Математические структуры и моделирование: Сб. научн. тр./ Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 1998. Вып. 2. 150 с.
ISBN 5-7779-0137-9
Сборник составлен из статей преподавателей и аспирантов
математического факультета Омского государственного университета.
Для научных работников, аспирантов и студентов старших курсов.
Фундаментальная математика
УДК 513.73, 513.8
В.Н. Берестовский, Е.В. Давыдова.
Линии кривизны и водораздела на поверхности
In given paper you can learn one of possible mathematical definitions of
watershad's and river's lines. Their equations are also given here,
and then their geometric propositions are studied.
УДК 513.73, 513.8
И.А. Грибанова.
Гауссовы кривизны двойственных поверхностей
On this paper we study some questions connected with the dual bodies.
The main result of the paper is the following universal lower
and upper evaluations for the Gaussian curvatures K and
K* ...
УДК 513.011
А.К. Гуц.
Локальная проблема Гельмгольца-Ли
In this note an answer is given to the following question: In what case
is the universal covering space of a metric space M
with metric p
isometric to the Euclidean space, the Lobachevsky space, or the sphere,
when M is assumed to permit rotation in Busemann's ...
УДК 514.77
А.А. Звягинцев.
Псевдоевклидовы пространства в моделях синтетической
дифференциальной геометрии
In this article the concept of the pseudo-Euclidean
space based on the axiomatics of the Synthetic Differential Geometry (SDG)
is being introduced. First part consists of basic definitions of the SDG,
notions of tangent bundle, pseudo-Euclidean metric, action on space of
(oriented) rays and rotation - structure.
Second part consists of some examples of pseudo-Euclidean space and
investigation the groups of action.
УДК 519.1
Р.Ю. Симанчёв.
Смежность вершин многогранника K-факторов.
In this paper the criterion of adjacency of the vertices one of the
polyhedral relaxations
of k-factors polytope was received. The particularity
given criterion
is that it is worded in graph terms. Received criterion gives
sufficient conditions of adjacency of vertices corresponding
integer polytope.
УДК УДК 513.82
Н.Л. Шаламова.
Гранично однородные порядки с трансверсвльным пересечением в
n-мерном аффином пространстве
It is shown that the order automorphisms of some disconnected
boundary-homogeneous orders in affine space are affine transformations.
Моделирование
УДК 519.1
Н.Ф. Жихалкина, Р.Т. Файзуллин.
Гравитационные аналогии в задаче оптимизации
The most spreaded optimization methods
are oriented on the looking for a local minimum
and results depend from an initial approximation. Therefore
it is frequently nessesary to use additional methods
but usually the payment for it is the complicating a structure of
the algorithm and reducing stability of its work.
The new method of looking for an extremum is suggested in this
paper. This algorithm we have named gravitational.
It is based on mechanics namely gravitational laws and genetics
analogies.
Besides it is represented some theoretical and numerical results.
УДК 517.958
Л.В. Недорезов, И.Н. Назаров.
Непрерывно-дискретные модели динамики изолированной
популяции и двух конкурирующих видов
At present paper there is the analysis of various mathematical models
of isolated populations dynamics and of competition between two species.
It is assumed, that in populations the death process of individuals
has a continuous nature and appearance of individuals of new generations
is realized at some fixed time moments. With the help of models there are
the investigations of the influence of winter conditions onto the
population dynamics and the determination of conditions of \лк deduction\пк\
of classic discrete models of isolated population dynamics from the models
with continuous time (in particular, Moran - Ricker and Hassell models).
Also there is the analysis of dynamic regimes of models under various
assumptions about the dependencies of birth and death rates with respect
to population states.
УДК 517.958
Н.В. Перцев.
Математическое моделирование процесса кроветворения
The new mathematical model of haemopoieses is considered.
Some problems of hemopoietic stem cells proliferation and differentiation
are discussed.
УДК 532.521
А.С. Толстуха.
Перенос завихренности: вариационный подход
Algorithm of the calculation of the steady fluid flow with vorticity through
three dimentional chanel is prsented.
The velocity field is decomposed in terms
of potential and vortex-induced parts.
Vorticity transport calculation
is based on the approximate calculation of the stream line
and the time scale functions of the flow particles.
Социокибернетика
УДК 519.6
Л.А. Паутова.
К вопросу о методике вычисления индикаторов и
пороговых значений стабильности общества
The purpose of this paper was to use the conceptual frameworks
of sociocybernetics to develop our understanding of social
systems stability. Stability can be considered as the whole
complex of different kinds of stability. The classification
of different kinds of stability lets analyzed the concrete
indicators, parameters, extreme meanings of social stability.
The system of indicators may be used in elaborating of
concrete recommendations for the management sphere and
scientific prognostication.
УДК 681.3.06:519.6
А.К. Гуц, Д.А. Ланин, С.В. Никитин.
Учебный пакет программ "ETNOS" для моделирования
эволюции этнических систем
The software "ETNOS" for simulation of evolution of ethnic systems
is presented. This software is created for school purposes and based
on the Gumilev's theory of ethnogenesis.
Теоретическая физика
УДК 530.12:531.51
А.А. Куталёв.
Теория Калуцы-Клейна в анизотропном пространстве
Can the five dimentions Kalutza-Klein theory of gravitation and
electric-magnetical fields be constructed for anisotropic spaces? This
will be a success if we will use formulas of Kalutza-Klein theory
for Finsler space instead of classic Riemannian space.
Вопросы преподавания
УДК 681.14
А.Ф. Кириченко, Р.Ю. Симанчёв.
Задачи математического моделирования и теория принятия решений
в курсе математики юридических вузов системы МВД
In this paper some questions of teaching mathematicians
in the legal higher school are discussed.