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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01.00.00 Physical-mathematical sciences
DescriptionThe article contains results of information research of acute myeloid leukemia (AML) as complicated multiple systems. The purpose of the research is creation an information presentation of AML and algorithms for determining the temporal characteristics of the disease. For describing the development of the disease we used the system of equations describing the growth of cells in populations of acute leukemia and considering decrease of protective forces of organism. A distinctive feature of this presentation is a more detailed description of the disease. For describing the processes of the division we used logistic equation. From the moment of an initiation of treatment the new parameters have been added into the system of equations, they are in charge of action of the applied preparations and responsive mutations the leukemic cells. On the basis of the submission of the information, we presented algorithms for calculating the temporal characteristics of the disease, namely, the development time of an irreversible condition in which the body is not able to destroy the leukemic clone of yourself, and the duration of remission. Also, as a result of the research we have made an evaluation of opportunities of the obtained algorithms. The article showed the wide range of possible solutions of the algorithm of determination the duration of remission
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DEVELOPMENT OF MATHEMATICAL MODEL OF PROCESS OF HEATING OF AIR FOR DRYING GRAIN
01.00.00 Physical-mathematical sciences
DescriptionIn the article, the analytical way of working out of mathematical model of process of heating of air for grain drying is shown. It is considered, that the temperature of a wall influences on dynamics of process of heating. Dynamic characteristics of the top internal device are considered. With use of package Mathcad schedules of transitive functions on operating and revolting influence are received. Results of modeling are presented
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DEVELOPMENT OF A METHOD FOR DIVIDING CARBON ISOTOPES WITH MAGNETIC AND NON-MAGNETIC NUCLEI
01.00.00 Physical-mathematical sciences
DescriptionThe dynamics of the state of spin of the radical oxygen-carbon pair are observed. By way of mathematical modeling, optimal conditions for conducting experiments to obtain the maximum meaningful coefficient of division of carbon isotopes was established
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THE DEVELOPMENT OF COUNTRIES' CREDIT RATING ASSESSMENT SYSTEM
01.00.00 Physical-mathematical sciences
DescriptionThis work presents a new approach to the countries’ credit rating definition, based on the advanced mathematical models, such as neural network model, multiple regression, cluster analysis and discriminant analysis. A range of the analyses such as discriminant, cluster, multiple regression models and a neural network were performed on the following economic figures: GDP per capita, GDP value, annual growth rate of GDP, FDI - foreign investment, rate of unemployment, consumer price inflation index, the size of government debt in percentage of GDP. The results, obtained for each model were combined in the countries’ credit rating estimation system called "7M"
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RECOGNIZING OF PREFRACTAL GRAPH ARISING FROM OF TWO FULL ZATRAVKAS
01.00.00 Physical-mathematical sciences
DescriptionThe private task of prefractal graph recognizing, aris-ing from pair of full zatravkas by alternations, was ex-amined. The offered algorithm of recognizing decide this task during the polynominal time.
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RECOGNITION OF PRE-FRACTAL COUNT, DESCENDANT COMPLETE DICOTYLEDONOUS PRIMER
01.00.00 Physical-mathematical sciences
DescriptionIn the article the algorithms of recognition of structures of complex network systems and objects are offered. As a model of structures we have considered a pre-fractal graph. Necessary and sufficient signs of pre-fractal structures are stated. The theorems proving work of offered algorithms are proved
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DISTRIBUTION OF PRIME NUMBERS. ALGORITHM OF TWINS NUMBERS AND THEIR INFINITE
01.00.00 Physical-mathematical sciences
DescriptionIn the article on the basis of numbers of the specific form, where the parameter elements, which form a semigroup under multiplication we have presented a method for determination and distribution of composite numbers and the prime numbers, and accurate calculation of the values of pi in the interval from 1 to N. We present a new algorithm for the distribution of primes. We have reached the law of distribution parameters of composite numbers and prime numbers (Distribution of the parameters of composite numbers and prime numbers (DCPN)). We have given a formula for of finding prime numbers by serial number in the set DCPN. Due to the law of distribution of parameters of composite numbers and prime numbers it becomes apparent disintegration set of prime numbers. We have also introduced a proposal that each element of the plurality of composite numbers can be represented by one of the specific types of works. The proof of Proposition 2 allows us to give one of the most effective ways of recognizing primes. The description of the algorithm for numbers of twins and proof of their infinity. All algorithms presented in the article is a listing of programs in Software Module ACCESS
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DISTRIBUTIONS OF REAL STATISTICAL DATA ARE NOT NORMAL
01.00.00 Physical-mathematical sciences
DescriptionIn the training courses on the theory of probability and mathematical statistics there are various parametric families of distributions of numerical random variables considered. Namely, we have been studying the families of normal distributions, log-normal distributions, exponential distributions, gamma distributions, Weibull-Gnedenko distributions, etc. All of them depend on one, two or three parameters. Therefore, for a complete description of the distribution it is sufficient to know or estimate one, two or three numbers. Parametric theory of mathematical statistics is widely developed, where it is assumed that the distribution of observations belong to one or another parametric family of distributions. This tradition comes from Karl Pearson, who in the early twentieth century proposed the use of four parametric family of distributions. The above families of distributions - are the subsets of a four-parametric family of Pearson. Unfortunately, parametric families exist only in the minds of the authors of textbooks on probability theory and mathematical statistics. In real life, they are not. Therefore, modern applied statistics and econometrics mainly use non-parametric methods, in which the distribution of observations can have arbitrary form. First, on an example of a normal distribution, we are discussing the impossibility of practical use of parametric families of distributions to describe specific statistical data. We give the results of research of metrologists and estimation of convergence in limit theorems. Then we discuss how the parametric methods can use for reject outlying observations. It is very unstable the significance levels for a fixed rejection rule and the parameter of the rejection rules for a fixed level of significance. Consequently, the rejection of the classic rules of mathematical statistics is not sciencebased
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PROPAGATION AND BRANCHING OF STRAIMERS IN CONDUCTING ENVIRONMENT
01.00.00 Physical-mathematical sciences
DescriptionIn this work, we develop a model describing the propagation and branching of a streamer in a conducting medium in external electric field. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, the streamer model is formulated in the form of nonlinear equations of parabolic type. In the framework of the proposed model, the problem of the propagation of a streamer in the form of a traveling wave is considered, which leads to the emergence of SaffmanTaylor streamers. For streamers of this type, the branching problem is formulated, which has a unique solution. The dependence of the branch point on the parameters of the problem-the speed of the streamer, the diffusion coefficient of the electrons and the strength of the external electric field, is found. The branching mechanism of the streamer head by dividing it into two parts has been well studied and several alternative models have been formulated for its description. The novelty of the problem in question is that the streamer splits into two three-dimensional channels that are symmetric with respect to the given plane. Numerical experiments also revealed the mechanism of branching of the streamer in the cathode region, connected with the separation of the main channel into several lateral branches. It is noted, that in nature both branching mechanisms are realized, whereas in theory the instability of the surface of the streamer head is investigated