtual\/} reality: an interantional directory of research projects. Ed.J.Thompson. Meckler, Westport, 1993; {\it Virtual\/} reality: applications and explorations. Ed.A.Wexelblat. Acad.Publ., Boston, 1993; {\it Kalawsky R.S.}, The science of virtual reality and virtual environments. Addison--Wesley, 1993; {\cyie Forman N., Vilp1son P.} /\!/ {\cyre Psihol.zhurn. 1996. T.17, \nom.2. \cyre S.64-79}. \item"[30]" {\it Wiesner S.} /\!/ SIGACT News. 1983. V.15, no.1. P.78-88; {\it Wiedemann D.} /\!/ SIGACT News. 1989. V.18, no.2. P.28-30; {\it Bennett C.H., Brassard G.} /\!/ SIGACT News. 1989. V.20, no.2. P.78-82; {\it Ekert A.K.} /\!/ Phys.Rev.Lett. 1991. V.67. P.661-663; {\it Bennett C.H., Brassard G., Mermin N.D.} /\!/ Phys.Rev.Lett. 1992. V.68. P.557-559; {\it Bennett C.H.} /\!/ Phys.Rev.Lett. 1992. V.68. P.3121-3124; {\it Bennett C.H., Wiesner S.J.} /\!/ Phys. Rev. Lett. 1992. V.69. P.2881-2884; {\it Bennett C.H., Brassard G., Cr\'epeau C., Jozsa R., Peres A., Wootters W.K.} /\!/ Phys.Rev.Lett. 1993. V.70. P.1895-1899. \item"[31]" {\cyie Belavkin V.P.} /\!/ {\cyre Avtomatika i telemehanika. 1983. T.44, \nom.2. \cyre S.50-63}; {\cyie Av\-do\-shin S.M., Belov V.V., Maslov V.P.} /\!/ {\cyre UMN. T.39, \nom.4. \cyre S.108-109}; {\cyie Av\-do\-shin S.M., Belov V.V., Maslov V.P.}, {\cyre Matematicheskie aspekty sinteza vy\-chis\-li\-telp1\-nyh sred. M., Izd-vo MIE1M, 1984}; {\cyie Kolokolp1tsov V.N., Maslov V.P.} /\!/ {\cyre Funkts. analiz i ego prilozh. 1989. T.23, \nom.1. \cyre S.1-14, \nom.4. \cyre S.53-62}; {\cyie Kolokolp1tsov V.N.} /\!/ {\cyre DAN SSSR. 1992. T.323, \nom.2. \cyre S.223-228}; {\it Idempotent\/} analysis. Eds.V.P.Maslov and S.N.Samborskii. Adv.Soviet Math.15, Amer. Math. Soc., R.I., 1992; {\cyie Maslov V.P., Ko\-lo\-kolp1\-tsov V.N.}, {\cyre Idempotentnye0 analiz i ego primenenie v optimalp1nom up\-rav\-le\-nii. M., Nauka, 1994.} \item"[32]" {\it Juriev D.}/\!/ Lett.Math.Phys. 1991. V.22. P.1-6; 1990. V.19. P.59-64; 1990. V.19. P.355-356; 1991. V.22. P.11-14; {\it Juriev D.}/\!/ Alg.Groups Geom. 1994. V.11. P.145-179; Russian J.Math.Phys. 1996. V.4, \nom.3; J.Geom.Phys. 1995. V.16. P.275-300. \item"[33]" {\cyie Kirillov A.A.}/\!/ {\cyre Funkts.anal.i ego prilozh. 1987. T.21, \nom.2. \cyre S.42-45}; {\cyie Kirillov A.A., Yurp1ev D.V.}/\!/ {\cyre Funkts.anal.i ego prilozh. 1986. T.20, \nom.4. \cyre S.79-80; 1987. T.21, \nom.4. \cyre S.35-46}; {\it Kirillov A.A., Yuriev D.V.}/\!/ J.Geom.Phys. 1988. V.5. P.351-363; {\cyie Yurp1ev D.V.}/\!/ {\cyre UMN. 1988. T.43, \nom.2. \cyre S.159-160}; {\it Juriev D.V.}/\!/ Russian J.Math.Phys. 1994. V.2. P.111-121; {\cyie Yurp1ev D.V.}/\!/ {\cyre Algebra i anal. 1990. T.2, \nom.2. \cyre S.209-226}; {\it Juriev D.}/\!/ Adv.Soviet Math. 1991. V.2. P.233-247. \item"[34]" {\cyie Leonov Yu.P.} / {\cyre Problemy tsveta v psihologii. M., Nauka, 1993, S.54-67; Psihol.zhurn. 1995. T.16, \nom.2. \cyre S.133-141.} \item"[35]" {\cyie Lee0 R., "Ue1e0t--Grup"}, {\cyre Napisanie drae0verov dlya {\rm MS-DOS}. M., Mir, 1995}; {\cyie Uilton R.}, {\cyre Videosistemy personalp1nyh kompp1yuterov {\rm IBM PC} i {\rm PS/2}. M., Radio i svyazp1, 1994}; {\cyie Frolov A.V., Frolov G.V.}, {\cyre Programmirovanie videoadaptorov {\rm CGA}, {\rm EGA} i {\rm VGA}. BSP-3. M., Dialog-MIFI, 1994}. \item"[36]" {\it Foley J.D., van Dam A., Feiner S.K., Hughes J.F.}, Computer graphics: Principles and practice. Addison--Wesley Publ., 1990; {\it Heiny L.}, Windows graphics programming with Borland C++. Wiley, 1992. \item"[37]" {\cyie Oue1n G.}, {\cyre Teoriya igr. M., 1971}; {\cyie Ae0zeks R.}, {\cyre Differentsialp1nye igry. M., Mir, 1960}; {\cyie Vorobp1ev N.N.}, {\cyre Teoriya igr. L., 1985}. \item"[38]" {\cyie Slavnov D.A.} /\!/ {\cyre TMF. 1996. T.106, \nom.2. \cyre S.264-272.} \item"[39]" {\cyie Evtihiev N.N., Onykie0 B.N., Perepelitsa V.V., Shcherbakov I.B.}/\!/ {\cyre Nee0rokompp1yuter. 1994. vyp.1/2. S.23-30; vyp.3/4. S.51-58}. \item"[40]" {\cyie Morozov V.N.}, {\cyre Optoe1lektronnye matrichnye protsessory. M., Radio i svyazp1, 1986}; {\cyie Uossermen F.}, {\cyre Nee0rokompp1yuternaya tehnika. Teoriya i praktika. M., Mir, 1992}. \endroster \enddocument