Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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615 kb

MODIFICATION OF WEIGHTED LEAST SQUARES BY USING THE OBSERVATIONS OF THE AMOUNT OF INFORMATION IN THEM AS WEIGHTS (MATHEMATICAL ASPECTS)

abstract 1051501050 issue 105 pp. 813 – 844 30.01.2015 ru 922
This 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
231 kb

PHYSICAL MEANING OF CERTAIN SIMILARITY CRITERIAS OF TRANSPORT PROCESSES IN THE DESALTING CHANNEL THE ELECTRODIALYSIS DEVICE WITH ELECTROCONVECTION

abstract 1051501051 issue 105 pp. 845 – 864 30.01.2015 ru 1229
The 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
238 kb

THEORY OF SIMILARITY OF ELECTRO MEMBRANE SYSTEMS WITH REGARD TO FORCED, GRAVITATIONAL AND ELECTRO CONVECTION

abstract 1051501052 issue 105 pp. 865 – 886 30.01.2015 ru 969
In 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
165 kb

THE METHOD FOR HYPOTHESIS TESTING BASED ON SET OF SMALL SAMPLES AND ITS APPLICATION IN THE THEORY OF STATISTICAL CONTROL

abstract 1041410003 issue 104 pp. 43 – 57 30.12.2014 ru 1090
We 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
257 kb

ABOUT THE METHODOLOGY OF STATISTICAL METHODS

abstract 1041410004 issue 104 pp. 58 – 85 30.12.2014 ru 1249
The 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
209 kb

TWO-SAMPLE WILCOXON TEST - ANALYSIS OF TWO MYTHS

abstract 1041410006 issue 104 pp. 96 – 116 30.12.2014 ru 1564
It was established that the two-sample Wilcoxon test (Mann-Whitney test) was designed to test the hypothesis H0: P(X
241 kb

ESTIMATION OF A CREDIT STATUS OF THE COMPANY BASED ON THE ALTMAN FIVEFACTOR MODEL USING FUZZY SETS AND INTEGRAL MEAN-SQUARE APPROXIMATION

abstract 1041410039 issue 104 pp. 546 – 561 30.12.2014 ru 1375
In 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
359 kb

MATHEMATICAL MODELING OF THE INFLUENCE OF SURFACE MORPHOLOGY OF HETEROGENEOUS ION-EXCHANGE MEMBRANE TO THE ELECTROCONVECTION

abstract 1041410046 issue 104 pp. 630 – 643 30.12.2014 ru 1117
This 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
268 kb

FORECASTING THE WATER LEVEL IN A RIVER WITH THE ABRUPT FALLING WATER BASED ON KALMAN-BUSY FILTRATION

abstract 1041410058 issue 104 pp. 775 – 786 30.12.2014 ru 1264
The 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
140 kb

CLIMATE-ECONOMIC MODEL WITH ENDOGENOUS CAPITAL DEPRECIATION RATE UNDER UNCERTAINTY OF TEMPERATURE PROJECTIONS

abstract 1041410089 issue 104 pp. 1206 – 1214 30.12.2014 ru 1015
A 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
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