Математические структуры и моделирование №2

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.