№ 123(9), November, 2016
Public date: 30.11.2016
Archive of journal: Articles count 141, 382 kb
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01.00.00 Physical-mathematical sciences
01.00.00 Physical-mathematical sciences
Description
Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we use initially proposed by its developers measure of the reliability of the models, which is essentially a fuzzy multiclass generalization of the classical F-measure (it is proposed to call it the L-measure). In this article, L-measure is mathematically described and its application is demonstrated on a simple numerical example
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MANAGEMENT OF THE FINANCIAL AND THE ECONOMIC STATE OF A COMPANY USING A MATHEMATICAL MODEL
01.00.00 Physical-mathematical sciences
Description
This article focuses on the mathematical modeling of evaluation of financial and economic activities of a company and on definition (based on this model) of such balance settings (line F1 and F2) which would make financial-economic indicators of the activities of the organization optimal, and the total cumulative score was the maximum. The knowledge and the use of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the company. The article analyzes the dependencies of each of the 15 basic indicators (profitability, turnover, financial stability, liquidity and solvency) of financial and economic activity of the organization on the balance parameters. The optimal values of the parameters of the balance and the main indicators of financial and economic activities of the organization have been found. We have also built a mathematical model of optimal control of financial and economic indicators in the form of a problem of mathematical programming. For example, for the company called "Nika" it is shown the possibility of improving estimation of financial and economic condition of the organization. Knowledge of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the organization. To solve this problem we have used the method of generalized reduced gradient implemented in Excel, with which there was found a maximum of the objective function for the article restrictions. The article describes the analysis algorithm of the optimization problem. A common assessment was carried out in stages, based on the calculation algorithm of sequentially improved target functions
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01.00.00 Physical-mathematical sciences
Description
This article is a continuation of the previous works of the authors [The influence of reaction dissociation / recombination of molecules of water on transportation of electrolyte 1:1 in the membrane systems in the diffusion layer. Part 1. Mathematical model // Scientific journal of Kuban State Agrarian University, 2016. No. 07(121) and The influence of the reaction of dissociation / recombination of molecules of water on transportation of electrolyte 1: 1 in membrane systems in the diffusion layer. Part 2. Asymptotic analysis // Scientific journal of Kuban State Agrarian University, 2016. – №08(122)] and devoted to assessing the possibility of gravitational convection due to the recombination of hydrogen and hydroxyl ions. The article presents the solution of a boundary-value problem, which is a mathematical model of electrodiffusion for the four types of ions at the same time (two ions of salts and hydrogen and hydroxyl ions) in the diffusion layer in electro-membrane systems with ideal selective membrane, with the heat transfer equation and the Navier-Stokes equation. The article shows the possibility of the emergence of gravitational convection due to the exothermic reaction of recombination of water molecules in the depth of the solution. The article considered the reaction of recombination of hydrogen ions and hydroxyl, although the main results can be applied, after appropriate modifications, and to amfolit-containing solutions, such as wine, juices, dairy products, microbiological processing of biomass (amino acids, anions of polybasic carboxylic acids), municipal effluent (anions of phosphoric acid), etc.
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THE ROLE OF QUANTUM ENTANGLEMENT IN TASKS OF THE GAMES THEORY
01.00.00 Physical-mathematical sciences
Description
This article discusses an economic game called "The struggle for markets". We have generated a mathematical model of quantum realization of this game. For clarity, the algorithms are derived for soft and hard quantum games for assessing the impact of the degree of entanglement to work and the result of the algorithm. There are step-by-step instructions for the sequence of actions and operations to create a quantum model of the game. The aim is to assess the influence of the degree of entanglement on work algorithms. Also, we investigate the influence of quantum entanglement on the win for two or more players. The article gives a comparison with classical results
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01.00.00 Physical-mathematical sciences
Description
We consider an approach to the transition from continuous to discrete scale which was defined by means of step of quantization (i.e. interval of grouping). Applied purpose is selecting the number of gradations in sociological questionnaires. In accordance with the methodology of the general stability theory, we offer to choose a step so that the errors, generated by the quantization, were of the same order as the errors inherent in the answers of respondents. At a finite length of interval of the measured value change of the scale this step of quantization uniquely determines the number of gradations. It turns out that for many issues gated it is enough to point 3 - 6 answers gradations (hints). On the basis of the probabilistic model we have proved three theorems of quantization. They are allowed to develop recommendations on the choice of the number of gradations in sociological questionnaires. The idea of "quantization" has applications not only in sociology. We have noted, that it can be used not only to select the number of gradations. So, there are two very interesting applications of the idea of "quantization" in inventory management theory - in the two-level model and in the classical Wilson model taking into account deviations from it (shows that "quantization" can use as a way to improve stability). For the two-level inventory management model we proved three theorems. We have abandoned the assumption of Poisson demand, which is rarely carried out in practice, and we give generally fairly simple formulas for finding the optimal values of the control parameters, simultaneously correcting the mistakes of predecessors. Once again we see the interpenetration of statistical methods that have arisen to analyze data from a variety of subject areas, in this case, from sociology and logistics. We have another proof that the statistical methods - single scientificpractical area that is inappropriate to share by areas of applications
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TESTING OF HOMOGENEITY OF PAIRED SAMPLES
