01.00.00 Physical-mathematical sciences
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THE INVERSE PROBLEM OF OPTIMAL ONESTEP AND MULTI-STEP FILTERING OF MEASUREMENT ERRORS IN THE VECTOR
01.00.00 Physical-mathematical sciences
DescriptionIn practice, we often encounter the problem of determining a system state based on results of various measurements. Measurements are usually accompanied by random errors; therefore, we should not talk about the definition of the system state but its estimation through stochastic processing of measurement results. In the monograph by E. A. Semenchina and M. Z. Laipanova [1] it was investigated for one-step filtering of the measurement errors of the vector of demand in balance model of Leontiev, as well as multistage optimal filtering of measurement errors of the vector of demand. In this article, we have delivered and investigated the inverse problem for the optimal one-step and multi-step filtering of the measurement errors of the vector of demand. For its solution, the authors propose the method of conditional optimization and using given and known disturbance to determine (estimate) the matrix elements for one-step filtering of measurement errors and for multi-stage filtration: for given variables and known disturbance to determine the elements of the matrix. The solution of the inverse problem is reduced to the solution of constrained optimization problems, which is easily determined using in MS Excel. The results of the research have been outlined in this article, they are of considerable interest in applied researches. The article also formulated and the proposed method of solution of inverse in a dynamic Leontiev model
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GENERAL RELATIVITY AND GALACTIC METRICS
01.00.00 Physical-mathematical sciences
DescriptionIt is shown that the metric of the galaxy should be universal, depending only on the fundamental constants. There are examples of universal metrics obtained in Einstein's theory of gravitation and Yang-Mills theory. The axial-symmetric solutions of Einstein’s equations for a vacuum are applied to explain the rotation of matter in spiral galaxies
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GENERAL RELATIVITY AND METRICS OF INHOMOGENEOUS ROTATING UNIVERSE
01.00.00 Physical-mathematical sciences
DescriptionThe metric of inhomogeneous rotating Universe is discussed. There are examples of universal metrics obtained in Einstein's theory of gravitation. On the basis of solutions of Einstein’s equation we have proposed universal metric describing the properties of galaxies, groups and clusters of galaxies in inhomogeneous rotating Universe
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RESTRICTED MANY-BODY PROBLEM IN THE RICCI FLOWS IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the restricted problem of three and more bodies in the Ricci flow in the general theory of relativity considered. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow proposed. A model describing the motion of particles in the Ricci flow derived. It is shown that the theory describing the Ricci flow in the many-body problem is consistent with the Einstein-Infeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, consider the metric having axial symmetry and contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponds to Newton's theory of the two centers of gravity, moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of bodies. We consider the statement of the problem of many bodies distributed at the initial time on the axis of symmetry of the system. 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 axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials we have justified transition from the relativistic motion of the particles to the dynamic equations in the classic theory
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01.00.00 Physical-mathematical sciences
DescriptionIn the article, the technique of experimental determination of dielectric permeability and a tangent of an angle of dielectric losses of mixed seeds of agro cultures – air by means of measurement of the electric capacity of the cell of a flat condenser which has been densely filled with seeds in a range of frequencies of 1 kHz – 1 MHz is presented
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01.00.00 Physical-mathematical sciences
DescriptionIn this article we propose a method of determining the share or the significance (weight) of indicators of Beaver and risks R in the portfolio formed by these parameters allowing us to minimize the mean square error evaluating the effectiveness of the portfolio (risk) in the assessment of the financial condition of the companies investigated. The proposed method is the minimization of a quadratic form in variables satisfying lengthy conditions, i.e. the quadratic programming. This technique is implemented using four methods of optimization: analytical method, using built-in function minimization block given, the penalty function method and the gradient method. More so, this technique allows, as shown by the results of the computational experiments, the expert without routine statistical data processing to obtain additional information on the credit worthiness of the investigated enterprise and make a more informed conclusion about its financial condition, which speeds up the decision on granting a loan required by a company. Based on the techniques proposed in this paper, other techniques of assessing the creditworthiness of businesses may be constructed using the results of optimization theory based on well-established applied research methods: Method of evaluating the creditworthiness of Russia, Credit scoring method, the American method, method of Altman and others
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01.00.00 Physical-mathematical sciences
DescriptionThe time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been designed. The algorithm has been developed to determine the parameters of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed. The region of existence of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been set. According to the results of the numeral experiment, the dependences of the duration of the cycle of movement of the executive body of the drive from prescribed displacement (rotation angle) for different values of the fifth derivative of the speed have been plotted
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OPTIMAL PLAN OF INVENTORY CONTROL CANNOT BE FOUND BASED ON THE FORMULA OF THE SQUARE ROOT
01.00.00 Physical-mathematical sciences
DescriptionInventory management (in other words, logistics) is an integral part of the work of firms, companies and organizations. We are talking about stocks of raw materials, fuel, tools, components, semi-finished products, finished products for industrial (or agricultural) firms, about stocks of goods to distribution centers, warehouses, shops, workplaces sellers, finally consumers. Stocks spent all the time and supplemented on various rules adopted in the firm. Optimization of these rules, ie, optimal inventory management, gives a big economic effect. The mathematical theory of inventory management, based on the models of movement of flows of goods, is an important area of economic-mathematical research. The classical model of inventory management proposed in 1915 by F. Harris is one of the simplest and most illustrative examples of application of the mathematical apparatus for decision-making in the economic field. This model is commonly referred to as the Wilson model, because this model became known after the publication of R.G. Wilson in 1934. The formula of the optimum batch size (the so-called "the formula of the square root"), obtained in the Wilson model, is widely used on various stages of production and distribution, since this formula is practically useful for decision-making in the inventory management, in particular, for generating significant economic effect. However, contrary to popular belief, by means of this formula it is impossible to calculate the optimal batch size (although it is a necessary step on the path of its finding). In strict economic-mathematical analysis of Wilson model, conducted in the article, it is shown that the formula of square root does not give the optimal batch size. We have given the algorithm for calculating the optimal batch size. It has been found that the formula of the square root gives asymptotically optimal plan. We have studied the stability of the conclusions in the economic-mathematical model and considered an example of the practical application of the classical model of inventory management
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ORBITAL SYSTEM OF DISTRIBUTION OF ELECTRONS IN ATOM AND STRUCTURE OF PERIODIC SYSTEM OF ELEMENTS
01.00.00 Physical-mathematical sciences
DescriptionIn the article, for the first time we have considered group of electrons radial to atomic nucleus with equal value of orbital quantum number and equal sequence of emergence on subshells. As a result of this consideration, the exclusion orbital principle which regulates distribution of electrons in atom on values of spin has been established. On the basis of this principle, the orbital system of distribution of electrons which adequately corresponds to the valid system installed according to the spectral analysis is developed. From positions of orbital system the new explanation of reasons for deviation of the valid system of distribution of electrons in atom from ideal system of consecutive filling of electron shells has been offered and the nature of the empirical rule is opened. The structure of periodic system is also considered and the explanation of the reasons pair repetition of the periods on number of elements is offered. It is thus shown that borders of the chemical periods are displaced relatively borders of the periods of orbital system on two elements to the left
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01.00.00 Physical-mathematical sciences
DescriptionThe method and results of forecasting of crops of agricultural crops in a steppe zone of territory of the Kabardino-Balkarian republic are resulted. The method is based on use of dependence of crops of agricultural crops from agrometeorological factors. Results of calculations on planning crops of some cultures are resulted.