01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionIn the article we have derived mathematical models of non-stationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of Nernst-Planck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a new approach to 2D modeling of transport of salt ions in EMC (electro systems: electrodialysis devices, electro-cells, etc.) under the condition of electrical neutrality with limiting and overlimiting current density. For definiteness as seen half of EMS channel EDA desalting (electrodialysis apparatus), the right border, which serves as a CEM (cation exchange membrane). The new approach in the use of partial differential equations of the first order, instead of equations of convective diffusion. A common method of transport modeling binary electrolyte in the EMS under the condition of electrical neutrality, is to use the equation of convective diffusion (partial differential equations of the second order). The article presents a new approach to modeling 2D transfer binary electrolyte in EMS under the same conditions, using partial differential equation of the first order for the decision, which does not require a boundary condition for concentration on the membrane surface. This allows you to simulate the transport of salt ions, as in prelimit and exorbitant current density and to determine the boundaries of the field of electrical neutrality
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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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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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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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MATHEMATICAL MODEL OF THE DYNAMICS OF HIV INFECTION WITHOUT TREATMENT
01.00.00 Physical-mathematical sciences
DescriptionThis article discusses the mathematical and numerical modeling of the immune system of the course of HIV infection without treatment. Presently a significant number of scientific papers are devoted to the study of this problem. However, HIV infection is highly volatile and there is no effective drug, in that HIV has the ability to mutate and reproduce itself in the presence of chemical substances that are meant to inhibit or destroy it. The mathematical models used in this paper are conceptual and exploratory in nature. The proposed mathematical model allow us to obtain a complete description of the dynamics of HIV infection, and also an understanding of the progression to AIDS. Thus, the results of the numerical solution of differential equations in this work show that: the disease develops, and at low concentration of the virus, a certain level of stability does not depend on the initial concentration of infestation. In the absence of treatment, for interesting competition between virus and the loss of virus caused by immune response should be strictly greater than the rate of multiplication of the virus in the blood; the reproduction rate of the uninfected cells should be stricly greater than the mortality rate of the uninfected cells
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PHYSICAL BASIS OF ISOTOPE-ENRICHED LAYERS FORMATION IN FIBER OPTICS
01.00.00 Physical-mathematical sciences
DescriptionIt is known that transmission coefficient of quartz glass containing the same amount of 28Si and 30Si in the silicon optical fiber is lesser than in commercial LEDs for telecommunications. Therefore it is topical to develop the method of optical glass formation with specified isotope composition in the core and in the shell. The article provides an analysis of physical and chemical processes occurring at the formation of quartz optical fiber blanks by vapor deposition from the gas phase. It is shown that the part of the silicon tetrachloride oxidation stages passes through the radical processes. Therefore for quartz glass formation with specified isotope composition it is possible to use the paramagnetic phenomena caused by the external magnetic field in a high-temperature flow at the quartz glass chemical deposition from the vapor phase. In this case alloy additive using is not necessary. Alloy additives can form density inhomogeneities in the glass. Simultaneous silicon glass formation and silicon isotope separation process bring to significant reduction of the fiber cost in comparison with isotope-enriched materials using. The permanent magnets can be used for magnetic field formation at existing process units
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SIMULATING AND PREDICTING GLOBAL CLIMATIC ANOMALIES SUCH AS EL NINO AND LA NINA
01.00.00 Physical-mathematical sciences
DescriptionThe paper discusses the modeling and prediction of the climate of our planet with the use of artificial intelligence AIDOS-X. We have developed a number of semantic information models, demonstrating the presence of the elements of similarity between the motion of the lunar orbit and the displacement of the instantaneous pole of the Earth. It was found that the movement of the poles of the Earth leading to the variations in the magnetic field, seismic events, as well as violations of the global atmospheric circulation and water, and particular to the emergence of episodes such as El Niño and La Niña. Through semantic information models studied some equatorial regions of the Pacific Ocean, as well as spatial patterns of temperate latitudes, revealed their relative importance for the prediction of global climatic disturbances in the tropical and temperate latitudes. The reasons of occurrence of El Niño Modoki and their relationship with the movement of elements of the lunar orbit in the long-term cycles are established. Earlier, we had made a forecast of the occurrence of El Niño episode in 2015. Based on the analysis of semantic models concluded that the expected El Niño classical type. On the basis of the prediction block AIDOS-X calculated monthly evolution scenario of global climate anomalies. In this paper, the analysis of the actual implementation forecast of El Niño since its publication in January 2015 - before June 2015. It is shown that the predicted scenario of climatic anomalies actually realized. Calculations of future climate scenarios with system «Aidos-X» recognition module indicate that further possible abnormal excess temperature indicators of surface ocean waters in regions Nino 1,2 and Nino3,4 for 2015 may be comparable with similar abnormalities in the catastrophic El Niño of 1997-1998.
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SIMULATION OF NONLINEAR COLOR OSCILLATIONS IN YANG-MILLS THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the simulation of non-linear spatial-temporal color oscillations in Yang-Mills theory in the case of SU (2) and SU (3) symmetry. We examined three systems of equations derived from the Yang-Mills theory, which describes the transition to chaotic behaviour. These transitions are caused by nonlinear vibrations of colour, depending on the model parameters - the coupling constants and the initial wave amplitude. Such transitions to chaotic behaviour by increasing the parameters are characteristic of hydrodynamic turbulence. A model of spatial-temporal oscillations of the Yang-Mills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three of five colors or vice versa - the first three five other colors. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. Note that the general property of physical systems described by nonlinear equations in the Yang-Mills theory and hydrodynamics is particularly strong in the formation of quark-gluon plasma and hadrons jets, when the Yang-Mills is involved in the formation of hydrodynamic flow. Note that there is a relationship between the Einstein and Yang-Mills theory, on the one hand, Einstein's equations and hydrodynamics - on the other. All of this points to the existence in the nature of a general mechanism of formation of a special type of turbulence - geometric turbulence
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01.00.00 Physical-mathematical sciences
DescriptionThe steady increase in demand for isotopes requires the development of methods to increase the efficiency of isotope separation technologies. Methods of isotope separation based on thermodynamic differences of isotopic forms of the molecules don't require significant investment, but characterized by a low rate of exchange. It's known that the magnetic effect leads to a change the vibrational frequency of the molecules, and therefore their thermodynamic parameters. The change increases the thermodynamic parameters, including the exchange rate. The results of the experimental determination of the thermal effect of dissolving the salts of NaCl, KCl, CuSO4, sodium amalgam decomposition by distillate in a magnetic field and without field were shown. Magnetic interference can have a significant effect on the amalgam exchange method which was shown by quantum and mechanical analysis of the results