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Laboratorul "Modelare Matematică"

Direcţii de cercetare

Proiecte în derulare

Arhiva proiectelor

Rezultate importante

Rezultatele ştiinţifice se axează pe elaborarea şi argumentarea algoritmilor de soluţionare a problemelor de control multicriterial discret, a problemelor de evoluţie markoviană aleatoare simetrică şi a problemelor mecanicii corpului solid privind modelarea impactului undelor explozive.

S-au obţinut estimaţii noi a coeficientului de trafic în modelul de aşteptare generalizat cu priorităţi. În baza metodei reţelei extinse s-a elaborat algoritmul de aflare a fluxului de cost minim în reţelele dinamice cu mai multe produse pentru cazul neliniar. A fost cercetat modelul dinamic de creştere economică pe perioada de lungă durată în care cunoaşterea se consideră ca factor de producere. Algoritmii elaboraţi au fost estimaţi din punct de vedere al complexităţii de calcul şi testaţi.

A fost obţinută într-o formă explicită evoluţia marcoviană aleatoare în spaţiul Euclid R^6.

A fost propusă metoda de calcul şi elaborat produsul program pentru modelarea impactului undelor explozive şi de şoc asupra învelişului cilindric întărit şi umplut cu lichid. Cercetările numerice au demonstrat caracterul dinamic semnificativ al impactulu: unda care cade se divizează în unda reflectată şi unda ce se răspîndeşt care, la rândul său, generează în apă încă o undă de intensitate mai mică.

S-au obţinut rezultate importante privind modelarea matematică şi elaborarea algoritmilor de calcul pentru soluţionarea problemelor din domeniul economiei, fizicii, ecologiei, astrofizicii şi altor domenii;

Monografia (autor dr. hab. B. Răbachin) este una din primele lucrări în Moldova în domeniului calculului paralel. În ea sunt prezentate rezultatele cercetărilor ştiinţifice a metodelor numerice de calcul paralel pentru calculatoarele cu multe procesoare. Metodele numerice de calcul sunt confirmate prin exemple de probleme concrete realizate în limbajul FORTRAN.

Lucrări de referinţă

Monografii, culegeri

  1. Рыбакин Б.П., Параллельное программирование для графических ускорителей. Москва: Издательство НИИСИ РАН, 2011, 261 p., ISBN 978-5-93838-046-2.
  2. Lozovanu D., Pickl Şt. Optimization and Multiobjective Control of Time-Discrete Systems. Springer, 2009, 300p
  3. Мишкой Г. Обобщенные приоритетные системы. Chişinău: Ştiinţa, 2009. 200p.
  4. Рыбакин Б., Численные методы для многопроцессорных ЭВМ. Chişinău, ed. USMold., 2008, 348 р.
  5. Ş. Buzurniuc, G. Secrieru, Programarea în limbajul C. Chişinău, Elena-V, 2008, 200p.
  6. Gh. Milcoi, Teoria probabilităţilor şi Statistica Matematică. Curs de lecţii. Elan Poligraf, 2007, 98p
  7. И.К. Навал, Б.П. Рыбакин, В.Г. Чебан, «Математическое Моделирование Экологических Процессов», Кишинэу, Эврика, 1998.

Capitole în monografii

  1. Lozovanu D., Fonoberova M. Optimal Dynamic Flows in Networks and Algorithms for Finding Them. Chapter in the book „Analisis of Complex Networks (Edited by Matthias Dehmer and Frank Emmert-Sterb) WILEY-VCH Verlag GmbH&Co. KGaA. 2009. p.377-400.
  2. D. Lozovanu, Multiobjective Control of Time-Discrete Systems and Dynamic Games on Networks. Chapter in the book “Pareto Optimality, Game Theory and Equilibria”, Springer Optimization and Its Applications, Vol. 17, 2008, Approx. 900 p. 30 illus., Hardcover, ISBN: 978-0-387-77246-2, p. 665-759.

Curs de lecţii

  1. Rîbachin B. DAAD SCHOOL “Параллельное программирование с помощью ОреnMP” (курс лекций). Chişinău: USM CECM, 2009, 50 p.

