## Математические структуры и моделирование №12 Математические структуры и моделирование (Выпуск 12)
Журнал / Под ред. А.К.Гуца. Омск: Омск. гос. ун-т, 2003. Вып. 12. 176 с.
ISBN 5-8239-0144-5
Для научных работников, аспирантов и студентов старших курсов.

Фундаментальная математика

М.И.Бродский. Применение FDP к многокритериальным методам принятия решения.
The applications of fuzzy dynamic programming to multicriteria multistage methods of decision-making is considered in the paper.

А.Г. Гринь. Уточнения центральной предельной теоремы для сумм зависимых случайных величин.
Some new estimations of the rate of convergence in the central limit theorem for weakly dependent variables are received in this article. Also there is proved the elementary asymptotic expansion for sums of dependent random variables.

А.В. Пролубников, Р.Т. Файзуллин. Класс графов, задача проверки изоморфизма для которых разрешима за полиномиальное время алгоритмом спектрального расщепления.

We propose an algorithm for solving the graph isomorphism problem. The problem is not known to be NP-complete or to be solvable in polinimial time for every pair of input graphs. Main heuristic used by the algorithm is inverse matrices of graphs' adjacency matrices which modified to positive defined matrices. These modified adjacency matrices can be viewed as adja- cency matrices of graphs with weighted loops. The two initial input graphs are isomorphic if and only if the two obtained graphs with weighted loops are isomorphic. The graphs' automorphism groups are consequently simplified and finally become trivial during iterations of the algorithm by perturbations of graphs (perturbations of their modified adjacency matrices). So we can solve the isomorphism problem both for perturbed graphs with weighted loops and so for the initial input graphs. Some results relating to computational efficiency are considered. It is shown that our algorithm can solve the isomorphism problem for the class of graphs for which the problem is solvable at polinimial time by the most universal algorithm designed for the graph isomorphism problem.

В.Н. Степанов. Определение выпуклых тел по проекционным функциям.

The brief review of known results devoted to questions of a convex body definition on its projection functions.

Моделирование

Г.А. Десятков, Е.В. Трофименко, В.С. Энгельшт. Компьютерное исследование процессов плазменного разложения зарина при высоком давлении и вариации добавок.
The thermodynamic analysis of processes of plasmachemical decomposition of poison gas sarin was carried out at the high pressure (0,1-1000 MPa) and influence of the oxide calcium addition on structure of reaction products and influence of CaO and $$CaCO_3$$ addition in the closed volume at the pressure 150 MPa. The adiabatic temperatures and product composition of processing were calculated. Results of research have shown that pyrolysis of sarin with the oxide calcium addition at pressure higher than 150 MPa is an ecologically clean process and reaction products do not contain dangerous connections. Replacement of CaO addition by cheaper $$CaCO_3$$ does not lead to increase of toxicity of pyrolysis products. Process is energetically effective, expenses for generation of plasma are minimal. The role of plasma is in initiation of course of reaction.

И.С. Кострикина, Ю.В. Фролова. Возможности моделирования в области психологии интеллекта с использованием системы WizWhy.
The persons of keen intellect are public and cultural property of society. The development and conservation of intelligence are chief task of university education. Cognitive psychology is situated in the methodological crisis. The findings rules of thumb are mutually contradictory. Nonlinear interconnections in deep structure of mental faculties, intellect threshold effect, compensation effect makes difficult of experimental data interpretation. Logical system "WizWhy" makes possible discovery of hidden knowledge and unexpected interdependences.

Н.М. Лыченко. Задачи децентрализованного слежения для взаимосвязанных систем: разработка алгоритмов и моделирование .
The procedures of synthesis of decentralized coordinated control of interconnecting continues and discrete systems with known disturbances are submitted. The trajectories of interconnecting systems should track some known trajectories. The initial continues problem is stated as optimization problem with performance index built on an errors between trajectories of subsystem states and etalon models. The initial discrete problem is reviewed as optimization problem with performance index, built on a difference between desirable trajectories and outputs of subsystems. The parallel calculation for coordination parameters was used. Illustrative examples are submitted.

Н.Н. Нескреба, А.К. Гуц, В.М. Семенюк, А.В. Артюхов. Математическая модель двукорневого зуба после сепарации.

Математическая физика

С.П. Барановский, И.В. Широков, С.В. Шмаков. Вычисление группы автоморфизмов конечномерной алгебры в системе Maple.
In the present work the algorithm for the calculating of an arbitrary finite-dimensional algebra's automorphism group has been proposed. The proper Maple procedure has been fully described.

А.А. Магазев. Причинная функция Грина на однородных пространствах с инвариантными и центральными метриками.
In this article the method of calculation of causal Green's function on the homogeneous spaces with central and Riemans's metrics is being developed. As an illustration of the proposed method the Green's function on the four-dimension solvable Lie group, which is the homogeneous space with trivial subgroup of isotropy, have been calculated.

Математическая экономика

М.А. Добренко, А.К. Гуц. Макроэкономические первичные структуры отношений Кулакова.
In this article the Kulakov initial structures in macroeconomics are considered. Early the Kulakov initial structures were applied to physics, sociology and microeconomics.

Теоретическая физика

А.К. Гуц. Силовые эффекты хода времени.
In this article is shown that fractal characteristic of time capable to manifest themselves as force, acting upon material bodies. The move of time creates the tidal forces and change of spin of classical particle.

Е.В. Палешева. Физические следствия многомерного Времени.
In this article we consider Time as many dimensional space. Existance of nongravitational field which influences on space-time curvature is shown. Potential of this field is positive.

Информационные технологии

В.И. Дулькейт, Д.Н. Лавров, П.И. Михайлов, А.А. Свенч. Анализ надежности алгоритма разделения секрета в сетевых потоках.
Analysis to reliability algorithm division of the secret in network flow is conducted in this article. Recommendations are given on the further improvement algorithm.

Т.А. Погромская. Модель процесса приема абитуриентов в ВУЗ.