01.00.00 Physical-mathematical sciences
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THE ASSESSMENT OF COMPLEXITY OF COMBINATORY METHOD OF NUMBERS’ FACTORIZATION
01.00.00 Physical-mathematical sciences
DescriptionThis article is devoted to the assessment of the calculating complexity of combinatory method of numbers’ factorization. The content of combinatory method is explained in the article of the same name published in the journal issued in November 2016. The author supposes that the reader has learnt its content and knows the basic notions of theory of calculating complexity of the algorithms. The following results of the learning of the given task are expounded in this article. The algorithm of combinatory method permits to accomplish the parallel calculations. Graph of any order is the separate structure, because its initial data are determined independently from the other graphs. So, the calculating complexity of the task about the factorization of numbers in the predetermined interval of the positive integers is defined by the complexity of the most laborious graph. The analysis of the graphs’ structure allows to state that it’s the graph of the third order. In any graph both branches of the first level give the separate structures- partitive graphs of the first level with independent input data. So, the calculating complexity of the graph complete is determined by the maximal complexity of the graph of the first level. The givenat random interval of positive integers stays without changes, if we observe the sequence of the adjacent intervals. In the results it’s stated that the assessment of complexity of combinatory method as well other present methods of numbers’factorization is exponential. In this aspect the combinatory method doesn’t compete with other actual methods. However, evaluating the scientific significance of the algorithm, the decisive factor is not the calculating complexity, but its originality, which permits to explain (if not to discover) any properties of the positive integers. In the conclusion of the article the author describes the advantages of combinatory method, permitting to appreciate the degree of its scientific novelty
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01.00.00 Physical-mathematical sciences
DescriptionIn this article we propose a method that uses the apparatus of the theory of fuzzy sets, together with the five-factor model of Altman in assessing the creditworthiness of an enterprise. Altman's model works in two ways: It applies the root mean square (RMS) integral approximation for the exact calculation of quantitative assessment of creditworthiness (probability of bankruptcy), and using the device of fuzzy sets for ordered sets by the degree of confidence in the resulting probability. In this paper we conducted simulation procedure for the credit assessment and showed the capabilities of the model. The model input parameters , forms system inputs (input variables), allowing you to get the value of the parameter z of Altman. With the help of Altman's model, approximating function L6, the decision function I(p) and the algorithm for calculating preference we obtain the number of the set i to which belongs a number of ordered sets as fuzzy logic . On the selected simulation parameters, stable statistics can be obtained. Altman's model with the use of computational function allows real values of the input parameters of the enterprise replaced by random values of the simulation model. This technique allows, as shown by the results of computational experiments, the creditor to obtain additional information on the creditworthiness of the investigated enterprise and make a more informed conclusion about its financial condition, which speeds up the decision on the possibility of issuing the required credit. The development of method of estimating fuzzy logic can be applied to other models of assessing the creditworthiness of a company: Davydov's model, Zaitseva's, Saifullina's, Kadykova's and others with appropriate modification
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01.00.00 Physical-mathematical sciences
DescriptionIn this article we have proposed a method using the apparatus of fuzzy sets theory in conjunction with the five-factor model of Altman to assess the creditworthiness of the investigated companies. The Altman model was improved in two ways: by using RMS integral approximation for the exact calculation of the quantitative credit assessment (probability of bankruptcy) and the application of the apparatus of fuzzy sets for ordered sets by the degree of confidence resulting probability
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ESTIMATES OF PROBABILITY DENSITY FUNCTION IN SPACES OF ARBITRARY NATURE
01.00.00 Physical-mathematical sciences
DescriptionLinear estimators of the probability of density in the spaces of an arbitrary nature and particular cases – nuclear, histogram, the Fix-Hodges type estimates are introduced. Consistency and asymptotic normality of linear estimates are proved under natural conditions. It is shown that the probability of the area can be found by linear density estimates. A special case of a finite set are discussed, it was found that sample mode converges to the theoretical one