Articole

  1. Lozovanu D., Pickl Şt. Discrete Control and Algorithms for Solving Antagonistic Dynamic Games on Networks. In: Optimization, 2009, v.58, No 8, p.665—683.
  2. Lozovanu D., Pickl Şt. Dynamic Programming Algoritme for Solving Stochastic Discrete Control Problems. In: Buletinul AŞ RM, Matematica. 2009, Nr. 2, p. 73-90.
  3. Lozovanu D., Pickl Şt Algorithms for Solving Discrete Optimal Control Problems with Infinite Time Horizon and Determining Mean Cost Cycles in a Directed Graph as a Decision Support tool. In: Central European Journal of Operation Research, Springer, 2009, v.17, No 3, p.255—264.
  4. Kolesnik A. D. The rxplicit probability distribution of a six-dimensional random flight. In: Theory Stochast. Process., 2009, v.15, issue 1, p. 82-90.
  5. Kolesnik A. D. The distribution of a planar random evolution with random start point. In: Buletinul AŞ RM, Matematica. 2009, v.1(59), p.79-86.
  6. Rybakin B., Shider N. Computer modeling of multidimensional problems of gravitational gas dynamics on multiprocessor computers. In: Computer Science Journal of Moldova, 2009, vol.2, No.1(49), p. 3-13.
  7. Aндронати Н.Р., Мишкой Г.К. Технологическое обеспечение надежности вычислительных систем. In: Proceedings of the International Conference on Mathematical methods in Reliability (MMR-2009). Theory, Methods, Applications. Moscow, 2009, p.466-470.
  8. Lozovanu D., Pickl St. Algorithmic Solution of Discrete Control Problems on Stochastic Networks. In: Proceedings of the Conference CTW 2008. Paris, France, June 2-4, 2009. p.21-224.
  9. Mishkoy Gh.,Vishnevsky V., Benderschi O. The algorithms of evaluation of the mean of length of the busy period and auxiliary characteristics for the class of generalized priority queueing systems. In: Proceedings of the International Conference Distributed Computer and Communication Networks, Sofia, Bulgaria, 2009 , p.183-191.
  10. Mishkoy Gh., Rykov V., Andronaty N., Bejenari D. Probabilities of State for Polling Systems with semi-Markov switching and exhaustive service. In: Proceedings of the Congress of the American Romanian Academy of Arts and Sciences, Sibiu, Romania, 2009, V. II, p.149-151.
  11. Рыбакин Б.П.. Параллельная трехмерная TVD схема для решения задач гравитационной газовой динамики. În: Международная конференция „Параллельные вычислительные технологии” (ПаВТ'2009) г. Нижний Новгород, 30 марта– 3 апреля 2009 г., стр.673-679.
  12. Рыбакин Б.П. Компьютерное моделирование гидродинамических задач на многопроцессорных ЭВМ. În: Межд. Конф. „Научный сервис в Internet . Технологии параллельного программирования”, Абрау-Дюрсо, 21-26.09.2009, стр. 422-425.
  13. Andronaty N., Mishkoy Gh. Technological methods of ensuring reliability in the production of computers. In: Proceedings of the International Conference , Mathematical methods in Reliability (MMR-2009). Theory, Methods, Applications. Moscow, 2009, p.466-470.
  14. Рыбакин Б.П. Численное моделирование воздействия ударной волны на подкрепленную оболочку. În: Межд. конф. Совре. проблемы „Газовой и волновой динамики”. МГУ, Москва, 2009, стр. 89-90.
  15. Rykov V.V., Mishkoy Gh. The new approach on study Polling Systems. In: Proceedings of the 4th International Conference on Control Problems, Moscow, 2009, p.1749-1758.
  16. Vishnevsky V., Mishkoy Gh., Semenova O. New models and methods to study Polling Systems. In: Proceedings of the International Conference Distributed Computer and Communication Networks, Sofia, Bulgaria, 2009 , p. 79-85.
  17. Lozovanu D., Pickl Şt. Multilayered Network Games: Algorythms for Solving Discrete Optimal Control Problems with Infinite Time Horison via Minimal Mean Cost Cycles and a Game-Theoretical Approach. In: Operation Research Proceedings. 2008, Springer, 2009, p. 513-518.
  18. Lugovoi P.Z., Meish V. F., Rybakin B. P., Secrieru G. V. Numerical simulation of the dynamics of a reinforced shell subject to nestationary load. In: Springer, International Appleid Mechanics. 2008. Vol.44, No 7, p. 788-793.
  19. D. Lozovanu, Şt. Pickl, A constructive algorithm for max-min paths problems on energy networks, Applied Mathematics and Computation. Elsevier. No. 3(2008), p.136-145
