01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionIn the article, the algorithm – a recurrent formula for calculation of determinants of prefractal graphs with the full primers, keeping old edges contiguity in a trajectory was received
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01.00.00 Physical-mathematical sciences
DescriptionClassical combinatorial formula to calculate the number of combinations from n on m: C(n,m)=n!/(m!(nm)!) involves the intermediate calculation of factorials, which is often impossible when n>170, due to limitations in the capacity of numbers that are used in programming languages and created through these systems. However, in some cases it is necessary to calculate the number of combinations for n and m much larger than this limit, such as when a value greater than 10000. In such cases, there is a definite problem, which manifests itself, for example in the fact that many on-line services meant to calculate the number of combinations with these parameters do not work properly. In this article, we present its solution in the form of an algorithm and software implementation. The essence of the approach is to first decompose the factorials into prime factors and reduce them, and then to produce multiplication. This approach differs from those cited in the Internet
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01.00.00 Physical-mathematical sciences
DescriptionThe article is dedicated to a numerical investigation of a plane problem of the oscillation amplitude of a buried source, depending on the frequency and motion speed in various isotropic media. Three types of the medium are considered: a two-layer package with a rigidly fixed base, a two-layer package with a mechanically free base, a half-space. The source, in the form of a stress jump simulating a rigid inclusion of small dimensions, moves in the interface plane at a constant speed. Homogeneous boundary value problems are considered in a moving coordinate system associated with a source. The solution method is based on the usage of integral Fourier transforms, the method of direct contour integration and algorithms for constructing symbols of Green's matrices. The method of direct contour integration significantly simplifies calculations in comparison with the traditional approaches to the calculation of Fourier integrals. We have presented calculations of nine amplitude-frequency and amplitude-velocity characteristics for different combinations of medium and source types, that give an exhaustive qualitative and quantitative description of the solutions for boundary value problems in a wide range of velocities and frequencies. Comparative analysis of calculations showed a primary influence of the type of an elastic medium on the investigated characteristics, as well as the large influence of the source type. Which, in turn, revealed some substantial connections between the boundary value problems with a moving source and the corresponding problems with a stationary source
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ANALYSIS OF METHODS OF GENERATION OF TIME SERIES WITH LONG-TERM CORRELATION STRUCTURE
01.00.00 Physical-mathematical sciences
DescriptionThis article gives a comparative analysis of six modeling techniques of fractal differential noise, including: direct definition method, the method of Hosking, the method of Davis and Hart's, the circulant embedding method, Paxson method and method of spectral simulation. Furthermore, the algorithms are given for the analysis and the method of estimation of Hurst`s parameter is selected, this method is the main criterion of quality when comparing the above mentioned methods of fractal differential noise
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ANALYSIS OF THE PROCESSES CAUSED THE MAGNETIC FIELD INFLUENCE ON A STRUCTURE AND PROPERTIES OF WATER
01.00.00 Physical-mathematical sciences
DescriptionThe scientific publications review about a magnetic field influence on cluster sizes and their concentration was carried out. These structural changes are attended by the water system physicochemical properties changes. For example, the surface tension coefficient changes. It is shown, that the conductivity and the dielectric constant of water change in a weak magnetic field. It is provided, that characteristics of water activated by a magnetic field can save in a significant time
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THE ANALISIS OF SAINT-VENANT EQUATION SYSYEM ANALYTICAL AND NUMERICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionDiffusion-convection equation that has been received from Saint-Venant differential equation system describing nonstationary fluid motion in a river canal is investigated. Analytical method is considered for the solution of equation with the fixed factors and finite-difference method is considered for the solution of equation system with the float factors. The results of test calculations executed for a reaches of the river Kuban are presented
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WATER STRUCTURE AND DILUTE WATER SYSTEM PROPERTIES ANALYSIS
01.00.00 Physical-mathematical sciences
DescriptionThe cluster structure in pure water (distilled) and water salt solution was considered. The experimental methods of the structural units’ registration in water were analyzed. It is shown that the clusters influence on water properties is insignificant by salt concentration more than 10-5 mole
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ANALYSIS OF APPLICATION CONDITIONS OF KOLMOGOROV’ PROBABILITY THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe article analyses well-known approaches to the explanations of Kolmogorov's conditions for probabilities studied in applications. It discusses better-founded explanations, offers and looks into new approaches to the explanations of connectedness of the conditions
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01.00.00 Physical-mathematical sciences
DescriptionIn the article an effective system of an estimation of a financial and economic status of the factories of a building sector of Krasnodar region (Armavir district), based on use of methods of the multidimensional statistical analysis is introduced. The programmatic complex "FAP-stroi", including MS Excel plug-in, macros of «Statistica 6» and exterior processing of «1С: Enterprise 8» is built
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01.00.00 Physical-mathematical sciences
DescriptionIn various applications it is necessary to analyze some expert orderings, ie clustered rankings of examination objects. These areas include technical studies, ecology, management, economics, sociology, forecasting, etc. The objects may make samples of the products, technologies, mathematical models, projects, job applicants and others. We obtain clustered rankings which can be both with the help of experts and objective way, for example, by comparing the mathematical models with experimental data using a particular quality criterion. The method described in this article was developed in connection with the problems of chemical safety and environmental security of the biosphere. We propose a new method for constructing a clustered ranking which can be average (in the sense, discussed in this work) for all clustered rankings under our consideration. Then the contradictions between the individual initial rankings are contained within clusters average (coordinated) ranking. As a result, ordered clusters reflects the general opinion of the experts, more precisely, the total that is contained simultaneously in all the original rankings. Newly built clustered ranking is often called the matching (coordinated) ranking with respect to the original clustered rankings. The clusters are enclosed objects about which some of the initial rankings are contradictory. For these objects is necessary to conduct the new studies. These studies can be formal mathematics (calculation of the Kemeny median, orderings by means of the averages and medians of ranks, etc.) or these studies require involvement of new information from the relevant application area, it may be necessary conduct additional scientific research. In this article we introduce the necessary concepts and we formulate the new algorithm of construct the coordinated ranking for some cluster rankings in general terms, and its properties are discussed