Математические структуры и моделирование: Сб. научн. тр./ Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 2002. Вып. 9. 184 с.
ISBN 5-8239-0071-6
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 519.715
А.К. Гуц.
Симметричное управление, не выводящее динамическую систему за пределы конуса.

We study a control dinamic system in \R^3 that is symmetric with respect to Lie group G which acts simple transitivelly and affinely in \R^3 and linear with respect to control parameters. The purpose is discription of all convex cones in which lies the system trajectory.

УДК 519.6
И.И. Еремин, И.М. Соколинская.
Фейеровские итерационные процессы для несобственных задач линейного программирования.

In this article, we consider the Fеjеr's methods of solving the intrinsic (having a solution) and non-intrinsic (having no solution) linear optimization problems of 1-st, 2-nd and 3-rd types. The method is based on the reduction of mentioned problems to consistent and inconsistent systems of linear inequalities. For these systems, we construct the various variants of Fejerian processes which are converging to a solution or quasi-solution of the linear inequalities system. We discuss some aspects concerned to constructing of the iterative Fejerian mappings and the iterative sequences generated by them.

УДК 514.763
В.А. Кыров.
Двумерные гельмгольцевы пространства.

The Helmholtz planes are defined and their motion groups are given. The quasi-metric tensor that is analogues of metric tensor of the Riemannian spaces is found.

УДК 517.91:510.642
А.А. Звягинцев.
Дифференциальные уравнения в Синтетической дифференциальной геометрии Ловера-Кока.

Theory of differential equations in intuitionistic Synthetic Differential Geometry of Kock-Lawvere is considered. The problem of solution uniquness is disscussed.

УДК 514:510.642
А.А. Звягинцев.
Связность Леви-Чевита в синтетической дифференциальной геометрии Кока-Ловера.

In the article we consider correspondence between connection and the Riemannian metric on a microlinear spaces.

УДК 007:681.517.2
В.А. Маренко.
Использование нечетких отношений для~формализации знаний.

The description of knowledge representation is given in terms of fuzzy sets.

УДК 007:681.517.2
Б.К. Нартов. Об одном методе оптимизации начальных условий в управлении динамическими системами.
In the paper the new method's possibilities of the orientation optimization the begining conditions in the dinamical sistems control are presented.

УДК 541.124+517.95
Р.К. Романовский, И.Д. Макарова, С.Е. Макаров.
Условия существования стационарного режима в реакторе с кипящим слоем катализатора.

Тhе article considers the boundary value problem, simulating the process in chemical reactor with the boiling layer of catalyst. The conditions of existence of stationary solutions are established.

А.В. Пролубников.
Оценка приближенного решения алгоритмом Хватала задачи о покрытии.

In the paper we consider the Set Cover Problem. This problem is NP-hard. So it becomes very important to find approximate solution of this problem in polinimial time. Algorithm developed by V. Chvatal is such algorithm and it is most effective algorithm developed for set cover problem. Followed statement true for this algorithm: \frac{c(Chv)}{c(Opt)}\leq \ln\, m+1. We have found another proof for this statement. Our proof is more simple and vivid by our opinion.

А.В. Пролубников, Р.Т. Файзуллин.
Эвристический алгоритм дешифровки шифра двойной перестановки.

In the paper we consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices. Modification of the algorithm allows to find a solution for Frobenius problem. Formulation of the Frobenius problem is following one. Given a pair of two matrices with the same number of rows and columns. We must find out whether one of the matrix can be acquired from another by permutation of it's rows and strings or not. Solution of Frobenius problem can give to us efficient way for decrypting of double permutation cyphers problem for high dimension matrices.

Р.Р. Файзуллин.
Об ультраметрических тетраэдрах и треугольниках.

In this article relationships between ultrametric spaces and spaces of negative curvature are considered.


Моделирование

УДК 519.17(075.8)
Н.Ф. Богаченко, Р.Т. Файзуллин Механические аналогии в задаче Штейнера.
The statement of the Shteiner problem and some approximate approaches are covered in this article. It is suggested the heuristic algorithm to the decision of the Shteiner problem which based on the mechanical analogies.

УДК 621.365.5:537.221
О.Т. Данилова
Алгоритм расчета технологических параметров нагрева порошковых образцов в высокочастотном электромагнитном поле.

The method for matematical description of the characteristics of high-frequency heating is developed.

