In this article we consider the many-body problem in
general relativity in the case of the distribution of N
singularities on the circle. It specifies the exact solution
of the problem for an arbitrary distribution of
singularities. It is shown that the static metric of N
singularities corresponds to Newton's theory of N centers
of gravity, moving around the central body in a circular
orbit in a non-inertial frame of reference, rotating with a
period of bodies revolving. We consider the statement of
the problem of many bodies distributed at the initial time
on the circle. In numerical calculations, we studied the
properties of the gravitational potential in the problem of
establishing a static condition in which multiple
singularities retain the initial position on the circle. This
is achieved due to relativistic effects, which have no
analogues in Newton's theory of gravitation. Using the
properties of relativistic potentials justified transition
from the relativistic motion of the particles to the
dynamic equations in the classical theory. A system of
non-linear parabolic equations describing the evolution
of the metric in the Ricci flow proposed. The problem of
the calculation of the potentials in the Ricci flow
formulated. The application of the theory to describe the
ring galaxy, planetary rings and the asteroid belt
considered
The main point of the complementary method of the analysis of motor transport functioning under transition to outsourcing technology consist in elaboratoin of complex of models including the model of driver’s work analysis. This work is dedicated to complex decision of this actual problem
It is offered to expand the classification of risks by
introducing a global risk of economic system,
which separates stages burdened with the local
risks having arbitrarily direction. Serial or parallel
origin of these risks is modeled dyadic chain
vectors or four-dimensional conglomerates of
quaternions in Clifford spaces. Multivariate risk is
to transform analytically, calculate quantitatively,
construct geometric vector operations in the
ensemble with the economic variables on which
part of the cost of the risk and that is lost or after
symptoms appear. Therefore, the cost of an asset
depends on a comprehensive cost of the "basis",
burdened risk ("common value"), and the
magnitude of the risk of leaving part - "risky value"
- from zero. Now, the risk emerges as a new
economic and mathematical category. Through the
study of risks and through research of their new
multi-dimensional performance value it is possible
to insight into understanding the mechanisms of
action of the economic laws worldwide and in
Russia
This article gives a review of mathematical methods of construction and using of classifications. The main approaches to solving the problems of cluster analysis and grouping are discussed. We have also proposed global and local natural classification criteria. The methods of discriminant analysis
(diagnosis, pattern recognition with the teacher) are discussed in connection with the construction of generalized indicators (ratings)
The article continues the cycle of their studies
associated with the formulation and development of
methods of construction of nonnegative solutions of
inverse problems for dynamic systems. In practice, we
have developed and tested mathematical models of
dynamic systems. The basis of these models was based
on the apparatus of linear algebra, mathematical
analysis, mathematical programming, differential
equations, optimization methods, optimal control
theory, probability theory, stochastic processes,
operations research, game theory, statistical analysis.
The inverse problem in various models of
mathematical Economics was considered rare. These
tasks were sufficiently well investigated in the study of
physical processes. As shown by the analysis of the
theoretical and applied studies of economic processes
they represent considerable interest for practice.
Therefore, the article considered the inverse problem
of the mathematical model, as shown already
introduced the results of other mathematical models,
are of considerable interest in applied and theoretical
research. In this article the authors formulated and
investigated the inverse problem for dynamical
systems zero-order and the model of Keynes. For their
solution, the authors propose to build a system of
algebraic equations, then, using methods of quadratic
programming, to find the best average of mean square
estimation of the model parameter, which are defined
in MS Excel
In the article we investigate the multicriteria task
arising at the organization of distributed calculations
in a corporate network. As a mathematical tool to
solve the problem we use prefractal graphs, which
naturally reflect the structure of relationships in
global and corporate networks. The corporate network
with the distributed computing system at the solution
of a particular task has to be reliable, quickly and
qualitatively to make decisions. And every computer
in the network should be a part in the solution of the
problem, since it is fixed for a certain function. The
problem is reduced to cover the prefractal graphs with
disjoint simple paths along the edges and vertices.
On the set of all admissible coverings we constructed
a vector-target function with specific criteria. All
these criteria have a specific meaningful
interpretation, allowing organizing the calculation of
maximum reliability, with minimum time information
processing and loading balancing between the
network elements. In the article we constructed
polynomial algorithms for finding optimal solutions
according to specific criteria. For the criteria which
are not optimizing the allocated coverings, estimates
of the lower and upper bounds are given. For all the
algorithms we constructed and substantiated
estimation of computational complexity, confirming
the advantage of using algorithms on prefractal
graphs to classical algorithms on graphs
In the article, we describe and illustrate a method of
mathematical modeling in relation to process of decision-making
in the conditions of risk and uncertainty
on the example of building of agricultural object
The article presents a mathematical model of the ion transport across phase boundary exchange membrane / solution. The border is considered as an object in space, endowed with all the physical and chemical properties that are inherent physical and chemical phases. It is regarded as a special physical and chemical environment, having a distributed exchange capacity in which there is space charge dissociation of water molecules. The size of this object is estimated in the range of 1-300 nm. The surface morphology of industrial membrane type MK-40, ÐœA-41 and ÐœA-41P was investigated experimentally by scanning electron microscopy (REM). There was analyzed the amplitude of average surface roughness. In this article, the reaction layer is modeled as a region that forms as a relief morphology of the membrane. Membrane properties are due to the properties of the solution and the properties of the membrane. To determine the dependence of Q(x) is proposed procedure for assessing the proportion of solid phase in the total volume of which can be seen in the vertical cross section microprofile on the membrane surface line. Height multivendors determine the reaction layer zone on frame of model. Influence of surface morphology on the V-A characteristics and the sizes of the convective instability of cation-exchange membrane evaluated numerically simulating the hydrodynamic flow conditions using a solution of the Navier-Stokes equations. The transfer of a strong electrolyte such as NaCl ions through the thin layer of the reaction layer is considered. The place of nanomodel in the structure of a three-layer membrane system is showed. The distribution of the concentration of ions in the system, the charge density distribution and the dependence of the integrate charge with extent nanolayer is present. How to change the shape of the space charge and its integral value with one is investigated
This article discusses the mathematical and numerical modeling of the immune system of the course of HIV infection without treatment. Presently a significant number of scientific papers are devoted to the study of this problem. However, HIV infection is highly volatile and there is no effective drug, in that HIV has the ability to mutate and reproduce itself in the presence of chemical substances that are meant to inhibit or destroy it. The mathematical models used in this paper are conceptual and exploratory in nature. The proposed mathematical model allow us to obtain a complete description of the dynamics of HIV infection, and also an understanding of the progression to AIDS.
Thus, the results of the numerical solution of differential equations in this work show that: the disease develops, and at low concentration of the virus, a certain level of stability does not depend on the initial concentration of infestation. In the absence of treatment, for interesting competition between virus and the loss of virus caused by immune response should be strictly greater than the rate of multiplication of the virus in the blood; the reproduction rate of the uninfected cells should be stricly greater than the mortality rate of the uninfected cells
This article investigates hydrodynamic of experimental electrochemical cell with rotating disk in the cation exchange membrane. We have also investigated the flow in open, with the free surface of the solution and in hermetically closed cells. The main regularities of the hydrodynamics of the experimental cell at its real size were set