01.00.00 Physical-mathematical sciences
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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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SOLVING PROBLEMS OF STATISTICS WITH THE METHODS OF INFORMATION THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents a theoretical substantiation, methods of numerical calculations and software implementation of the decision of problems of statistics, in particular the study of statistical distributions, methods of information theory. On the basis of empirical data by calculation we have determined the number of observations used for the analysis of statistical distributions. The proposed method of calculating the amount of information is not based on assumptions about the independence of observations and the normal distribution, i.e., is non-parametric and ensures the correct modeling of nonlinear systems, and also allows comparable to process heterogeneous (measured in scales of different types) data numeric and non-numeric nature that are measured in different units. Thus, ASC-analysis and "Eidos" system is a modern innovation (ready for implementation) technology solving problems of statistical methods of information theory. This article can be used as a description of the laboratory work in the disciplines of: intelligent systems; knowledge engineering and intelligent systems; intelligent technologies and knowledge representation; knowledge representation in intelligent systems; foundations of intelligent systems; introduction to neuromaturation and methods neural networks; fundamentals of artificial intelligence; intelligent technologies in science and education; knowledge management; automated system-cognitive analysis and "Eidos" intelligent system which the author is developing currently, but also in other disciplines associated with the transformation of data into information, and its transformation into knowledge and application of this knowledge to solve problems of identification, forecasting, decision making and research of the simulated subject area (which is virtually all subjects in all fields of science)
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PROBABILISTIC-STATISTICAL MODELING THE INTERFERENCES FROM ELECTRIC LOCOMOTIVES
01.00.00 Physical-mathematical sciences
DescriptionThe movements of electric locomotives create the interferences affecting the wired link. The creation of sufficiently technical effective and at the same time cost-effective means of protection from wireline interferences generated traction networks assumes as a preparatory phase to develop mathematical models of interference caused by electric locomotives. We have developed a probabilistic-statistical model of interferences caused by electric locomotives. The asymptotic distribution of the total interference is the distribution of the length of the two-dimensional random vector whose coordinates - independent normally distributed random variables with mean 0 and variance 1. Limit theorem is proved for the expectation of the total amplitude of the interferences. Monte-Carlo method is used to study the rate of convergence of the expectation of the total amplitude of the interferences to the limiting value. We used an algorithm of mixing developed by MacLaren-Marsaglia (M-algorithm). Five sets of amplitudes are analyzed, selected in accordance with the recommendations of experts in the field of traction AC networks. The most rapid convergence to the limit takes place in the case of equal amplitudes. It was found that the maximum possible average value of the amplitude of the random noise by 7.4% less than the previously used value, which promises a significant economic impact
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CURRENT STATUS OF NONPARAMETRIC STATISTICS
01.00.00 Physical-mathematical sciences
DescriptionNonparametric statistics is one of the five points of growth of applied mathematical statistics. Despite the large number of publications on specific issues of nonparametric statistics, the internal structure of this research direction has remained undeveloped. The purpose of this article is to consider its division into regions based on the existing practice of scientific activity determination of nonparametric statistics and classify investigations on nonparametric statistical methods. Nonparametric statistics allows to make statistical inference, in particular, to estimate the characteristics of the distribution and testing statistical hypotheses without, as a rule, weakly proven assumptions about the distribution function of samples included in a particular parametric family. For example, the widespread belief that the statistical data are often have the normal distribution. Meanwhile, analysis of results of observations, in particular, measurement errors, always leads to the same conclusion - in most cases the actual distribution significantly different from normal. Uncritical use of the hypothesis of normality often leads to significant errors, in areas such as rejection of outlying observation results (emissions), the statistical quality control, and in other cases. Therefore, it is advisable to use nonparametric methods, in which the distribution functions of the results of observations are imposed only weak requirements. It is usually assumed only their continuity. On the basis of generalization of numerous studies it can be stated that to date, using nonparametric methods can solve almost the same number of tasks that previously used parametric methods. Certain statements in the literature are incorrect that nonparametric methods have less power, or require larger sample sizes than parametric methods. Note that in the nonparametric statistics, as in mathematical statistics in general, there remain a number of unresolved problems
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OPTIMAL PLAN OF INVENTORY CONTROL CANNOT BE FOUND BASED ON THE FORMULA OF THE SQUARE ROOT
01.00.00 Physical-mathematical sciences
DescriptionInventory management (in other words, logistics) is an integral part of the work of firms, companies and organizations. We are talking about stocks of raw materials, fuel, tools, components, semi-finished products, finished products for industrial (or agricultural) firms, about stocks of goods to distribution centers, warehouses, shops, workplaces sellers, finally consumers. Stocks spent all the time and supplemented on various rules adopted in the firm. Optimization of these rules, ie, optimal inventory management, gives a big economic effect. The mathematical theory of inventory management, based on the models of movement of flows of goods, is an important area of economic-mathematical research. The classical model of inventory management proposed in 1915 by F. Harris is one of the simplest and most illustrative examples of application of the mathematical apparatus for decision-making in the economic field. This model is commonly referred to as the Wilson model, because this model became known after the publication of R.G. Wilson in 1934. The formula of the optimum batch size (the so-called "the formula of the square root"), obtained in the Wilson model, is widely used on various stages of production and distribution, since this formula is practically useful for decision-making in the inventory management, in particular, for generating significant economic effect. However, contrary to popular belief, by means of this formula it is impossible to calculate the optimal batch size (although it is a necessary step on the path of its finding). In strict economic-mathematical analysis of Wilson model, conducted in the article, it is shown that the formula of square root does not give the optimal batch size. We have given the algorithm for calculating the optimal batch size. It has been found that the formula of the square root gives asymptotically optimal plan. We have studied the stability of the conclusions in the economic-mathematical model and considered an example of the practical application of the classical model of inventory management
