Математические структуры и моделирование (Выпуск 1) УДК 513; 514; 519; 530; 681 Математические структуры и моделирование: Сб. научн. тр./ Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 1998. Вып. 1. 122 с. ISBN 5-7779-0090-9 Сборник составлен из статей преподавателей и аспирантов математического факультета Омского государственного университета. Для научных работников, аспирантов и студентов старших курсов.

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УДК 530.12:531.51
Can the Past be restored? Poincare and Costa de Beauregard showed that the past is not restored statistically. This follows from Bayes formula. In given paper two new Principles are postulated which forbid the restoration of the Past.

УДК 519.62
The ordinary differential equation of the second order with a small parameter affecting the highest derivative on the infinite interval is considered. Method of the transition of the boundary conditions to the conditions for a finite interval is proposed. The estimates of the replacement error are got.

Р.Ю. Симанчёв. Структура нецелочисленных вершин релаксации многогранника K-факторов. (44 Kb)

УДК 519.1
In this paper the graph structure of the k-factor polytope vertices is described.

О.В. Червяков. Аффинные симметрии многогранника системы независимости. (39 Kb)

УДК 519.1
In the present work in the terms of inseparable sets is received criterion of existence of symmetry of independence system polyhedron for any shift. On the basis of it is developed polynomial (accurate to oracle of independence) algorithm of construction of the appropriate symmetry.

Н.Л. Шаламова. Порядковые автоморфизмы внешне неоднородных несвязных порядков. (34 Kb)

УДК 514.82
It is shown that the order automorphisms of some disconnected exteriory non-homogeneous orders in affine space are affine transformations.

М.А. Шевелин. Разрешимые p-алгебры Ли без кручения. (53 Kb)

УДК 519.49
Some facts concerning with structure of solvable restricted Lie algebras satisfying finiteness conditions on commutative restricted subalgebras are proved. For metabelian restricted Lie algebra without nontrivial finite-dimensional restricted subalgebras some cohomological sufficient condition to be of finite rang is obtained. Restricted Lie algebra over GF (2) providing an example when this condition is not necessary is found.

УДК 519.6
The problem of modeling of social psychological processes in society. The basis for mathematical model is the Bekhterev's collective reflexology. The relation this model with ethnic and social processes is discussed.

Д.Н. Лавров. Совместная плотность распределения ошибок в многошкальном измерителе. (48 Kb)

УДК 621.317
The joint density function of errors in multi scale a measuring device is deduced by a method of a maximum entropy. Is shown, that this density function is well approximated by a truncated normal density function, which is usually used for a construction of estimations.

Н.В. Перцев. Вероятностная модель динамики взаимодействующих частиц с ограниченным временем жизни. (59 Kb)

УДК 519.711.3
A stochastic model of interacting populations of the particles with a limited life span is concidered. The population -- size and age -- dependent branching process is used for the construction the model equations. The Monte -- Carlo approach for the simulation the population dynamics is presented here.

Н.В. Перцев. Об одном классе интегродифференциальных уравнений в моделях динамики популяций. (62 Kb)

УДК 517.958
The paper is concerned with a class of the integral and integrodifferential equations, arising in the mathematical models of the interacting individuals with a limited life span. The models of haemopoieses, cyclic infection disease and logistic growth of the populations are discussed.

С.Ю. Полякова. Некоторые вопросы математического моделирования общественных процессов. (47 Kb)

УДК 519.6:681.14
The problems of mathematical modeling of social processes are discussed. The different points of view on the mathematical models and modeling are given.

Р.Т. Файзуллин, Ф.Г. Хике. Квазистационарные решения задачи N тел с конечным радиусом взаимодействия. (32 Kb)

УДК 523.8
The consideration of the N-body gravitational problem equations can give us some class of boundary-valued problems defined on the "beam's" construction. One can consider it as finite element method's approximation with the linear function's basis. There are time and coordinate dependent beam's as distances between points and unknown coordinate functions which are defined on the beam's. The possible sample from this class is wave equation where our 'constellation' can be considered as stabilized with help of more wide volume. Simple iterative procedure give us well-known mathematical objects-configurations on the spherical planes where nodes and viewpoints are mass locations. May be it can give us similar visual configurations on the planes of spherical coordinates ( galactic, equatorial, ecliptic). For some scales of mass distribution - light stars brighter than 1^m, brighter than 2^m, brighter than 6^m, light galaxies brighter than 8.4^m, and for automodel parameter as a visual brightness (M ³/R ² ), there are configurations where geometry and arithmetics are tightly coupled (http://www.univer.omsk.su/~rtf). There are isotropy and invariancy by time.

Р.Т. Файзуллин. Обобщенная задача на собственные значения в модели межотраслевого баланса. (34 Kb)

УДК 530.51
Application of nonsymmetric eigenvalue's problem for interindustry analysis with variable coefficients of productivity.

УДК 681.14
The problems of mathematical educations in the aspect of mathematical modeling of social pricesses are considered.