01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionThis article briefly discusses the mathematical nature of the author's proposed modification of the weighted least squares, in which the amount of the data is used as the weights of observations. There are two variants of this modification. In the first one, the weighting of the observations was made by replacing one observation with a certain amount of the information in it by the corresponding number of observations for unit weight, and then we applied the standard method of least squares. In the second method, the weighting of the observations was performed for each value of the argument by replacing all observations with a certain amount of information in one observation of unit weight which had been obtained as a weighted average of them, and then we applied the standard method of least squares. We have described in detail the technique of numerical calculations of the amount of information in the observations, based on the theory of automated system-cognitive analysis (ASC-analysis) and implemented it with a help of software tools - intelligent system called "Eidos". The article provides an illustration of the proposed approach on a simple numerical example. In the future, we are planning to give more detailed mathematical basis of the method of weighted least squares, which is modified by using the amount of information as weights, but also to explore its properties
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01.00.00 Physical-mathematical sciences
DescriptionThe phenomenon of electro convection in membrane systems is of considerable interest, because it is, according to many authors, the main mechanism of overlimiting mass transfer. A great number of theoretical and experimental works, in which, as a rule, dimensional values were used, are devoted to electro convection study. Because of that, in actual fact, there is investigated the influence of individual factors on the transfer process. For example, the influence of voltage jumps, the average speed of a forced stream of the solution, the geometric characteristics of the channel, the initial concentration, etc. However, the influence of these factors appears not separately, at the same time. Thus, there is the problem of introducing dimensionless complexes of dimensional values that have a physical meaning and that allow to evaluate the inner links of the process. As it is known, for solving that problem, there is applied a theory of similarity, based on the transition towards dimensionless parameters in equations and formulas describing the process, and using values, typical of the system under study. This work is devoted to the determining of physical meaning of similarity criteria of salt ions processes, taking into account electro convection in the desalting channel of electro dialysis apparatus. The channel is bounded with perfectly selective, homogeneous anion-exchange and cation-exchange membranes. The introduced similarity criteria are used so as to conduct the theoretical study of the effect of a number of parameters of a desalting process on electro convection
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01.00.00 Physical-mathematical sciences
DescriptionIn the article, we have suggested a general mathematical model of non-stationary and non-isothermal process of a binary electrolyte transfer in dilute solutions in an electro-membrane system (EMS), taking into account the joint action of gravitational convection, forced convection and electro convection in potential dynamic mode. This model is a boundary problem for a system of two-dimensional quasi-linear Navier-Stokes equation and Nernst-Planck-Poisson in partial derivatives equation. We have developed a theory of similarity of the process of heat and mass transfer in electro-membrane systems, specifically, in a desalting channel of electro dialysis apparatus, taking into account joint actions of concentration polarization, space charge, gravity convection, forced convection and electro convection. It is shown that the criterion of electro convection does not directly depend on the initial concentration, and, therefore, electro convection occurs at any initial concentration. At the same time, the criterion of concentration convection linearly dependents on the initial concentration, and, therefore, at high concentrations, concentration convection prevails, while at lower concentrations, the role of gravitational convection begins to fall whereas the role of electro convection increases. The theory of similarity of the process of heat and mass transfer in the desalting channel of electro dialysis apparatus built in this work taking into account the joint action of concentration polarization, space charge, gravity convection, forced convection and electro convection is important for engineering calculations, for scaling the results of experiments in an electro-membrane cell for industrial electro dialysis water desalting apparatus
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01.00.00 Physical-mathematical sciences
DescriptionWe have proposed the method for testing of independence of two alternative variables on the basis of statistics of non-numeric data. The method is aimed at application in problems of statistical quality control. Testing of independence is based on set of small samples, i.e., in the Kolmogorov’s asymptotics, when the number of unknown parameters of the distribution increases in proportion to the data size
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ABOUT THE METHODOLOGY OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionThe purpose of the article - to justify the need to develop the methodology of statistical methods as an independent scientific direction. The models of mathematician and applied specialist are presented. We have obtained the conclusions on teaching and research and discussed five major unsolved problems of statistical methods: the effect of deviations from the traditional prerequisites; use asymptotic results for finite sample sizes; selecting one of the many specific tests for the hypothesis; organization of theoretical work in the field of statistical methods; conduct applied research and teaching of statistical methods
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TWO-SAMPLE WILCOXON TEST - ANALYSIS OF TWO MYTHS
01.00.00 Physical-mathematical sciences
DescriptionIt was established that the two-sample Wilcoxon test (Mann-Whitney test) was designed to test the hypothesis H0: P(X
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01.00.00 Physical-mathematical sciences
DescriptionIn this article we have proposed a method using the apparatus of fuzzy sets theory in conjunction with the five-factor model of Altman to assess the creditworthiness of the investigated companies. The Altman model was improved in two ways: by using RMS integral approximation for the exact calculation of the quantitative credit assessment (probability of bankruptcy) and the application of the apparatus of fuzzy sets for ordered sets by the degree of confidence resulting probability
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01.00.00 Physical-mathematical sciences
DescriptionThis article continues the works [1,2], devoted to the theoretical study of the basic laws of electroconvection caused by natural or artificial inhomogeneous conductivity of ion-exchange membranes in a smooth rectangular channel electrodialysis desalination unit. For this purpose, a mathematical model was created for a binary electrolyte electroconvection at overlimiting current modes in the form of a boundary value problem for a coupled system of the Nernst-Planck-Poisson and Navier-Stokes equations. We have studied the influence of heterogeneity on the ion-exchange membranes and ion transport electroconvection salt, calculated currentvoltage characteristic. The possibility of intensification of mass transfer due to the surface modification of ion exchange membranes was also shown
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FORECASTING THE WATER LEVEL IN A RIVER WITH THE ABRUPT FALLING WATER BASED ON KALMAN-BUSY FILTRATION
01.00.00 Physical-mathematical sciences
DescriptionThe technique of short-term forecasting of the water level in a vein of a mountain type river, based on a method of Kalman-Busy filtration in the make assumption of natural simplifications, characterized for natural objects is offered
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01.00.00 Physical-mathematical sciences
DescriptionA simple climate–economic model based on the AK model of economic growth with the endogenous depreciation rate linear in temperature and on the exogenous climate scenario with temperature linear in time is considered. The analytical solution of the model is obtained. The uncertainty of temperature projections is introduced in the model, and the moments of model state variable are calculated analytically. Numerical examples are provided