УДК 517.958
Л.В. Недорезов, Е.В. Волкова.
Об одной модели динамики численности изолированной популяции.

At present paper there is the analysis of continuous-discrete model of isolated population dynamics. It's assumed that population has nonoverlapping genera\-tions and appearance of individuals of new generation correlates with the death of previous. Also it's assumed that during the winter period there isn't the activity of individuals in population (for example, it's typical for insects in boreal forests), and part of individuals eliminates. Productivity of individuals is constant and death rate during the winter period depends on the food conditions (i.e. the respective function in model depends on the values of integral on any time intervals). For model there is the analysis of dynamic regimes and, in particular, determination of conditions of stability of origin and existance of nontrivial equilibrium. For one partial case of model it was shown that the chaotic regimes can be realized under certain values of parameters.

УДК 517.958
Л.В. Недорезов, Ю.В. Утюпин.
Об одной непрерывно-дискретной модели динамики численности двуполой популяции.

In present paper there is the consideration of parametric model of isolated population dynamics with sex structure. It's assumed that appearance of individuals of new generations is realized at any fixed time moments tk and death rate has a continuous nature. The dynamic regimes of model are analyzed. In particular, it was obtained that cyclic and chaotic regimes can be realized in model under certain values of it's parameters.

УДК 519.6:611.716.4:616.716.4-089.28-053:612.015
В.М. Семенюк, И.Н. Путалова, А.В. Артюхов, А.В. Сырцова, А.К. Гуц.
Применение метода конечных элементов в стоматологии (обзор литературных источников).

The world scientific press has paid more attention to publications on studies based on FEAM. This article is devoted to medical articles published by researchers from Russia, Japan, USA and other contries, who use FEAM in dentistry. FEAM applications are not exhausted. Compilers of the abstract consider that it is interesting and necessary to apply modern methods of mathematical analysis in their own scientific studies.

УДК 519.6:611.716.4:616.716.4 - 089.28 - 053:612.015
В.М. Семенюк, А.К. Гуц, Н.И. Панова.
Компьютерные эксперименты с моделью штифтовой конструкции с большим диаметром штифта.

Mathematical model of the tooth with a cast and core with diameter 2mm was built with the help of a special software package for simulating. The model was tested with simulating loads of various values and directions. The model shows that core with diameter 2mm can not be strong and can not be used.

УДК 681.32
Р.И. Нужин, В.А. Шапцев.
Инструмент моделирования процесса дозирования активности компьютера.

The computer activity dozing algorithm and its general architecture are announced. Characteristics of a simulation system are described as a some engineering tool for a creation of effective information source dozing activity algorithms.


Теоретическая физика

УДК 536.763/764
С.В. Белим.
Зависимость критического поведения однородных сжимаемых систем от размерности параметра порядка.

The renormalization-group method is applied to analysis of phase transitions in systems where the order parametr is coupled to nonordering additional elastic variable. A variety of critical and tricritical behavior is found as function of the physical variables and possible macroccopic constraints imposed on the system. The tricritical exponents were calculated in two-loop order with using Pade-Borel summation technique.

УДК 530.12:531.51
Е.В. Палешева.
Вклад спинорных духов в интерференцию квантовых частиц.

In this article a question of the ghost spinors's influence to the quantum particles's interference is investigated. The interaction between spinors and ghost spinors are considered. Furthermore the conditions of zero stress-energy tensor in private cases are found. Also we consider a question of experimental test of existanse of Deutsch's shadow pacticles.


Информационные технологии и искусственный интеллект

УДК 681.3
Т.Б. Бигильдеева, В.В. Таркаев.
О пакете программ недифференцируемой оптимизации.

In the article the complex of the nondifferential optimization programs including special means of maintenance of input-output of the data and visualization of optimization process is considered. These features of the software package make its convenient as by development both research of new algorithms and methods of optimization, and with use it in educational process.

УДК 681.518
И.А. Земсков.
Сбор информации о доступных ресурсах Интернет.

We first study the generic search engine architecture, then review all problems of collecting information about Web's resources and finally describe three building conception of search engine's module for collecting information about Web's resources.


Преподавание математики и физики

УДК 378.147:539.196
М.П. Ланкина.
Задачи с элементами исследования при обучении физике.

In this article is presented one example of estimation task on physics solution as the means of projective and cognitive skills formation on the way of physicist training.