№ 105(1), January, 2015
Public date: 30.01.2015
Archive of journal: Articles count 64, 130 kb
-
01.00.00 Physical-mathematical sciences
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
-
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
-
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
-
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