01.00.00 Physical-mathematical sciences
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CENTERS PLACEMENT ON MANY-WEIGHTED PREFRACTAL GRAPHS
01.00.00 Physical-mathematical sciences
DescriptionMulticriterial formulation for centers placement problem on many-weighted prefractal graph is proposed. Estimation of the radial criterion of prefractal graph generated by seed-star is shown. Polynomial algorithm centers placement on prefractal graph with preserving contiguity old edges is suggested. Estimation of computational complexity of the algorithm and the example of the work algorithm are considered
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FUNDAMENTAL THEOREM OF ARITHMETIC AND SOME OF ITS ASPECTS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we present the fundamental theorem of arithmetic and its role. We consider various rings for its performance
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a mathematical model of the effect on ion transport electro convection salt in non-smooth camera channel desalting electro dialysis apparatus in the presence of forced convection. The basic rules of process of electro convection are revealed
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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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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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01.00.00 Physical-mathematical sciences
DescriptionIn the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form
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CALCULATION AND ANALYSIS OF TIME BEHAVIOR OF ELECTROCONVECTION IN MEMBRANE SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe aim of this work is to carry out numerical analysis of time behavior of electroconvection in membrane systems, such as a desalting channel of electrodialysis apparatus. The current-voltage curve and the solution flaw were analyzed theoretically using mathematical models of ions transfer taking into account electroconvection in smooth desalting channel consisting of ideally selective anion- and cation-exchange membranes. The Hurst numbers for different parts of the current-voltage curve were calculated in order to determine whether the parts were persistent. The Fourier-analysis of the oscillating term of the current-voltage curve was carried out for the first time so as to determine predominant frequencies in the signal. Frequencies of passing of complexes of vortexes through the cross-section of the desalting channel were calculated. Frequencies of oscillations of concentration profiles were determined. It was found that the frequencies of oscillations of the concentration profiles coincide with the frequencies of passing of complexes of vortexes through the cross-section of the desalting channel. The oscillations of the current-voltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the current-voltage curve corresponds to the frequency of oscillations of the concentration profiles. The oscillations of the concentration profiles, produced by the passing of complexes of vortexes, cause oscillations of conductivity and, consequently, cause oscillations of resistance and of the current density. It was shown that the main frequency of the signal corresponds to the frequency of passing of complexes of vortexes through the cross-section of the desalting channel
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GRAVITY FIELD IN THE VICINITY OF STARS AND GEOMETRIC TURBULENCE
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the solutions of Einstein's equations for empty space, describing the gravitational field near the Sunlike star have been investigated. We have accounted the own field of the star, the motion of the star around the galactic center, the motion of the galaxy relative to the center of the local supercluster and the expansion of the Universe. The resulting gravitational field near the star has a complex structure, which leads to large-scale geometric turbulence linking large and small scales in this problem
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Warm, warmth and internal energy of a body
01.00.00 Physical-mathematical sciences
DescriptionThe article discusses the question of the concepts of heat and internal energy of a body. The analysis of these concepts in the historical aspect and the views of the author, based on the new photon theory of atomic structure were presented in this study. The analysis of the historical aspect of this question tells that the concepts of heat and internal energy of the body for a long time were associated with the concept of caloric, which can flow in the substance. The next step was the identification of the concept of heat with energy linked with the movement and work. In accordance with this, Clausius proved the equivalence of heat and work as the first principle of the theory of heat and introduced the concept of internal energy, which can be increased in two ways - making work on body, and summing heat to it. Thus, energy was the main uniting factor of work and heat. Then, the kinetic theory of heat, as the energy of motion of molecules, was developed by Maxwell and caloric model turned out to be a hindrance in the development of the theory of heat. In fact, the internal energy of the body is determined photons, rotating around charged particles in atoms in their orbitals. The series of photons are combined into a single photon orbital direction of rotation of the photons, which are different from each other. Thus, the body has an internal energy or internal heat. It is due to the energy of photons, orbiting electrons in the outer shell of each atom, as well as around the charged particles - electrons and protons in the nucleus of an atom. This internal energy may be increased by mechanical action on the body, leading to an increase in resulting oscillation frequency of photons around charged particles of atoms and the internal heat contained in the body can flow of the body with a higher concentration of heat to the body with a lower concentration of heat