Математические структуры и моделирование:
Сб. научн. тр./ Под ред. А.К.Гуца.
Омск: Омск. гос. ун-т, 2000. Вып. 5. 199 с.

ISBN 5-7779-0109-1

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 519.62

**О.В.Величко, А.И.Задорин.
Численное решение уравнения с точечным источником на бесконечном интервале.**

The second order equation of the type reaction-diffusion with a small parameter effecting a higher derivative and a point source on the infinite interval is considered. The question of the transformation of the boundary conditions to the finite interval is investigated. For reduced to finite interval problem difference scheme is constructed. The uniform convergence of the difference scheme is proved.

УДК 519.63

**А.И.Задорин.
Разностная схема для эллиптического уравнения со степенным пограничным слоем в полосе.**

Elliptic equation with a power boundary layer in a strip is considered. The difference scheme with the property of the uniform in a small parameter convergence is constructed. Then the scheme is reduced to the finite number of nodes.

УДК 515.123.4 : 517.983.2

**Е.В.Мельников.
О продолжении равномерно непрерывных отображений.**

In this paper we prove that each uniformly continuous mapping from one uniform space to other closable and its closure is uniformly continuous. Based on this fact we prove the theorems about extension of uniformly continuous mappings and continuous linear operators having (sequentially) dense domain and (sequentially) complete range. Also it is proved that each uniform space and each (locally convex) topological vector space has a sequential completion.

УДК 513.573:513.81

**А.В.Парамонов.
Геометрия трехмерного конуса.**

In present paper the problems of three-dimensional cone visualization are considered. In particular the behavior of 3-cone geodesics is analyzed. Besides in the paper formulae of the Ricci and the scalar curvatures of 3-cone have been obtained. Also the bounds of the sectional curvature are given.

УДК 517.55

**Г.И.Сечкин.
Фундаментальные проблемы звездообразного анализа.**

The paper is concerned with some fundamental problems in several complex variables for starlike domains

УДК 517.583

**С.Д.Симонженков.
О вычислении эллиптических интегралов третьего рода.**

The algorithm for numerical evaluating the Legendre's incomplete integral of the third kind with parameter (character) less than one is described. The Fourier cosinus-expansion of the integrand part involving a character is used. Termwise integration gives a series for which summation a Clenshaw's technique is applicable

**Моделирование**

УДК 519.6

**В.В.Коробицын.
Модель территориального распределения пассионарной энергии этноса.**

The model of dynamic of drive energy of ethnos is described. The drive energy is extended for the territory of ethnos. The model is a system of the parabolic differential equations. The result of computer simulation of ethnic model is given

УДК 517.9

**В.В.Коробицын.
Доказательство теоремы существования и единственности решения для одного параболического уравнения.**

We consider the some semi-linear differential equation with partial derivatives. It has the constant coefficients. We prove the theorem of existence and uniqueness of the solution.

УДК 621.317

**Д.Н.Лавров.
Алгоритм параллельной обработки многошкальных фазовых измерений нескольких источников излучения.**

In this article the estimation algorithm of several wave vectors on measurements made on system of dipoles arrays is presented. Such antenna structure allows enough simply to use the methods of theory of multiscale meters. The additional conditions superimposed on structure of antenna system allow to create the procedure of efficient parallel processing

УДК 517.958

**Н.В.Перцев, А.Н.Перцева.
Интегральная модель Лотки-Вольтерра и некоторые свойства ее решений.**

The paper is concerned with a generalization of Lotka-Volterra model, arising under the consideration of some populations with a limited life span of its individuals. The system of nonlinear integral equations of the renewal type is used for the construction of the model. Some properties of the model solutions are established

УДК 530.51

**О.А.Реутова, О.В.Ирискина.
Модель реактора риформинга. I. Кинетическая модель для полифункционального катализатора.**

The mathematical (kinetic) model for the cascade from three reforming reactors is offered. The model takes into account Pt-catalyst polyfunctionality and allows to calculate temperature and concentration profilies

УДК 681.3

**Ю.В.Фролова.
Мульти-агентное моделирование социальных процессов в SWARM.**

In the paper the Swarm software for Multi-Agent Simulation is described

УДК 681.3

**Ю.В.Фролова, В.В.Коробицын, А.А.Лаптев.
Компьютерная модель влияния ресурсообеспечения мужчин на поведение женщин.**

This paper is devoted to idea of modeling and simulation of women's behavior in various situations. The environmental resources distribution influence upon type of forming the family. Simulation modeling was used to confirm this hypothesis.

