Êàðåëüñêèé íàó÷íûé öåíòð Ðîññèéñêîé àêàäåìèè íàóê Èíñòèòóò ïðèêëàäíûõ ìàòåìàòè÷åñêèõ èññëåäîâàíèé Karelian Research Cent...
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Êàðåëüñêèé íàó÷íûé öåíòð Ðîññèéñêîé àêàäåìèè íàóê Èíñòèòóò ïðèêëàäíûõ ìàòåìàòè÷åñêèõ èññëåäîâàíèé Karelian Research Center of the Russian Academy of Sciences Institute of Applied Mathematical Research
ÒÐÓÄÛ ÈÍÑÒÈÒÓÒÀ ÏÐÈÊËÀÄÍÛÕ ÌÀÒÅÌÀÒÈ×ÅÑÊÈÕ ÈÑÑËÅÄÎÂÀÍÈÉ
Ìåòîäû ìàòåìàòè÷åñêîãî ìîäåëèðîâàíèÿ è èíôîðìàöèîííûå òåõíîëîãèè
Âûïóñê 7
Ïåòðîçàâîäñê 2006
PROCEEDINGS OF THE INSTITUTE OF APPLIED MATHEMATICAL RESEARCH
Methods of mathematical modeling and information technologies
Volume 7
Petrozavodsk 2006
Редакционная коллегия: В.В.Мазалов (главный редактор), д.ф.-м.н., проф. Ю.Л.Павлов, д.ф.-м.н., проф. Ю.В.Заика, д.ф.-м.н., проф. В.Т.Вдовицын, к.ф.-м.н., доцент В.А.Лебедев, к.э.н., ст.н.с. А.В.Соколов, к.ф.-м.н., доцент Т.П.Тихомирова (ответственный за выпуск), к.т.н. доцент
ISBN 5-9274-0257-7
© Карельский научный центр РАН, 2006 © Институт прикладных математических исследований КарНЦ РАН, 2006
Ñîäåðæàíèå Ïðåäèñëîâèå. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ÌÅÒÎÄÛ ÌÀÒÅÌÀÒÈ×ÅÑÊÎÃÎ ÌÎÄÅËÈÐÎÂÀÍÈß Àáàêóìîâ Þ. Ã., Áàíèí Ì. Â. Î ìíîæåñòâàõ ñõîäèìîñòè, ãàðàíòèðóåìîé òåîðåìàìè òåñòîâîãî òèïà. . . . . . . . . . . . . . . . . Èâàíîâ À. Ï., Îñòîâ Þ. ß. Äâîéñòâåííîñòü è ïðèíöèï ðàñøèðåíèÿ â çàäà÷å äèíàìèêè ïîëåòà.. . . . . . . . . . . . . . . . . . . . . Ïîïîâ Â. Â. Ìîäåëèðîâàíèå ïðîöåññîâ òåïëîìàññîïåðåíîñà â ãèäðèäíîì àêêóìóëÿòîðå âîäîðîäà. . . . . . . . . . . . . . . . . Ïîïîâ Â. Â., Ñåìèí Ï. À. Ðåàëèçàöèÿ è èñïîëüçîâàíèå çàäà÷ ìîäåëèðîâàíèÿ âçàèìîäåéñòâèÿ âîäîðîäà ñ òâåðäûì òåëîì â ñïåöèàëüíîì ïðîãðàììíîì êîìïëåêñå. . . . . . . . . . . . Ñòàôååâ Ñ. Â. Î ïàðàìåòðè÷åñêîé èäåíòèôèöèðóåìîñòè ìîäåëè ôàêòîðíîãî àíàëèçà ñ çàâèñèìûìè ôàêòîðàìè è îñòàòêàìè. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Òàðàðèí Â. Ì., ×åïëþêîâà È. À. Î äåéñòâèè ñëó÷àéíîãî sîòîáðàæåíèÿ êîíå÷íîé áóëåâîé ðåøåòêè. . . . . . . . . . . . . Ôàëüêî À. À. Èãðà íàèëó÷øåãî âûáîðà ñ âîçìîæíîñòüþ îòêàçà îò ïðåäëîæåíèÿ è ïåðåðàñïðåäåëåíèåì âåðîÿòíîñòåé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Õâîðîñòÿíñêàÿ Å. Â. Î âîçíèêíîâåíèè ãèãàíòñêîãî ϕïðèìèòèâíîãî èäåàëà ñëó÷àéíîãî àâòîìîðôèçìà ϕ êîíå÷íîé áóëåâîé ðåøåòêè. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ×åðíîâ È. À. Ñõîäèìîñòü ñåòî÷íûõ àïïðîêñèìàöèé ðåøåíèÿ êðàåâîé çàäà÷è ñ íåëèíåéíûì ãðàíè÷íûìè óñëîâèåì è ïîäâèæíîé ãðàíèöåé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
Ðàçäåë I.
