Математические структуры и моделирование: Сб. научн. тр./ Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 2001. Вып. 7. 174 с.
ISBN 5-7779-0232-4
Сборник составлен из статей преподавателей и аспирантов математического факультета Омского государственного университета и других вузов.
Для научных работников, аспирантов и студентов старших курсов.
Полная версия сборника

Фундаментальная математика

УДК 523.164
Т.Б. Бигильдеева, О.П. Гайдукова, С.А. Никитина.
О вычислении аппроксимационного градиента для некоторых классов разрывных функций.

In the article the economic scheme of calculation of approximate gradient being the integrated operator for piecewise linear and piecewise smooth functions of a special kind are submitted. These schemes allow rather precisely to calculate approximate gradient for acceptable time for the given classes of functions, that allows to use methods of approximate gradient for discontinuous optimization problems of large dimension.

УДК 519.62
О.В. Величко, А.И. Задорин.
Численное решение системы уравнений с малым параметром и точечным источником на бесконечном интервале.

A system of second order nonlinear equations with a small parameter effecting higher derivatives and a point source on an infinite interval is considered. The question of the transformation of the boundary problem to the finite interval is investigated. For reduced to finite interval problem difference scheme is investigated.

УДК 512.54
Е.С. Есып.
Системы уравнений от одной неизвестной для свободных произведений абелевых групп.

According to the algebraic geometry over groups, presented by Myasnikov and Remeslennikov, we give a classification of alebraic sets in G1, where G is a free product of abelian groups without involutions. It is used the theory of ultraproducts.

УДК 517.968
Н.В. Перцев, Б.Р. Кеменгеров.
Применение М-матриц в задачах устойчивости решений некоторых систем дифференциальных уравнений с последействием.
(210 Kb)
We consider mixed monotone technique for study stability of steady-states of one class delay differential equations. The sufficient conditions for stability of steady-state susing properties of M-matricies are established.

УДК 514.821
Н.Л. Шаламова.
Асимптотически линейчатый порядок.

Let an order in affine space An, n > 2, satisfies the conditions: 1) x , where Px={y : x y }; 2) it is invariant with respect to the group of parallel translations; 3) the cone Cx= , where is a ray with the origin x passing through y, is the cone which does not contain the line; 4) it is asymptotic lined. Then investigation of order can be reduced to study of the conal order.


УДК 51-77
Д.Н. Лавров.
Компьютерное моделирование транзактных процедур в группе индивидов.

In given work is presented the computer model of interactions in group of individuals on base of theory of transactionses (E.Berne). The model consists of three component: space, the individuals, and rules of behaviour.

УДК 519.711.3
Б.Ю. Пичугин, Н.В. Перцев.
Статистическое моделирование популяций взаимодействующих частиц с произвольным распределением времени жизни.

We consider a stochastic model of interacting populations of the particles with arbitrary distributions of the life spans. The Monte-Carlo approach for the simulation the population dynamics is presented here.

УДК 535
Р.Т. Файзуллин.
О решении систем нелинейных алгебраических уравнений специального вида.

New fast and effective algorithm for systems of nonlinear hydraulic like equations is developed. There are theorem of uniqueness and some conditions for convergence.

УДК 51-77
Ю.В. Фролова.
Имитационная модель формирования брачных пар.

The article presentes the simulation model of family formation process. It describes the algorithm of the marriage partner choose in social environment. The computer model was realized on SWARM.

Теоретическая физика

УДК 530.12:531.18
А.К. Гуц.
Стохастические свойства времени и пространства.

We introduce two time: deterministic Newton time-stream τ and stochastic time-epoch τ. The relation of uncertainty for time-epoch of physical events

where c0=const, is proved. The function
characterizes velocity of disorganization of the event-phenomena; fτ is density of probability of time-epoch τ. The relation (*) is verified not by means of experiment that is traditional for physics, but with the help of the reference to datas of historical science.

УДК 530.12:531.51
М.С. Шаповалова.
Статистическая сумма и вероятность больших флуктуаций времени.

The 5-dimensional spacetime V 5 with foliation of codimension 1 is considered. The leaves of foliation are 4-dimensional spacetimes Vα4. We construct the fluctuations of 5-metric such that their contribution in the Feynmann path integral over 5-dimensional trajectories is the same the contribution of the real physical spacetime. We also construct the statistical summ Z of canonical ensemble of 5-metrics determinated by the parameter γ and using Z we find the probablity of the metric with given parameter γ. Using the analogue of the formula of Einstein we evaluate the probablity of the metric fluctuations.

УДК 512.815.8
В.В. Варламов.
Дискретные симметрии на пространствах фактор-представлений группы Лоренца.

An extension of an algebraic description scheme of discrete symmetries is given. The charge conjugation is represented by a pseudoautomorphism of the complex Clifford algebra. A new class of quotient representations of the Lorentz group for physical fields with a breached reflection group is introduced.

УДК 517
N. Langdon.
The Explicit Formulas for the Stress Field of a Prismatic Dislocation Loop.

The objective of this paper is to obtain the explicit formulas for the stress field of a prismatic dislocation loop when Burgers vector is normal to the plane of the loop. Prismatic dislocation loop has numerous theoretical and practical applications that can benefit from knowledge of exact formulas for the components of its stress tensor. The intractability of general analytic solutions even for simple curved dislocations is well known. However, use of the comprehensive mathematical system "Mathematica" provided a necessary breakthrough resulting in the explicit formulas for the components of stress tensor of a prismatic dislocation loop. In addition, the formulas for the stress tensor of an infinitesimal prismatic loop and the asymptotic formulas at infinity are derived. Fascinating 'topographical maps' of stress field generated by a prismatic dislocation loop are included with the paper

Информационные технологии

УДК 681.3
С.В. Зыкин.
Разработка прикладных программ для баз данных.

In this article the technology of development of the applied programs for corporate databases is considered. The technology contains conventional components: documenting, testing and support of the software. All these components are considered from the point of view of specific character of work with databases.

УДК 681.518
Е.А. Костюшина.
Автоматизированная подсистема «Абитуриент». Формализация алгоритма функции «Автозачисления».

The algorithm of automation the process of enrolment entrants is discussed.

Преподавание математики

УДК 51:372.851
В.А. Далингер.
Учебное исследование как компонент технологии развивающего обучения математике.

Some theoretical aspects of the question of organization and realization of the students educational research in the process of mathematics training are examined in the article: the essence of the conception of the educational research is specified, its didactic functions are revealed and different aspects of research are marked out. The article gives sufficient number of examples of various educational researches showing those spheres of mathematics where they can be possibly and expediently carried out.