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
Моделирование
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
А.К.Гуц.
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