  20. A. Kolesnik, An asymptotic formula for the density of a multidimensional random evolution with rare Poissonian switchings. Ukrainen Mathematical Journal, 2008, V. 60, no 12, pp. 1631-1641.
  21. 2. E. Naval, Macroeconomic modeling of the economy in transition, Materialele Conferinţei Internaţionale „Modelare Matematică, Optimizare şi Tehnologii Informaţionale”, Chişinău, 19-21 martie 2008, p. 211-225.
  22. Г. С. Бисноватый-Коган, С. Г. Моисеенко, Б. П. Рыбакин, Г. В. Секриеру Моделирование взрыва сверхновой звезды на многопроцессорных ЭВМ. Труды Mежд. Научной конф. "Параллельные вычислительные технологии (ПаВТ 2008)", Санкт-Петербург, Россия, c. 319-323
  23. Gh. Mishkoy, A. Bejan, O. Benderschi. Evaluating of the traffic coefficient in priority queueing systems. Computer Science Journal of Moldova. V. 16, N.2(47), pp.269-285, 2008
  24. Луговой П., Мейш В.Ф., Рыбакин Б.П., Секриеру Г.В. Численное моделирование динамики подкрепленной оболочки при нестационарной нагрузке. Киев, Мехдународный научный журнал “Прикладная Механика”, т. 44, № 7, с. 83-90, 2008.
  25. Mishkoy Gh.K., Rykov V.V., Giordano S., Bejan A. Iu. Multidimensional Analogs of the Kendall Equation for Priority Queueing Systems: Computational Aspects. Automatics and Remote Control. Vol. 69, no 6. Pleiades Publishing, USA, pp.980-992, 2008.
  26. V. Geru, spects of Programming Macroeconomic Models. Rezumatele Conferinţei Internaţionale “Mathematical Modeling. Optimization and Informational Technologies”, Chisinau, Moldova, 19-21 Martie 2008, p. 249-254.
  27. A. D. Kolesnik, Random motions at finite speed in higher dimensions. Journal of Statistic Physics. 2008, no 131, pp.1039-1065.
  28. P. Bogatencov, G. Secrieru, V. Sidorenco, Modern Grid Services for Wide Utilization. Proceedings of the VIII-nd Int. Conf. BIT+ “Information Technologies – 2008”, Chisinau, 15 – 17 April 2008, p. 156 - 161
  29. A. D. Kolesnik, limit theorem for symmetric Markovian random evolutions in . Theory Stochastic Process. 2008, 14(30), no. 1, pp. 69-75.
  30. G. Bisnovatyi-Kogan, S. Moiseenko, B. Rybakin, G. Secrieru. Modeling of explosive magneto rotational phenomena: from 2D to 3D. Buletinul Academiei de Stiinţe a Republicii Moldova, Matematica, N.3(55), pp. 55-63, 2007.
  31. B. Rîbachin, , P. Lugovoi, V. Meish, G. Secrieru. Mathematical Simulation of Explosion Deformation of Cylindrical Shells . The Annual Symposium of the Institute of Solid Mechanics Romanian Academy. SISOM 2005, Bucharest May 17-19, 2005, pp 87-96.
  32. B. Rîbachin. Mathematical model of biochemical decomposition of organic in landfill. CSJM, V.11,N3(33), 2003, pp. 347-359.
  33. Г.Мишкой, С.Нистрюк, Приоритетные очереди с полумарковскими переключениями, Материалы IV Международной научно-практической конференции, Тирасполь,2005.
  34. Kolesnik A.D. and Orsingher E. A planar random motion with an infinite number of directions controlled by the damped wave equation, J. Appl. Prob., 2005, v.42, no.4.
  35. Fonoberova, M., Lozovanu, D.: Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding. The Bulletin of Academy of Sciences of Moldova, Mathematics, 1(53), 107-119 (2007)
  36. Lozovanu, D., Pickl, S.: Algorithms and the calculation of Nash Equilibria for multi-objective control of time-discrete systems and polynomial-time algorithms for dynamic c-games on networks. European Journal of Operational Research, 181(3), 198-216 (2007)
  37. Lozovanu, D., Pickl, S.: Algorithms for solving multiobjective discrete control problems and dynamic c-games on networks. Discrete Applied Mathematics, 155(14), 158-180 (2007)
  38. Lozovanu, D., Pickl, S.: Multiobjective Hierarchical Control of Time-Discrete Systems and Determining Stackelberg Strategies. CTW 2007 Proceedings, 111-114 (2007)
  39. Mishkoy Gh., Giordano S., Bejan A. Benderschi O. Priority Queueing Systems with Switchover Times: Generalized Models for QoS and CoS Network Technologies. Computer Sciences Journal of Moldova, v. 15(44), n.2, pp.217-242, 2007.
  40. A.D.Kolesnik, A note on planar random motion at finite speed J. Appl. Prob., 2007, 44(3) pp. 838-842 .Ed. UK.
  41. Naval, E.: Experience of macroeconomic models realization in transition economy. Computer Science Journal of Moldova, 12(2(35)) (2004)