01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionIn the article we present a spatial structure of largescale transport systems. The model of a transport network can be presented in the form of a graph, with a set of the nodes corresponding to elements of a network and a set of edges – to sections of roads the connecting these nodes. As the model of a card of roads, it is offered to use prefractal graphs which naturally reflect structure of communications when reviewing a transport network in different scales (the states, regions, areas). Prefractal graphs allow describing structural dynamics of the studied system in the discrete time. One of the most widespread scenarios of structural dynamics is the growth of structure. The statement of tasks of the organization of transport routes contains requirements criteria to finding of optimal solutions. Often these requirements and criteria are contradicting each other. It leads to appearance of a multicriteria problem definition. The multicriteria problem definition on a class of prefractal graphs is considered. The optimum algorithm of separation of the greatest maximum paths by the given criterion is constructed and estimates by remaining criteria are given. In operation computing complexity of the constructed algorithm of separation of the greatest maximum paths on a prefractal graph is calculated and advantage of operation of algorithm on last before algorithm of separation of the greatest maximum paths on normal graphs is justified. The constructed algorithm on prefractal graphs has polynomial complexity
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LIMIT THEOREMS IN STATISTICAL CONTROL
01.00.00 Physical-mathematical sciences
DescriptionThe article analyzes the development of the theory of statistical control (from the XVIII century to the present). Prof. M.V. Ostrogradskii (1846) clearly describes the practical needs (ie, arising from the quality assurance of large quantities of bags of flour or pieces of cloth), to meet whom he spent his research. At the same time Simpson was among the ideas of probability theory XVIII century. Therefore prof. M.V. Ostrogradskii may be regarded as the founder of the theory of statistical process control (not only in our country but all over the world). Limit theorems of probability theory and mathematical statistics have provided a number of asymptotic results in problems of statistical quality control, offer based on these best practices. However, we must find out how much interest among specialists characteristics are different from limit for finite sample sizes. Such research for the synthesis algorithm control plan on the basis of the limit average output level of defects is made in this article, and for the synthesis algorithm control plan on the basis of the acceptance and the rejection levels of defects - not yet (clarification of the conditions of applicability of this algorithm - unsolved problem of applied mathematics). We have briefly reviewed the development of our researches on the statistical control. Control units can be not only some units of production, but also documents (with internal and external audit), and standard units of air, water and soil in the environmental monitoring. One of the achievements can be regarded as the transfer of statistical control of production for environmental monitoring
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HEEDING OF HETEROGENEITY OF ENVIRONMENT WHEN CALCULATING A MAGNETIC FIELD
01.00.00 Physical-mathematical sciences
DescriptionThe formula for definition of magnitude and direction of secondary sources of a field as surface currents for the registration of heterogeneity of environment is found. We have shown that it is possible to solve non-linear field problems, using the mathematical deduc-tions shown in this article
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METRIC OF ACCELERATING AND ROTATING REFERENCE SYSTEMS IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionMetric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Consequently, there exist a metric in general relativity, in which the Coriolis theorem and classic velocity-addition formula are true. This means that classical mechanics is accurate rather than approximate model in general relativity. A theory of potential in non-inertial reference systems in general relativity is considered. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It is shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
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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
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01.00.00 Physical-mathematical sciences
DescriptionMicro and nanofluidics are the new multidisciplinary sciences. One of the tasks of which is creation and management of flow of fluid in the thin channels size of a few nano- or micrometer which exposed the external electric field, where the walls are the ion exchange membrane. Electroosmosis (electroconvection) plays an important role in these tasks. A large number of articless were devoted to electroosmosis. One of the first, Dukhin S.S., Mishchuk N.A. and Rubinstein I. gave a theoretical explanation of the overlimiting current by electroosmosis. They used two-dimensional Stokes equation to calculate the flow of the electrolyte, and one-dimensional equations of Nernst-Planck and Poisson to calculate the electric power. These researches have multiple limitations because of the computational complexity the mathematical simulation. Thus, there is an actual problem of the asymptotic solution of boundary value problems for the two-dimensional systems of equations of NernstPlanck and Poisson without these restrictions. These researches we derived in simplified models of electroosmosis in galvanic dynamical mode using the decomposition method. We have created a hierarchical system of two-dimensional mathematical models of ion transport of salt and electroosmosis in micro- and nanochannels formed by selective ion-exchange membranes
