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.
Моделирование
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
 | (*) |
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.