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.