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01.00.00 Physical-mathematical sciences
DescriptionFollowing the absence of a definite treatment for the human immunodeficiency virus (HIV) or the acquired immune deficiency syndromes (AIDS) since their appearance, many scientific studies with the help of mathematical models have been formulated to the extent possible to prevent and eradicate the disease. In this article we have formulated a mathematical model that explores the dynamics of the impact of the use of condom and therapeutic treatment simultaneously, as a means (tools) against the spread of HIV/AIDS in the heterosexual population. The proposed model uses a nonlinear differential equation system consisting of seven (7) differential equations in seven (7) groups of the population. The model takes into account natural birth rate of the studied population, and the proportion of infected males, which simultaneously uses condom and antiretroviral therapy. The model explores the behavioral change of proportion of infected individuals in the population following the application of control measures (condom use and antiretroviral therapy). It is proved that the effectiveness of preventive measures greatly depends on a number of parameters described. In addition, the results of numerical experiments showed that in the absence of both preventive measures, the entire population is contaminated with the infection. The interaction of the model parameters show that the population with high levels of condom use in the presence of significant adherence to antiretroviral therapy as prophylaxis significantly reduces the level of HIV/AIDS. Thus, prevention of infection is significantly improved with the increasing number of the infected population using condoms and antiretroviral therapy simultaneously
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01.00.00 Physical-mathematical sciences
DescriptionSince there are many artificial intelligence systems, there is a need of comparable quality assessment of their mathematical models. For this purpose, these systems can be tested on the same database source data, for which it is very convenient to use a public database of the UCI repository. This work is aimed at the study and development of model practices of the database of the UCI repository to assess the quality of mathematical models of artificial intelligence systems
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A CLASSICAL PROBLEM FOR LOADED HYPERBOLIC-PARABOLIC EQUATION OF SECOND ORDER
01.00.00 Physical-mathematical sciences
DescriptionThe investigated and correct boundary value problem for mixed hyperbolic-parabolic equation of second order in a bounded domain is posed and studied in this work. Boundary conditions are of a classical nature. On line of type changes, which is also the line of the parabolic degeneracy for hyperbolic equations considered in the lower half-plane, a continuous bonding condition for the function itself and the breaking condition for the trace of the derivative is given. The main result is the proof of its unique solvability in the required class of functions. In particular, based on the properties of the operators of fractional integro-differentiation and in view of the ratio of the first boundary value problem for the heat equation, the question of the solvability of the original problem was equivalently reduced to the problem of solvability of the corresponding integral equation of the Voltaire second kind. In the hyperbolic part of the region, the question of solvability of the problem has also been reduced to the problem of solvability of the integral equation Voltaire second kind. The properties of the hypergeometric function of Gauss, as well as classical methods of integral equations were used. Thus it is proved the uniqueness and the existence of classical solution to the initial problem
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01.00.00 Physical-mathematical sciences
DescriptionIn the article the application of systemic-cognitive analysis, its mathematical model - the system theory of the information and its program toolkit - "Eidos" system for synthesis of the generalized images of classes, their abstraction, classification of the generalized images (clusters and constructs) comparisons of concrete images with the generalized images (identification) are examined. We suggest a new approach to the digitization of images, based on the use of the polar coordinate system, the center of gravity of the image and its contour. Before digitizing images we can use their changes to standardize the position of the picture-frames, their size and rotation. Therefore, if you specify this option, the results of digitization and image ASC-analysis can be invariant (independent) to their position, size and rotation. This means that in the model on the basis of a number of specific examples we will create one image of each class of images, independent of their specific implementations, i.e., the "Eidos" of these images (in the sense of Plato) - a prototype or archetype (in the Jungian sense) images. But the "Eidos" system provides not only the formation of prototype images, which quantitatively reflects the amount of information in the image elements of the prototype, but the removal of all irrelevant to identification (abstraction), and the comparison of specific images with generic (identification) and the generalized images of images together (classification). The article provides a detailed numerical example of ASC- analysis of images