Ðàçäåë II.
13 26 35 47 63 80 87 95 97
ÈÍÔÎÐÌÀÒÈÊÀ
Äîâåðèòåëüíîå îöåíèâàíèå âåðîÿòíîñòè ïåðåïîëíåíèÿ áóôåðà íà îñíîâå óñêîðåííîãî ðåãåíåðàòèâíîãî ìîäåëèðîâàíèÿ äëÿ ñèñòåìû M/M/1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Êèñåëåâà Í. Ñ. Îá îäíîé ìîäåëè ñëó÷àéíîãî ãðàôà "Èíòåðíåò" òèïà. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Êóêèí Â. Ä. Êîìïîçèòíûé ýâîëþöèîííûé àëãîðèòì äëÿ ïîòîêîâîé çàäà÷è Øòåéíåðà. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Áîðîäèíà À. Â., Ìîðîçîâ Å. Â.
6 Ëàçóòèíà À. À. Îïòèìàëüíîå óïðàâëåíèå òðåìÿ ñòåêàìè â ñëó÷àå ïàðàëëåëüíîãî âûïîëíåíèÿ îïåðàöèé. . . . . . . . . . Ïå÷íèêîâ
154
À. À. Çàäà÷à ðàöèîíàëüíîãî ðàçìåùåíèÿ ññûëîê
â ðåãëàìåíòèðóåìîé ëîêàëèçîâàííîé ñèñòåìå èíòåðíåò -ðåñóðñîâ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ðîä÷åíêîâà
Í. È. Ðàçíîñòíàÿ
ñõåìà
äëÿ
176
ìîäåëèðîâàíèÿ
ÒÄÑ-ñïåêòðà äåãèäðèðîâàíèÿ ìåòàëëîâ ñ ó÷åòîì òåïëîïîãëîùåíèÿ è ñæàòèÿ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
Ðåòòèåâà À.Í., Ðîäèîíîâ À.Â. Ìîäåëèðîâàíèå ýêîíîìè÷åñêèõ îòíîøåíèé â ëåñíîì êîìïëåêñå Ðåñïóáëèêè Êàðåëèÿ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
199
Ùåðáàê Ì. Ï. Ïðèìåíåíèå ïàðàëëåëüíûõ âû÷èñëåíèé äëÿ ðåøåíèÿ íåêîòîðûõ çàäà÷ ìåõàíèêè òâåðäîãî äåôîðìèðóåìîãî òåëà. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
206
Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
216
Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Section I.
METHODS OF MATHEMATICAL MODELLING
On sets of convergences guaranteed by test type theorems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ivanov A.P., Ostov Yu.Ya. Duality and principle of expansion in the problem of dynamics of flight. . . . . . . . . . . . . . . . . . . . . . . Popov V.V. Modelling of heat-mass transfer processes in hydride accumulator of hydrogen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Popov V.V., Semin P.A. Implementation and use of modelling problems of hydrogen interaction with solids in special software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stafeev S.V. On the parameter identifiability of a factor analysis model with correlated residuals and correlated factors. Tararin V.M., Cheplyukova I.A. On the action of a random smapping of a finite Boolean lattice.. . . . . . . . . . . . . . . . . . . . . . Falko A.A. A best-choice game with the possibility of an applicant refusing an offer and with redistribution of probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Khvorostyanskaya E.V. On emergence of the giant ϕprimitive ideal of a random automorphism ϕ of a finite Boolen lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chernov I.A. Convergence of the lattice approximations of the solution to the boundary-value problem with nonlinear boundary condition and moving bound. . . . . . . . . . . . . . . . . . . . Abakumov Y.G., Banin M.V.
13 26 35 47 63 80 87 95 97
COMPUTER SCIENCE Borodina A.V., Morozov E.V. Overflow probability estimation with acce lerated regeneration simulation in the queue M/M/1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Kiseleva N.S. On an "Internet" type random graph model.. . . . 136 Kukin V.D. A composite evolutionary algorithm for solving the weighted Steiner tree problem. . . . . . . . . . . . . . . . . . . . . . . . . 143 Section II.
8 Lazutina A.A. On the problem of optimal control of three parallel stacks in bounded space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
154
Pechnikov A.A. The problem of rational allocation of links in a controlled and localized Internet-resource system. . . . . . . .
176
Rodchenkova N.I. A differences scheme for modelling the TDSspectrum of dehydriding of metals with heat absorption and a size reduction effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
Rettieva A.N.,Rodionov A.V. The model of dynamic game of forest resources management problem is constructed . . . . . .
199
Shcherbak M.P. Parallel computing in application to analysis of some problems in mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . .
206
Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
216
Ïðåäèñëîâèå Íàñòîÿùèé ñáîðíèê ñòàòåé ïðîäîëæàåò ñåðèþ ðàáîò Èíñòèòóòà ïðèêëàäíûõ ìàòåìàòè÷åñêèõ èññëåäîâàíèé Êàðåëüñêîãî íàó÷íîãî öåíòðà ÐÀÍ. Îí èçäàåòñÿ â þáèëåéíûé äëÿ Êàðåëüñêîãî íàó÷íîãî öåíòðà ÐÀÍ ãîä, ÊàðÍÖ èñïîëíÿåòñÿ 60 ëåò. Ðàçäåë, êàñàþùèéñÿ ìåòîäîâ ìàòåìàòè÷åñêîãî ìîäåëèðîâàíèÿ, ñîäåðæèò ðÿä ðàáîò, ïðåäñòàâëåííûõ íà Ðîññèéñêî-Ñêàíäèíàâñêîì ñèìïîçèóìå "Òåîðèÿ âåðîÿòíîñòåé è ïðèêëàäíàÿ âåðîÿòíîñòü", êîòîðûé ñîñòîÿëñÿ â Ïåòðîçàâîäñêå 26-31 àâãóñòà 2006 ã., à òàêæå íà Ðîññèéñêî-Ôèíñêîé øêîëå-ñåìèíàðå "Äèíàìè÷åñêèå èãðû è ìíîãîêðèòåðèàëüíàÿ îïòèìèçàöèÿ", êîòîðàÿ ñîñòîÿëàñü â Ïåòðîçàâîäñêå 2-7 ñåíòÿáðÿ 2006ã. Ïðîâåäåíèå ýòèõ íàó÷íûõ ìåðîïðèÿòèé áûëî ïîääåðæàíî Ðîññèéñêèì ôîíäîì ôóíäàìåíòàëüíûõ èññëåäîâàíèé (ïðîåêòû 06-01-10090, 06.01.10123) è Ïðåçèäèóìîì ÐÀÍ ïî ïðîãðàììå "Ïîääåðæêà ìîëîäûõ ó÷åíûõ". Ðàçäåë, ïîñâÿùåííûé èíôîðìàöèîííûì òåõíîëîãèÿì, ñîäåðæèò ðÿä ðàáîò, êîòîðûå äîêëàäûâàëèñü íà ìåæäóíàðîäíîé êîíôåðåíöèè "Ðàçâèòèå âû÷èñëèòåëüíîé òåõíèêè â Ðîññèè è ñòðàíàõ áûâøåãî ÑÑÑÐ: èñòîðèÿ è ïåðñïåêòèâû", êîòîðàÿ ñîñòîÿëàñü â Ïåòðîçàâîäñêå 3-7 èþëÿ 2006 ã.
Äèðåêòîð Èíñòèòóòà ïðèêëàäíûõ ìàòåìàòè÷åñêèõ èññëåäîâàíèé, ä.ô.-ì.í., ïðîô.
Â.Â.Ìàçàëîâ
Ðàçäåë I.