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PARAMETRIC TRINOMIALS WITH ALTERNATING GALOIS GROUPS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we construct polynomials of third, fourth and fifth degrees with Galois groups as and respectively. In addition, we give examples of polynomials different degrees with Galois groups isomorphic transitive subgroup of group , but calculations with help Maple show that Galois groups of this polynomials is . Also Polynomials with as Galois groups are shown
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INTENSITY PARAMETERS OF NEODYMIUM IONS IN STRONTIUM TUNGSTATE CRYSTAL
01.00.00 Physical-mathematical sciences
DescriptionIntensity parameters of neodymium ions in doped SrWO4 monocrystals, grown by modified Czochralski method, are calculated. Changes in the values of these parameters when replacing the tungsten atoms W6+ atoms of molybdenum Мo6+ in the matrices SrMeO4 with the scheelite structure due to less screening of the nucleus Мo6+ compared with W6+ are shown
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INTENSITY PARAMETERS OF ERBIUM IONS IN LEAD TUNGSTATE CRYSTALS
01.00.00 Physical-mathematical sciences
DescriptionLead tungstate monocrystals doped by erbium were investigated in this article. Judd-Ofelt intensity parameters, radioactive lifetimes and emission cross-sections were calculated
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01.00.00 Physical-mathematical sciences
DescriptionThis article is a continuation of the works [1,2], which were devoted to the study of hydrodynamics and transport of salt ions in the experimental electrochemical cell with a rotating disk with a cation exchange membrane of exact current modes, when the condition of local electroneutrality. This article presents a mathematical model of transport of salt ions in a cell with a rotating disk with a cation exchange membrane exorbitant current regimes, taking into account electroconvection. Under these conditions, fluid dynamics depends on the ion transport process salt and described by the system of Navier-Stokes equations in cylindrical coordinate system with the electric forces
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01.00.00 Physical-mathematical sciences
DescriptionThis article describes a mathematical model of transport of salt ions in a cell with a rotating disk cation exchange membrane at transcendent current regimes, taking into account electroconvection. Based on this model, we had a theoretically study of the process of transfer of salt ions and the dependence of the thickness of the diffusion layer from the fall of potential. This article is a continuation of [8] and [9], it conducted a numerical analysis of boundary value problem for a system of equations Nernst-Planck-Poisson and Navier-Stokes equations, modeling the transport of salt ions in a cylindrical cell with a rotating disc cation exchange membrane based on electroconvection. It is shown there is an electroconvection vortex in the center of the membrane disc. The solution flows around this vortex and forms a stagnation zone in front of it. With the increase in the size of the fall of potential, the electroconvective vortex decreases and at some value, the electroconvective vortex disappears. The study was conducted in the 1000 s when the angular velocity of 30 turns in a minute and change of the potential difference of 0.2V to 1.4V with a step 0.1. As a result, in this study it is shown that the thickness of the diffusion layer is practically linearly dependent on the fall of potential. The linear dependence of the thickness of diffusion layer from the fall of potential, in the first approximation, is disturbed by a slight deflection curve, the causes of which are needed to be found by means of extra experiments
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01.00.00 Physical-mathematical sciences
DescriptionIn this article, we have proposed a forecast of labor resources by sectors of the labor market of the Russian Federation until 2018 inclusive. The probabilistic parameters of the dynamics of labor resources were calculated using the considered model (articles [1-4]). Further, these probabilities were used to estimate and parameterize the trends of employed and unemployed (with a known last place of employment) specialists in each industry. For each sector of the Russian economy, the type of trend that best approximates the long-term (more than three years) dynamics of labor resources in this sector was selected. It is shown that the forecast error for 1 year is less than 1% using the selected trend models. Further, identified long-term trends were used in forecasting. Based on the results of the forecast of the number of people employed in the sectors of the Russian economy, the sectors were divided into two groups. The first group contains sectors with a significant change in the number of employed in. The second group contains sectors, changes in employed in which were insignificant. At the end of the article, an example of an analysis of two sectors from the first group is given. Causes of changes in the dynamics of labor resources in the researched sectors of the economy were identified. Ones of the main sectors of the economy were considered in this example: "Manufacturing industries" and "Financial activities, real estate transactions, leasing and provision of services"