01.00.00 Physical-mathematical sciences
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PROBABILISTIC MODEL OF THE PROCESS OF REDUCTION OF THE PRICE FOR PLANNED ACTIONS
01.00.00 Physical-mathematical sciences
DescriptionThe soil fertility increase issues are very relevant now. Intensive development of agriculture cannot be made effectively without complex actions for farmlands protection from different types of degradations. On the one hand, it is necessary to ensure the maximum harvest of crops, and to preserve and increase the fertility of the soil and prevent negative anthropogenic impact on the environment on the other. For an extended reproduction of soil fertility, a system of measures is necessary for introduction of mineral and organic fertilizers into the soil, agrotechnical and reclamation methods, stimulation of humus formation processes, and so on. Therefore, methods are important that allow us to estimate the planned measures in advance to improve soil fertility and to eliminate environmental damage. In the article, the estimated parameters are treated by random variables. This allows us to consider the uncertainty in terms of probability distributions. It is offered a probabilistic model of the process of reducing the price of the proposed activity. Mathematical expectation, variance, distribution density of the considered random variable probabilities as the main characteristics of the object state price are calculated. The model can be used to address issues of rational use of land, scientifically based land management organization, when drafting land reclamation project
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PROBABILISTIC-STATISTICAL METHODS IN KOLMOGOROV’S RESEARCHES
01.00.00 Physical-mathematical sciences
DescriptionFrom a modern point of view we have discussed Kolmogorov’s researches in the axiomatic approach to probability theory, the goodness-of-fit test of the empirical distribution with theoretical, properties of the median estimates as a distribution center, the effect of "swelling" of the correlation coefficient, the theory of averages, the statistical theory of crystallization of metals, the least squares method, the properties of sums of a random number of random variables, statistical control, unbiased estimates, axiomatic conclusion of logarithmic normal distribution in crushing, the methods of detecting differences in the weather-type experiments
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PROBABILISTIC-STATISTICAL METHODS IN GNEDENKO’S RESEARCHES
01.00.00 Physical-mathematical sciences
DescriptionWe analyze the probabilistic-statistical methods in the researches of Boris Vladimirovich Gnedenko – the academician of Ukrainian Academy of Science, which are very important for the XXI century. We have also discussed the limit theorems of probability theory, mathematical statistics, reliability theory, statistical methods of quality control and queuing theory. We give some information about the main stages of scientific career of B.V. Gnedenko, his views on the history of mathematics and teaching
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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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PROBABILITY MODELS FOR OBTAINING NON-NUMERICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionThe statistics of objects of non-numerical nature (statistics of non-numerical objects, non-numerical data statistics, non-numeric statistics) is the area of mathematical statistics, devoted to the analysis methods of non-numeric data. Basis of applying the results of mathematical statistics are probabilistic-statistical models of real phenomena and processes, the most important (and often only) which are models for obtaining data. The simplest example of a model for obtaining data is the model of the sample as a set of independent identically distributed random variables. In this article we have considered the basic probabilistic models for obtaining non-numeric data. Namely, the models of dichotomous data, results of paired comparisons, binary relations, ranks, the objects of general nature. We have discussed the various options of probabilistic models and their practical use. For example, the basic probabilistic model of dichotomous data - Bernoulli vector (Lucian) i.e. final sequence of independent Bernoulli trials, for which the probabilities of success may be different. The mathematical tools of solutions of various statistical problems associated with the Bernoulli vectors are useful for the analysis of random tolerances; random sets with independent elements; in processing the results of independent pairwise comparisons; statistical methods for analyzing the accuracy and stability of technological processes; in the analysis and synthesis of statistical quality control plans (for dichotomous characteristics); the processing of marketing and sociological questionnaires (with closed questions like "yes" - "no"); the processing of socio-psychological and medical data, in particular, the responses to psychological tests such as MMPI (used in particular in the problems of human resource management), and analysis of topographic maps (used for the analysis and prediction of the affected areas for technological disasters, distributing corrosion, propagation environmentally harmful pollutants, various diseases (including myocardial infarction), in other situations), etc.
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INTERCONNECTION LIMIT THEOREMS AND MONTE-CARLO METHOD
01.00.00 Physical-mathematical sciences
DescriptionThe purpose of mathematical statistics is development of methods for the data analysis intended to solve applied problems. Over time, approaches to the development of data analysis methods have changed. A hundred years ago, it was assumed, that the distributions of the data have a certain type, for example, they are normal distributions, and on that assumption they developed a statistical theory. The next stage, in the first place in theoretical studies there are limit theorems. By "small sample" we mean a sample, which can not be applied to conclusions based on the limit theorems. In each statistical problem there is a need to divide the final sample sizes into two classes - those for which you can apply the limit theorems, and those for which you can not do it because of the risk of incorrect conclusions. To solve this problem we often used the Monte Carlo method. More complex problems arise when studying the effect on the properties of statistical procedures for data analysis of various deviations from the original assumptions. To study such impact, we often used the Monte Carlo method as well. The basic (and not solved in a general way) problem of the study of the stability of the findings in the presence of deviations from the parametric families of distributions is the problem of choosing some distributions for using in modeling. We consider some examples of application of the Monte Carlo method, relating to the activities of our research team. We have also formulated basic unsolved problems
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VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physical-mathematical sciences
DescriptionIn this work, we consider two types of vortex currents-cyclones and anticyclones in the Northern and Southern Hemispheres. Numerical modeling of turbulent flows of these types uses the model of the planetary boundary layer developed by the author. The purpose of the study is to test hypotheses about the influence of the Coriolis force on the formation of cyclones and anticyclones in the northern and southern latitudes. The first hypothesis on the direction of circulation in cyclones was verified in the case of axisymmetric radially converging and vertically rising turbulent flows with a natural Coriolis parameter and viscosity. From the obtained data of numerical experiments, it follows that the current in the northern latitudes circulates in a counter clockwise direction, and in the south - in a clockwise direction, in full accordance with the observational data. Thus, we have shown that a cyclonic flow is formed in a turbulent radially converging flow under the influence of the Coriolis force. The second hypothesis on the formation of anticyclones was verified in the case of radially divergent and vertically descending turbulent flows. Because of numerical experiments, it was established that in this case, the current in the northern latitudes circulates clockwise, and in the south - in a counter clockwise direction, which corresponds to observations for anticyclones. To test the effect of the cyclone (anticyclone) center velocity on circulation, a nonstationary 3D model of turbulent flow was developed. Within the framework of this model, flows in cyclones and anticyclones moving at a constant speed, as well as in shear flow, are studied. Some types of loop protuberances on the Sun are explained by the presence of a vortex turbulent flow starting in the bowels of the Sun and encompassing the chromosphere
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01.00.00 Physical-mathematical sciences
DescriptionA model is developed for stress-dependent surface generation and recombination of point defects in silicon. Using the model, such phenomena as stacking fault growth and stress-mediated dopant diffusion in silicon are simulated
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01.00.00 Physical-mathematical sciences
DescriptionThe influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the space-charge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work
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01.00.00 Physical-mathematical sciences
DescriptionThis 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.