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01.00.00 Physical-mathematical sciences
DescriptionThe article is devoted to the solution of the problem which is the fact that on the one hand, the rating of Russian universities is in demand and on the other hand it hasn’t been created yet. The proposed idea of solving the problem consists in the application of domestic licensing of innovative intelligent technologies for these purposes: we have suggested using an automated system-cognitive analysis (ASC-analysis) and its software tools – the intelligent system called "Eidos". These methods are described in detail in this context. It is proposed to consider the possibility of applying these tools on the example of the Guardian University ranking. The article discusses its private criteria (indicators of universities). We specify the sources of data and the methods of their preparation for processing in "Eidos" system. In accordance with ASC-analysis methodology the article describes the installation of "Eidos", the data input into it, and the formalization of the subject area, synthesis and verification of models, their display and use to solve problems of assessment of the Guardian rating for Russian universities and research object modeling. It also discusses the prospects and ways of development of the integrated rating of Russian universities and operation of rating in adaptive mode. We have also specified the limitations of the proposed approach and the prospects of its development
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THE PROBLEMS OF IMPLEMENTATION OF MATHEMATICAL AND TOOL METHODS OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionStatistical methods are based on the developed theory and demonstrated its usefulness in the sectors of the economy. However, the analysis of the situation in the application of statistical methods shows obvious distress, in which accumulated in our country's scientific potential is not used to the full. As practice shows, it is not enough to develop promising modern theory-based effective mathematical and instrumental methods of controlling. For using such methods in mass, it is necessary that they would be implemented. Management of innovations, i.e. innovation management, quite rightly is currently one of the most debated sections of the economy and the organization of production, of the entire economic science in general. However, the implementation of applied statistics and other statistical methods, more generally, mathematical and instrumental methods of controlling, has its own specifics. It is considered in the article. We have highlighted the developmental vulnerabilities - low scientific level of many individuals applying statistical methods, the lack of organizational structure of applied statistics as a field of applied activities and others. We regret to note that the very idea of the need to establish requirements for the methods of data analysis and project formulations such requirements remained outside the attention of those professionals who need them and were addressed. We have no adequate system of guidance for documents on concrete statistical methods performed on modern scientific level. According to the author, the desired future of applied statistics is reorganization according to the model of Metrology. We have analyzed the application of statistical methods as a specialty. The analysis of state standards on statistical methods and the causes of them blunders are given. We have discussed the status of documents for statistical methods for standardization and quality control. We discuss a new system of "Six Sigma" for implementation advanced mathematical and instrumental methods of controlling
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ECONOMETRICS FOR THE CONNROLLERS
01.00.00 Physical-mathematical sciences
DescriptionRequirements for the professional training of сontrollers include, in particular, the requirements for an intelligent tool that controllers must possess. One of such tools is the econometrics. Organization of training, in particular, preparation of curricula, programs, teaching materials and textbooks, involves discussion of the scope and content of the relevant discipline. We have given the description of the econometric tools of controlling, including the courses of "Econometrics-1" and "Econometrics-2", which the Department of the IBM-2 "Economics and organization of production" is on the faculty "Engineering and Business Management" of Bauman Moscow State Technical University. We have discussed the external environment of econometrics and the necessary changes in it. For example, the course of "Probability Theory and Mathematical Statistics" is the basis for the study of econometrics. However, it has to be brought into line with modern requirements. In particular, it is necessary to consider such things as random elements with values in an arbitrary space, empirical and theoretical means in such spaces, to prove the laws of large numbers in general statements. Simultaneously with the specified extension course content is reasonable to exclude from the program methods based on those assumptions are not met in the concrete economic situations. In particular, we have to eliminate the one-sample and two-sample Student's t tests and replace them with the corresponding nonparametric tests. We do not need the "classical" and geometric probability, etc. We have given the importance of the problem of constructing integral indicators in various problems of econometrics; issues of analysis of the situation by means of a system of indicators are discussed in detail
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ECONOMETRIC TOOLS OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionEconometrics is one of the most effective mathematical tools of controlling. The article deals with general problems of application of econometric methods in solving problems of controlling. Econometric methods - is primarily a statistical analysis of concrete economic data, of course, with the help of computers. In our country, they are still relatively little known, even though we have the most powerful scientific school in the foundations of econometrics - the probability theory. The article shows that to decide the problems of controlling is necessary to apply econometric methods. Classification of econometric tools can be carried out on various grounds: on methods, by type of data, in tasks, etc. Mass introduction of software products, including modern econometric analysis tools of concrete economic data can be regarded as one of the most effective ways to accelerate scientific and technological progress. The whole arsenal currently used econometric and statistical techniques (methods) can be divided into three streams: high econometric (statistical) technology; classical econometric (statistical) technology, low (inadequate, obsolete) econometric (statistical) technology. The main problem of modern econometrics is to ensure that the concrete econometric and statistical studies used only the first two types of technology. To get a broader representation of the use of econometric methods in the management of production organization we analyze basic textbook "Organization and planning of engineering production (production management)," prepared by the Department of "Economics and organization of production" of the Bauman Moscow State Technical University. It has more than 20 times using econometric methods and models that testify to the effectiveness of such a tool of manager as econometrics
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GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory