01.00.00 Physical-mathematical sciences
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TELLURIUM DOPING OF EPITAXIAL LAYERS GaxIn(1-x)PySb(1-y)
01.00.00 Physical-mathematical sciences
DescriptionThe results of the research of the influence of tellurium dopant on the opto-electrical properties of the GaxIn(1-x)PySb(1-y) , are reviewed in this article. The mostly important results are discussed
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LOGARITHMIC LAW FOR DYNAMICAL SYSTEMS FROM QUARKS TO GALAXIES
01.00.00 Physical-mathematical sciences
DescriptionThe article discusses various examples of dynamical systems in which the motion is determined by the logarithmic law - quark systems, hydrodynamic systems, galaxies. Set the general nature of angular motion on a hypersphere in a space of arbitrary dimension and radial movement 6D in the metric of a logarithmic potential. We investigate the 6D metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity center coordinates. It was established that in spiral galaxies the orbital motion is due to the logarithmic potential, which is the exact solution of the field equations of Einstein's theory of gravity. The most well-known and widespread in nature case is turbulent flow over a smooth or rough surface, in which the mean velocity depends logarithmically on the distance from the wall. We derivate the logarithmic velocity profile in turbulent flow from the NavierStokes equations. An analogy of the logarithmic velocity profile and the logarithmic law in the case of erosion of materials under impacts been proposed. In electrodynamics, Ampere's law, which describes the interaction of current-carrying conductors, is a consequence of the logarithmic dependence of the vector potential of the distance from the conductor axis. There is, however, an alternative derivation of Ampere law of the Riemann hypothesis about the currents due to the motion of charges
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LOGARITHMIC LAW AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe work discusses various examples of physical systems which state is determined by the logarithmic law - quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrally-symmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension
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01.00.00 Physical-mathematical sciences
DescriptionThe question of construction of electrodynamics in the framework of the metric theory of gravitation is discussed. It is shown that the energy-momentum tensor of the electromagnetic field creates a space in which Faraday's law of induction is true. In such a space the scalar curvature vanishes identically, although space contains matter in the form of an electromagnetic field. It is proposed to call such space Faraday's magnetic universe as historically Faraday first established experimentally that "empty space is a magnet." We consider the metric of the expanding universe and metrics that describe the local gravitational field in the Newtonian theory. It was established that the field equations in spaces containing matter only in the form of an electromagnetic field in these metrics are reduced to hyperbolic equations describing the propagation of waves at the speed of light. However, in the field containing matter, the field equations are the equations of parabolic type, which describe diffusion or probability waves of Schrödinger quantum theory type. It is assumed that the potentials of the two metrics are connected, as with the potentials of the electromagnetic field, and the potentials of the Yang-Mills theory. Hence, the total output for all interactions law establishing the primacy of the gravitational field as the fundamental interaction, generating other interactions
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MATHEMATICAL MODEL OF THE DYNAMICS OF HIV INFECTION WITHOUT TREATMENT
01.00.00 Physical-mathematical sciences
DescriptionThis 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
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01.00.00 Physical-mathematical sciences
DescriptionIn 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
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01.00.00 Physical-mathematical sciences
DescriptionThe 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, МA-41 and МA-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
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01.00.00 Physical-mathematical sciences
DescriptionIn 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
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MATHEMATICAL THEORY OF RATINGS
01.00.00 Physical-mathematical sciences
DescriptionWhen developing management solutions with the aim of joint consideration and comparison of various factors, partial removal of uncertainty is widely used ratings. In the theory of decisionmaking in almost the same sense, we use the terms "composite index" or "integrated indicator". The article is devoted to the mathematical theory of ratings as tools for studying socio-economic systems. We considered, primarily, linear ratings which is a linear function from a single (private) indicators (factors, criteria), constructed using the coefficients of importance (weightiness, importance). The study discusses the factors affecting the magnitude of the ratings. Three groups of causes affect the value of a line ranking: the ways of measurement of individual indicators, the choice of the set of indicators; the values of the coefficients of importance. We considered binary ratings when the rating takes two values. To compare the proposed rankings we use a new indicator of the quality of diagnostics and prognostic power. Significantly, in many managerial situations, significant differences between objects are identified using any rating. According to the fundamental results of stability theory, the same source data should be processed in several ways. Matching findings, obtained using multiple methods, likely reflect the properties of reality. The difference is the result of a subjective selection method. When using the results of the comparison of objects according to several indicators (criteria ratings), including in dynamics, very useful is the selection of the Pareto set. We discuss the examples of the application of the decision theory, expert evaluations and rankings when developing complex technical systems
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MATHEMATICAL METHODS OF RESEARCH OF INVERSE DYNAMIC ECONOMIC SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe 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