Section I.
Ìåòîäû ìàòåìàòè÷åñêîãî ìîäåëèðîâàíèÿ Methods of Mathematical Modelling
ethl
Òðóäû ÈÏÌÈ ÊàðÍÖ ÀÍ
Âûïóñê 7, 2006
ÓÄÊ 517.51
Î ÌÍÎÆÅÑÒÂÀÕ ÑÕÎÄÈÌÎÑÒÈ, ÀÀÍÒÈÓÅÌÎÉ ÒÅÎÅÌÀÌÈ ÒÅÑÒÎÂÎ Î ÒÈÏÀ
Þ. . À ÁÀÊÓÌÎÂ, Â. . Á ÀÍÈÍ àññìîòðåíû ìíîæåñòâà â ïðîñòðàíñòâå C [a; b℄, íà êîòîðûõ èç ñõîäèìîñòè ïîñëåäîâàòåëüíîñòè ëèíåéíûõ îïåðàòîðîâ íåêîòîðûõ êëàññîâ íà òåñòîâîì ìíîæåñòâå ñëåäóåò
ñõîäèìîñòü
ìíîæåñòâå.
ýòîé
Ïîêàçàíî,
ïîñëåäîâàòåëüíîñòè
è
÷òî
ìíîæåñòâà
ðàñøèðèòü
ýòè
íà
âñåì
ñ ñîõðàíåíèåì ñõîäèìîñòè íåëüçÿ. àññìîòðåíà îáùàÿ ñõåìà äëÿ ïîñëåäîâàòåëüíîñòè ëèíåéíûõ óíêöèîíàëîâ â áàíàõîâîì ïðîñòðàíñòâå.
 1953 ã. Ï.Ï. Êîðîâêèí
[1℄ äîêàçàë òåîðåìó
î ñõîäèìî-
ñòè ïîñëåäîâàòåëüíîñòè ëèíåéíûõ ïîëîæèòåëüíûõ îïåðàòîðîâ Ln
:
[ ℄ ! C [a; b℄ (îïåðàòîðû ïîëîæèòåëüíûå, åñëè èç óñëî( ) > 0 ñëåäóåò L (f (t); x) > 0 äëÿ ëþáûõ x 2 [a; b℄), ñîãëàñíî
C a; b
âèÿ
f t
n
êîòîðîé âûïîëíÿåòñÿ ñëåäóþùåå óòâåðæäåíèå:
(kL (t ; x)
k ! 0 äëÿ 2 f0 1 2g) ) (k ( ( ) ) ( )k ! 0 äëÿ ëþáîé ( ) 2 [ ℄) Çäåñü k k - ÷åáûøåâñêàÿ íîðìà, ò.å. k ( )k = max j ( )j 2[ ℄ n
i
i
x
i
;
;
f t
Ln f t ; x
f x
C a; b
f x
f x
x
a;b
Ïî òåðìèíîëîãèè, èñïîëüçóåìîé â ðàáîòå Ë. . Ëàáñêåðà [2℄, ïðîñòðàíñòâî
[
℄
C a; b
äëÿ ìíîæåñòâà
f
ÿâëÿåòñÿ
1; t; t2
òåëüíûõ îïåðàòîðîâ,
g (çäåñü
I
(S00 fI g)
- çàìûêàíèåì Êîðîâêèíà
0 îáîçíà÷àåò ìíîæåñòâî ïîëîæè-
S0
- òîæäåñòâåííûé îïåðàòîð).
Ìû áóäåì èñïîëüçîâàòü èíóþ òåðìèíîëîãèþ.  àíàëîãè÷íûõ ñèòóàöèÿõ áóäåì ãîâîðèòü, ÷òî òåîðåìà òåñòîâîãî òèïà ãàðàíòèðóåò ñõîäèìîñòü ïîñëåäîâàòåëüíîñòåé îïåðàòîðîâ äàííîãî êëàññà (ïîëîæèòåëüíûõ â òåîðåìå Êîðîâêèíà) íà ýëåìåíòàõ äàííîãî ìíîæåñòâà (ïðîñòðàíñòâà
[
C a; b
℄ â ñëó÷àå âûøå íàçâàííîé òåîðå-
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