01.00.00 Physical-mathematical sciences
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CYCLONE REGIME MODIFICATIONS IN NORTHERN AND SOUTHERN HEMISPHERE IN CONDITIONS OF CHANGING CLIMATE
01.00.00 Physical-mathematical sciences
DescriptionThe main objective of this article is to solve a problem of a numerical identification of cyclones based on the reanalysis data. The results show that the amount of cyclones is increasing during last 66 years, the number and depth of cyclones are larger in Northern Hemisphere than in Southern, and Northern Hemisphere cyclones become deeper and deeper with time. Cyclonic activity in the Northern Hemisphere mainly is caused by large number of cyclones, in the Southern Hemisphere – by their depth. In the Northern Hemisphere cyclone characteristics change significantly
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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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01.00.00 Physical-mathematical sciences
DescriptionMicro and nanofluidics are the new multidisciplinary sciences. One of the tasks of which is creation and management of flow of fluid in the thin channels size of a few nano- or micrometer which exposed the external electric field, where the walls are the ion exchange membrane. Electroosmosis (electroconvection) plays an important role in these tasks. A large number of articless were devoted to electroosmosis. One of the first, Dukhin S.S., Mishchuk N.A. and Rubinstein I. gave a theoretical explanation of the overlimiting current by electroosmosis. They used two-dimensional Stokes equation to calculate the flow of the electrolyte, and one-dimensional equations of Nernst-Planck and Poisson to calculate the electric power. These researches have multiple limitations because of the computational complexity the mathematical simulation. Thus, there is an actual problem of the asymptotic solution of boundary value problems for the two-dimensional systems of equations of NernstPlanck and Poisson without these restrictions. These researches we derived in simplified models of electroosmosis in galvanic dynamical mode using the decomposition method. We have created a hierarchical system of two-dimensional mathematical models of ion transport of salt and electroosmosis in micro- and nanochannels formed by selective ion-exchange membranes
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01.00.00 Physical-mathematical sciences
DescriptionThe article by continues the cycle of their studies related to the formulation and development of methods of constructing non-negative solutions of inverse problems of balance models (in this case, the model of world trade). Method of constructing nonnegative solutions of the studied inverse problems is developed. This technique is based on the following scheme of the solution. Initially we convinced of a correct formulation of the direct problem, then of the solvability of the inverse. Further, by specified tabular solutions of the direct problem, a system of algebraic equations containing the unknown, the estimated parameters of the studied model is built. Then the inverse problem reduces to solving the following quadratic programming, the solution of which is determined in MS Excel. The theoretical material is accompanied by solution of specific example, using statistical data of the Karachay-Cherkess Republic that shows how actually in practice it is possible to solve the inverse problem, i.e. to organize a process of balanced trade of the Karachay-Cherkess Republic with each of the subjects of Noth – Caucasion Federal District. Found the non-negative elements of a matrix, by which we can judge what proportion of national income, y, the subject has to spend on the purchase of goods in the Karachay-Cherkess Republic, to trade between this pair was balanced. So, the inverse problem posed in relation to the trading countries, it is possible to put and solve the following method and to trade between the subjects of one country
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GENERAL RELATIVITY AND THEORY OF ELECTROMAGNETIC DRIVE
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the theory of the electromagnetic type of rocket motor. The apparatus consists of a magnetron and a conical cavity in which electromagnetic oscillations are excited. We explain the mechanism of trust in such a device based on Maxwell's theory and the Abraham force. We built a dynamic model of the motor and calculated the optimal parameters. It is shown, that the laws of conservation of momentum and energy for the rocket motor of electromagnetic type are true, taking into account the gravitational field. In simulation, the movement used the theory of relativity. The source of the motion in an electromagnetic drive is the mass conversion in various kinds of radiation. The optimization of the operating parameters of the device is done, namely by the excitation frequency, the magnitude of heat losses of electromagnetic energy by thermal radiation in the IR spectrum, the parameters of heat transfer and forced from the temperature dependence of the resistance of the material of the cavity walls. It was found that the effective conversion of electromagnetic energy in the trust force necessary to minimize the deviation of the excitation frequency of the primary resonance frequency of the cavity. The mechanism of formation of trust under change the metrics of space-time, taking into account the contribution of the Yang-Mills theory and electromagnetic field tensor of energymomentum has been proposed
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01.00.00 Physical-mathematical sciences
DescriptionThe article discusses the application of automated system-cognitive analysis (ASC-analysis), its mathematical model which is system theory of information and its software tool, which is intellectual system called "Eidos" for solving problems related to identification of types and models of aircraft by their silhouettes on the ground, to be more precise, their external contours: 1) digitization of scanned images of aircraft and creation of their mathematical models; 2) formation of mathematical models of specific aircraft with the use of the information theory; 3) modeling of the generalized images of various aircraft types and models and their graphic visualization; 4) comparing an image of a particular plane with generalized images of various aircraft types and models, and quantifying the degree of similarities and differences between them, i.e., the identification of the type and model of airplane by its silhouette (contour) on the ground; 5) quantification of the similarities and differences of the generalized images of the planes with each other, i.e., clusterconstructive analysis of generalized images of various aircraft types and models. The article gives a new approach to digitizing images of aircraft, based on the use of the polar coordinate system, the center of gravity of the image and its external contour. Before digitizing images, we may use their transformation, standardizing the position of the images, their sizes (resolution, distance) and the angle of rotation (angle) in three dimensions. Therefore, the results of digitization and ASC-analysis of the images can be invariant (independent) relative to their position, dimensions and turns. The shape of the contour of a particular aircraft is considered as a noise information on the type and model of aircraft, including information about the true shape of the aircraft type and its model (clean signal) and noise, which distort the real shape, due to noise influences, both of the means of countering detection and identification, and environment. Software tool of ASC-analysis, i.e. Eidos intellectual system, provides identification of the type and the model of airplane by its silhouette, as it was shown in a simplified numerical example
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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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ADAPTIVE TIME SERIES MODELS OF A MOUNTAIN RIVER LEVEL
01.00.00 Physical-mathematical sciences
DescriptionThe article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
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NON-PARAMETRIC CYCLES ESTIMATORS
01.00.00 Physical-mathematical sciences
DescriptionIn many applications, we study the time series (or a random process), which is the sum of the periodic deterministic function of time and random errors that distort the periodic signal. It is required to estimate the length of the period and the periodic component. It does not assume that the periodic function is included in any parameter family of functions, such as finite sums of sines and cosines. It is obvious that the assumption of occurrence of a periodic function in parametric family does not meet the characteristics of the real world, ie, is conditional, internal mathematical (look for the keys under the lamp because there is a light, not in the bush, where lost, because there are dark). For similar reasons, it is impossible to assume that the distribution function of the random errors is included in any parameter family of distributions. In accordance with the new paradigm of mathematical statistics in this article we studied the problem of nonparametric estimation (minimum) length of the period and the periodic component of the signal. On the basis of natural variation and scope of indicators is suggested a new class of nonparametric estimators of the length of the period and the periodic component in the time series. Based on the general results of statistics of objects of non-numeric nature we proved the consistency of these estimates. From the practical point of view it is necessary to minimize the numerical (one parameter - ability length of period of time) one or more of the 66 functionals, described in the article