01.00.00 Physical-mathematical sciences
Description
The article begins with the letter of the chief engineer of chemical plant near Moscow. He requests to analyze of data by means of modern statistical methods and give an opinion on the presence (or absence) of the relationship between the two methods of determining the viscosity of the mastic. For each of the batches of mastic It was presented two numbers - the viscosity measurement results of the two methods. These numbers form two paired samples. We want to install, give whether two specific methods similar results. The true values of viscosity in different batches are not equal. Their difference is not allows us to combine the results of the first measurement method in first sample, the results of the second method - in the second sample, as we can do in the case of testing the homogeneity of two independent samples. For solutions to this problem we discuss four statistical criterions, based on a study of the differences between corresponding values in two paired samples. We test the hypothesis of equality 0 of median of these differences (sign test) and of equality 0 of the mathematical expectation of these differences. Hypothesis of testing of equality of the distribution functions of two paired samples is reduced to the hypothesis of symmetry of the distribution function of these differences with respect to 0. In the alternative of the shift is proposed to use the Wilcoxon signed rank criterion. In the total alternative is proposed to use criterion of the omega-square type which is developed by the author of this article
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01.00.00 Physical-mathematical sciences
Description
An analysis of the experimental data obtained by the authors, as well as reference books, allowed to hypothesize about the essential role of gravitational convection in electromembrane systems with ampholytes even in underlimiting current regimes. The article is devoted to the development of the mathematical model of ion transport in a flow elecrtomembrane system during electrodialysis of ampholyte-containing solutions with taking into account a possible appearance of gravitational convection, in particular, due to nonisothermal protonation–deprotonation reactions of ampholytes. The article presents the boundary value problem that is the new mathematical model for diffusion, convection and electromigration of four components of the solution (ions of sodium, dihydrogen phosphate and hydrogen, as well as molecules of orthophosphoric acid) in a half of an electrodialysis desalination channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and homogeneous. The system of partial differential equations, that is the base of the model, also includes equations of Navier-Stokes, material balance, convective heat conduction and the electroneutrality condition. The system of equations is supplemented by a number of natural and original boundary conditions. A distinctive feature of this study is the absence of assumptions about the equilibrium of chemical reactions in a diffusion layer. The results of the study can be used for the development of environmentally rational and resource saving membrane technologies for a processing of products of agro-industrial complex
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01.00.00 Physical-mathematical sciences
Description
There is a 2D mathematical model of ion transport binary salt with the main conjugate effects of concentration polarization in the overlimiting current mode: the bulk charge and the dissociation/ recombination of water, gravity and electroconvection and Joule heating the solution in the form of a boundary value problem for systems of differential equations with partial derivatives in the article. This system is presented in a form convenient for numerical solution. We describe the necessary boundary conditions. This article presents a theoretical study of the interaction of forced, gravitational and electroconvection, the dissociation / recombination of water molecules, and Joule heating of the solution and heat transport through membranes. We have constructed a mathematical model of two-dimensional non-stationary ion transport binary salt in a smooth rectangular channel desalting electrodialysis device using equations Nernst-Planck-Poisson, heat conduction and Navier-Stokes equations and the natural boundary conditions. For numerical solution we use the finite element method, with the splitting of task at each new time layer into three subtasks: electrochemical, thermal conductivity, hydrodynamic. Such approach to the development of numerical methods is the original and can solve arising in modeling boundary-value problems for a nonlinear system of partial differential equations
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01.00.00 Physical-mathematical sciences
Description
The creation of artificial intelligence systems is one of important and perspective directions of development of modern information technology. Since there are many alternatives of mathematical models of systems of artificial intelligence, there is a need to assess the quality of these models, which requires their comparison. To achieve this goal we require free access to the source data and methodology, which allows to convert these data into a form needed for processing in artificial intelligence. A good choice for these purposes is a database of test problems for systems of artificial intelligence of repository of UCI. In this work we used the database "Iris Data Set" from the bank's original task of artificial intelligence – UCI repository, which solved the problem of formalization of the subject area (development of classification and descriptive dials and graduations and the encoding of the source data, resulting training sample, essentially representing a normalized source data), synthesis and verification statistical and system-cognitive models of the subject area, identify colors with classes, which serve varieties of Iris, as well as studies of the subject area by studying its model. To solve these problems we used the automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit – intellectual system called "Eidos"
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COMBINATORY METHOD OF NUMBERS′ FACTORIZATION
01.00.00 Physical-mathematical sciences
Description
Problem having elementary formulation makes us look for its easier solution. So the combinatorial method of positive integer’s factorization is an attempt to do it. The combinatory method possesses simple algorithm, leading immediately to finding out all the factorizations and identification of all prime numbers on any interval of the positive integers. Prime numbers don’t carry any information except their own magnitude. Composite numbers, possessing divisibility properties provide possibility to discover the law of their distribution. The achievement of this purpose also completely solves the problem of finding out the law of prime numbers’ distribution
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