**Математическая социология**

УДК 519.24

**А.К.Гуц, Р.Т.Файзуллин.
Математическое исследование методики организации одного социального мониторинга.**

This article is publication of scientific report which was done for Omsk Center of humanitarian, social, economic and political investigations in 1996. The purpose of given work was seach of mathematical basis for "non-representative" selection of information, which could be used for social monitoring in Omsk city.

УДК 519.24

**Н.Ф. Жихалкина.
Динамический подход к задаче кластеризации.**

In this article the dynamic approach to the cluster-analyze problems is suggested. Algorithm which based on the gravitational laws is used to look for clusters.

**Эконометрика**

УДК 519.281:330.115

**И.П.Геращенко.
Методы прогнозирования в регрессионных и адаптивных моделях при анализе динамических рядов.**

Theoretical foundations of forecasting in adaptive and regression models and applications of these models in dynamic sequences analysis are regarded in the article. The statistical conditions of adequacy of the chosen model to the investigated process are discussed. The efficiency of the adaptive and regression models using for demographic processes forecasting is shown. A level of birth rate in Omsk region is analyzed with the help of considered models. The conclusion is made about the greatest conformity of the investigated process to the adaptive model with the factor of smoothing 0.6 and to the regression polynomial model with

*k*=3. It is emphasized that it is better to use the adaptive model to forecast demographic parameters when a non-stable socio economic situation holds. Regression models should be applied to the analysis of the phenomena having stable general laws of development during the period of the forecast.

**Методика преподавания**

УДК 51:372.851

**Т.Н.Алешкова.
Гуманитаризация общего математического образования.**

A general achievment in culturalogical field was origin of new educational philosophy. Its aims are to educate personality which is responsible for destiny of civilisation to create conditions for forming and opening of creative potential of each personality. One of directions realizing aims of philosophy is humanitarization. It proposes to turn educational process to personality, to account its interests and to create conditions for personal development by means of learning subjects. This intends to find contents richable by general culture, new forms and educational methods directing to creative activity. In this article psychological and methodical approaches to solution of problem of humanitarization are considered.

УДК 51:372.851

**Т.Н.Алешкова.
Психолого-педагогические основы обучения истории математики.**

Psycologists notes that for successful learning of knowledge, learning material should to acquire meaning for scoolar. For this, motivs and needs shoud to arise at scoolar. One of the means of forming motivation is teaching of history of mathematics. It does some didactional functions: 1) it is tool of developmrnt of interest to mathematics, 2) it activates learning process, 3) it creates positiv emotions. In this article psycological investigations in the field of motivation are considered and the role of teaching of history of mathematics in forming of motivation is ascertained.

УДК 51:378

**Л.И.Боженкова.
Модели взаимосвязи знаний и приемов учебно-познавательных действий их усвоения.**

Various models of intercommunication of knowledges and methods of pupil's educational-cognitive activity are considered in the article. There is also considered the question of the forming at the pupil the modelling method as one of the most frequently used one during the mathematics studying.

УДК 51г(о)(077)

**Н.А.Бурова.
Историко-математический информационный поток.**

In the processes of humanizatin and humanitarization of mathematical education an important role is played by the course of the history of mathematics for the students of mathematical faculties of pedagogical high schools. The problems of correction of the motivation set of the students and the increase of their information culture by means of introducing a new historico-mathematical information flow are examined.

**Образование**

УДК 51:378

**В.А.Далингер.
От педагогики авторитарной к педагогике авторитетной.**

The article analyses the peculiarities of the system of education that has been established in Russia by the end of the XX century. Positive and negative aspects of teaching technology directed to the subject and personality are shown here. Factors of educational children desolation are also shown in the article and the ways of elimination of school disadaptation are pointed out. The analysis of different aspects of authoritarian and authoritative pedagogics is given in the article and in this connection the question of different types of educational process organization is examined in the article.