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.
Полная версия сборника (в формате pdf)
Метафизика
УДК 530.12:531.51
А.К. Гуц.
Миф о свободе восстановления исторической правды
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.
Фундаментальная математика
УДК 519.62
А.И. Задорин.
Перенос краевого условия из бесконечности в случае
линейного уравнения второго
порядка с малым параметром
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.
УДК 519.1
Р.Ю. Симанчёв.
Структура нецелочисленных вершин релаксации многогранника
K-факторов
In this paper the graph structure of the k-factor polytope
vertices is described.
УДК 519.1
О.В. Червяков.
Аффинные симметрии многогранника системы
независимости
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.
УДК 514.82
Н.Л. Шаламова.
Порядковые автоморфизмы внешне неоднородных несвязных
порядков
It is shown that the order automorphisms of some disconnected exteriory
non-homogeneous orders in affine space are affine transformations.
УДК 519.49
М.А. Шевелин.
Разрешимые p-алгебры Ли без кручения
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.
Моделирование
УДК 519.6
А.К. Гуц.
Моделирование социально-психических процессов
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.
УДК 621.317
Д.Н. Лавров.
Совместная плотность распределения ошибок
в многошкальном измерителе
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.
УДК 519.711.3
Н.В. Перцев.
Вероятностная модель динамики взаимодействующих частиц
с ограниченным временем жизни
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.
УДК 517.958
Н.В. Перцев.
Об одном классе интегродифференциальных уравнений в моделях
динамики популяций
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.
УДК 519.6:681.14
С.Ю. Полякова.
Некоторые вопросы математического моделирования
общественных процессов
The problems of mathematical modeling of social processes are
discussed. The different points of view on the mathematical models
and modeling are given.
УДК 523.8
Р.Т. Файзуллин, Ф.Г. Хике.
Квазистационарные решения задачи N тел с конечным радиусом
взаимодействия
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
1m, brighter than 2m, brighter than 6m,
light galaxies brighter than
8.4m, and for automodel parameter as a visual
brightness (M 3/R 2 ),
there are configurations where geometry and arithmetics are
tightly coupled.
There are isotropy and invariancy by time.
УДК 530.51
Р.Т. Файзуллин.
Обобщенная задача на собственные значения
в модели межотраслевого баланса
Application of nonsymmetric eigenvalue's problem for
interindustry analysis with variable coefficients of
productivity.
Вопросы преподавания
УДК 681.14
С.Ю. Полякова.
Некоторые вопросы математического образования и моделирования
общественных процессов
The problems of mathematical educations in the aspect of
mathematical modeling of social pricesses are considered.