Математические структуры и моделирование: Сб. научн. тр./ Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 2000. Вып. 6. 160 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

УДК 523.164
Н.С. Кардашев.
Скрытая масса и поиск внеземных цивилизаций.

It is proposed a two new directions of astrophysical investigations and search of extraterrestrial intelligence: mirror world and multiconnected Universe with wormholes.

Фундаментальная математика

УДК 517.5
С.И. Бигильдеев.
Потенциальные свойства аппроксимационного градиента.

Approximate gradient is used for investigation of extremal properties of nondifferential functions. In this paper approximate gradient is presented as convolution operator of investigated function and some weight function. The connection between this concept and garmonic analysis is established. Proposed interpretation of approximate gradient demonstrates it connection with Riesz transformation. It is shown that approximate gradient is the gradient of Poisson integral, Bessel and Riesz potentials when the weight function is specially chosen.

УДК 513.813
Ю.Ф. Борисов.
Геометрическое доказательство тождества Бианки.

The geometric proof of Bianchi identity in the Riemannian geometry without torsion is given.

УДК 519.46
В.М. Гичев.
Замечание о полярных представлениях компактных групп Ли.

A finite dimensional representation of a compact Lie group is called polar if there exists a linear subspace which meets each orbit orthogonally. It is proved that the representation is polar if the family of convex hulls of orbits is closed under the Minkovsky addition, and the converse is announced.

УДК 519.62
А.И. Задорин.
Разностная схема для задачи со степенным погранслоем.

Second order ordinary differential equation with a power boundary layer is considered. Suppose, that coefficient before first derivative may change a sign. The difference scheme with the property of the uniform in a small parameter convergence on any uniform mesh is constructed.

УДК 514.765
И.А. Латыпов.
Инвариантные CR-структуры на SU(3)/U(1).

In this article invariant CR-structures on SU(3)/U(1) are described.

УДК 517.587
С.Д. Симонженков.
О чебышевских коэффициентах некоторых функций.

Polynomial Chebyshev approximation have been computed for the functions


УДК 62.50
С.Р. Алеева.
Стратегия преследователя в дифференциальной игре «мальчик и крокодил» с интегральным ограничением.

In this article is presented the solution of "boy and crocodile" differential game with integral restriction on choice of control parameter of persecutor.

УДК 621.396.24
А.В. Богданов, Р.В. Ивченко, В.Ф. Маренко.
Программно-имитационная модель антенно-согласующих устройств декаметрового диапазона.

In present article we deal with the way of finding parameters of an agreeing chain elements of an antenna-agreeing device with the algorithm of adjusting a search type with the help of a software-simulation model of an antenna-agreeing device.

УДК 541.15
В.В. Кеба, Н.А. Семиколенова.
Математическая модель радиолиза воды и водных растворов.

In this article the mathematical (kinetic) model of water radiolysis is presented. The model allows to calculate the dependence of concentrations of water radiolysis products on the time of irradiation, dose, dose intension, temperature or initial concentration.

УДК 510.644
В.В. Киселев.
Обучение в системах нечеткого управления.

Fuzzy control systems typically have a knowledge base, which can be obtained from experienced experts. But such knowledge base isn't appropriate in problems with variable environment and with rapidly changed constants. This paper is an overview of various methods used in learning process of fuzzy control systems. Here you can find only methods based on genetic algorithms. Genetic algorithms being promising optimization methods are successfully applied in many areas. Fuzzy control systems trained by methods based on genetic algorithms were successfully applied in industrial control, consumer electronics, finance markets.

УДК 51-77
В.В. Коробицын, Ю.В. Фролова.
Имитационное моделирование социализации индивида.

The article presentes the simulation model of individual socialization process. It describes the algorithm of individual behaviour in social environment. The individual actions base on their experience. They acquire it in various situations. The computer model was realized on SWARM. The result of simulation is a calculation of socialization time.

УДК 517.958
Н.В. Перцев.
Об одной модели динамики численности населения с учетом формирования и распада семейных пар.

The paper is concerned with a mathematical models using for study the problems of human demography. Some mathematical models for pair formation in bisexual populations in the form of the system of nonlinear delay integro - diferential equations are discussed here.

Теоретическая физика

УДК 530.12:531.18
Время и топология человеческого тела.

The Philosopher Kant declared the time is given us a piori, i.e. is defined for person from birth. Has it relation with the topology and geometry of human body? In Minkowsky space-time the four-dimen\-sional topology of human body is trivial and diffeomorphic to R = [0,1] ´ B, where B Ì R3. Such topology allows to perceive the sensations by consecutively any point of body. If body has other four-dimensional topology which is not diffeomorphic to R, then there exists full collapse of memory in an effort to observe the sensation consecutively. Hence, other topology of body means the absence of time in that form to which we got accustomed.

УДК 514.77
А.К. Гуц, А.А. Звягинцев.
Решение почтивакуумных уравнений Эйнштейна в синтетической дифференциальной геометрии Кока-Ловера.

In the article by using ideas SDG, non-classical spherically symmetric solution of the vacuum Einstein equations is given and considered at different stages of smooth topos Sh(L). Infinitesimal "weak" gravitational field can be strong at some stagies, for which we have the additional dimensions. For example, the cosmological constant is not constant with respect to additional dimensions. Signature of space-time metric can depend of density of vacuum and cosmological constant.}

УДК 530.12:531.51
Е.В. Палешева.
Новое решение уравнений Эйнштейна, допускающее Машину времени.

In this article a new stationary solution of the Einstein's equations with cosmological constant and Time machine is given. The garavitational field is created by ideal liquid with two massless scalar fields or by ideal liquid with electric-magnetic field.

УДК 517
Р.Т. Файзуллин.
Уравнение свободного падения с задержкой сигнала.

For Newton equation with time delay we have conditions for solution unexistence:

Информационные технологии

УДК 681.3.053
В.В. Ворошилов, О.Л. Епанчинцева.
Шифрование данных в DBF-файлах.

The technology of coding database files based on the RC5-algorithm is given.

УДК 681.518
О.Л. Епанчинцева, И.А. Земсков.
Интеграция информационных ресурсов ОмГУ в сеть Интернет.

This article describes technology of www-publication from specialize information systems of OmSU. Information systems have developed by havn't built-in instruments for www-publication programs (Visual FoxPro). This technology based on Lotus Notes.

Преподавание математики

УДК 378.143
С.Н. Горлова.
Алгоритм оптимизации учебной программы дисциплины «Алгебра».

Algorithm of definition of an optimum volume and sequences analyses of sections of a course "Algebra" is worked up and numerically realised.

История математики

УДК 510(09)
N.V. Berestovskaya.
History and Philosophy of Mathematics.

We consider the Appropriateness of Utilization of Non-Euclidean Mathematics in Relativistic Philosophies