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Lebedev Konstantin Andreyevich
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Articles count: 13
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Description
In the article the mathematical model of the space charge region in the bipolar membrane is considered. The structure of the space charge region under passing of electric current, and without electric current is discussed. The results of experimental studies of water dissociation in the bipolar membrane in the presence of chromium(III) are discussed
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FORECASTING THE WATER LEVEL IN A RIVER WITH THE ABRUPT FALLING WATER BASED ON KALMAN-BUSY FILTRATION
01.00.00 Physical-mathematical sciences
DescriptionThe technique of short-term forecasting of the water level in a vein of a mountain type river, based on a method of Kalman-Busy filtration in the make assumption of natural simplifications, characterized for natural objects is offered
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
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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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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 propose a method of determining the share or the significance (weight) of indicators of Beaver and risks R in the portfolio formed by these parameters allowing us to minimize the mean square error evaluating the effectiveness of the portfolio (risk) in the assessment of the financial condition of the companies investigated. The proposed method is the minimization of a quadratic form in variables satisfying lengthy conditions, i.e. the quadratic programming. This technique is implemented using four methods of optimization: analytical method, using built-in function minimization block given, the penalty function method and the gradient method. More so, this technique allows, as shown by the results of the computational experiments, the expert without routine statistical data processing to obtain additional information on the credit worthiness of the investigated enterprise and make a more informed conclusion about its financial condition, which speeds up the decision on granting a loan required by a company. Based on the techniques proposed in this paper, other techniques of assessing the creditworthiness of businesses may be constructed using the results of optimization theory based on well-established applied research methods: Method of evaluating the creditworthiness of Russia, Credit scoring method, the American method, method of Altman and others
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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
DescriptionIn this article we consider a mathematical model of effect of non-compliance with the prevention of HIV/AIDS among a heterogeneous population based on known model by Kimbir et al (2006). The effectiveness of a condom use and implications of non-compliance with a population of preventive measures (condoms) are the aim of this research work. In this work, with definite coefficients, nonlinear model is used, which consists of system of six differential equations for different population groups (six groups of the population) to obtain the model equations. Compared with the existing model by Kimbir, the proposed model to a large extent, takes into account the birth rate of the studied population. Numerical simulation of the model equations shows that reducing the rate of transmission of HIV/AIDS can be effectively achieved within a certain time, and only where relatively high condom efficacy and high compliance by susceptible and infected are observed. From the obtained results, we can see that the control of HIV/AIDS in the heterosexual population depends on the net compliance and effectiveness of the recommended prevention (condom use). As a recommendation, the model focuses on intensive training and ongoing campaigns to raise the awareness of the population by governmental and non-governmental agencies on the effective use of the condom
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01.00.00 Physical-mathematical sciences
DescriptionIn the article we build a mathematical model of elec-tro-diffusion of ions in the diffusion layer of a mem-brane system complicated by the occurrence of the previous slow homogeneous chemical reaction with the condition of electrical neutrality of the solution. We have set a two-point boundary value problem and developed a method to solve it; we have given an algorithm and a numerical method for solving it in Comsol 3.5 environment. The formula for limiting kinetic current was derived. Some of the model’s capabilities to describe the properties of the system are given
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Description
Theoretically and experimentally, we investigated the process of adjusting the pH of natural water of hydrocarbonate class electrodialyzer with bipolar membranes with channel length of 40 cm. We experimentally measured concentration of components, pH of the solutions in alkaline and acid channels of electrodeposition depending on the current density. The article describes a mathematical model for long channels; to scale the mass transfer characteristics of the process there was applied and verified a method of compartmentalization, which gave the possibility to calculate the dependence of the component along the channel length at different velocities of flow of the solution. Numerical calculations were compared with experimental data on electrodialyser of 10 cm and 40 cm length