#### International Journal of Mathematics and Physics

Journal Information

ISSN / EISSN :
2218-7987 / 2409-5508

Current Publisher: al-Farabi Kazakh National University (10.26577)

Total articles ≅ 109

Current Coverage

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#### Latest articles in this journal

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 41-44; doi:10.26577/ijmph.2020.v11.i2.06

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 27-31; doi:10.26577/ijmph.2020.v11.i2.04

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 28-35; doi:10.26577/ijmph.2020.v11.i1.04

**Abstract:**

The initial-boundary value problem with parameter for higher-order partial differential equations is considered. We study the existence of its solution and also propose a method for finding approximate solutions. We are established a sufficient conditions for the existence and uniqueness of the solution to the identification parameter problem under consideration. Introducing new unknown functions, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for second-order hyperbolic equations with functional parameters and integral relations. An algorithm for finding an approximate solution to the problem under study is proposed and its convergence is proved. Sufficient conditions for the existence of a unique solution to an equivalent problem with parameters are established. The conditions for the unique solvability of the initial-boundary value problem with parameter for higher-order partial differential equations are obtained in terms of the initial data. Unique solvability to the initial-boundary value problem with parameter for higher-order partial differential equations is interconnected with unique solvability to the nonlocal problem with parameter for secondorder hyperbolic equations. The initial-boundary value problem with parameter for higher-order partial differential equations is considered. We study the existence of its solution and also propose a method for finding approximate solutions. We are established a sufficient conditions for the existence and uniqueness of the solution to the identification parameter problem under consideration. Introducing new unknown functions, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for second-order hyperbolic equations with functional parameters and integral relations. An algorithm for finding an approximate solution to the problem under study is proposed and its convergence is proved. Sufficient conditions for the existence of a unique solution to an equivalent problem with parameters are established. The conditions for the unique solvability of the initial-boundary value problem with parameter for higher-order partial differential equations are obtained in terms of the initial data. Unique solvability to the initial-boundary value problem with parameter for higher-order partial differential equations is interconnected with unique solvability to the nonlocal problem with parameter for secondorder hyperbolic equations.

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 51-57; doi:10.26577/ijmph.2020.v11.i1.07

**Abstract:**

When burning any fossil fuels, one of the most harmful combustion products are nitrogen oxides NOx, which damage both the environment and human health in particular. Reduction of NOx emissions from fuel combustion at TPPs plays an important role in reducing the total level of nitrogen oxides NOx emitted into the atmosphere. One way to reduce the concentration of nitrogen oxides NOx is the stepwise combustion of the pulverized coal mixture, in particular the «Over fire Air» technology. The essence of this method is that the main volume of air is fed into the pulverized burners, and the rest of the air is further along the height of the torch through special nozzles. Structurally, the method of stepwise combustion of fuel can be carried out in boilers with a two-tier arrangement of burners along the height of the combustion chamber. In this case, practically no significant reconstruction of the boiler is required, which is associated with additional costs. In the present work, computational experiments on the use of modern overfire air technology (OFA) in the combustion chamber of the PK-39 boiler of the Aksu TPP were carried out and the fields of the main characteristics of heat and mass transfer, as well as the influence of the mass flow of the oxidant through the OFA injectors on the combustion process were obtained. When burning any fossil fuels, one of the most harmful combustion products are nitrogen oxides NOx, which damage both the environment and human health in particular. Reduction of NOx emissions from fuel combustion at TPPs plays an important role in reducing the total level of nitrogen oxides NOx emitted into the atmosphere. One way to reduce the concentration of nitrogen oxides NOx is the stepwise combustion of the pulverized coal mixture, in particular the «Over fire Air» technology. The essence of this method is that the main volume of air is fed into the pulverized burners, and the rest of the air is further along the height of the torch through special nozzles. Structurally, the method of stepwise combustion of fuel can be carried out in boilers with a two-tier arrangement of burners along the height of the combustion chamber. In this case, practically no significant reconstruction of the boiler is required, which is associated with additional costs. In the present work, computational experiments on the use of modern overfire air technology (OFA) in the combustion chamber of the PK-39 boiler of the Aksu TPP were carried out and the fields of the main characteristics of heat and mass transfer, as well as the influence of the mass flow of the oxidant through the OFA injectors on the combustion process were obtained.

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 4-12; doi:10.26577/ijmph.2020.v11.i1.01

**Abstract:**

Design of electrical monitoring of dams and barriersis an actual task in geophysics. A primary purpose is an exposure of change of structure, erosion, cracks and losses of weir on the early stages. Then it is important to remove and repair a weir and prevent destructions of dike overall. For mathematical modeling of electrical monitoring of dams and barriers, the authors consider the method of ERT. The paper shows a mathematical model of the electrical survey of dams and barriers based on the method of integral equations and the Fourier transform. Numerical calculations for this model are performed. The simulation results for studying the influence of the location of the water-dam boundary with respect to the sounding array are presented. For the purposes of mathematical modeling, two extreme cases were considered: a) a fluid is assumed to be infinitely conductive, b) a fluid is not conductive, i.e. distilled. The effect of a change in the position of the supply electrode at a fixed water level was also studied. The simulation results are presented in the form of apparent resistivity curves, as it is customary in geophysical practice. Distribution of density of secondary charges is also shown for the cases of infinitely conducting and distilledwater. Design of electrical monitoring of dams and barriersis an actual task in geophysics. A primary purpose is an exposure of change of structure, erosion, cracks and losses of weir on the early stages. Then it is important to remove and repair a weir and prevent destructions of dike overall. For mathematical modeling of electrical monitoring of dams and barriers, the authors consider the method of ERT. The paper shows a mathematical model of the electrical survey of dams and barriers based on the method of integral equations and the Fourier transform. Numerical calculations for this model are performed. The simulation results for studying the influence of the location of the water-dam boundary with respect to the sounding array are presented. For the purposes of mathematical modeling, two extreme cases were considered: a) a fluid is assumed to be infinitely conductive, b) a fluid is not conductive, i.e. distilled. The effect of a change in the position of the supply electrode at a fixed water level was also studied. The simulation results are presented in the form of apparent resistivity curves, as it is customary in geophysical practice. Distribution of density of secondary charges is also shown for the cases of infinitely conducting and distilledwater.

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 58-63; doi:10.26577/ijmph.2020.v11.i1.08

**Abstract:**

Transportation of highly viscous and high-curing oils through main pipelines requires significant energy costs. Thus, the task of choosing the cheapest pumping modes is very relevant. The article describes and proposes a solution to the oil flow problem in a pipeline using two methods: with preheating and using a Laval nozzle at the inlet of the pipeline. Mathematical models of the flow of highviscosity oil in the main oil pipeline for the two named pumping methods have been compiled. An algorithm has been developed for calculating temperature, viscosity and pressure along the length of the Uzen-Atyrau pipeline at various oil flow rates. The results of temperature and pressure distribution are analyzed and compared at different oil flow rates along the length of the pipeline for two pumping methods. It is shown that the use of cavitation improves the rheological properties of oil and can significantly reduce the cost of pumping. The research results can be used to predict the operation of main oil pipelines pumping oil both in a heated state and in isothermal mode with a Laval nozzle. Transportation of highly viscous and high-curing oils through main pipelines requires significant energy costs. Thus, the task of choosing the cheapest pumping modes is very relevant. The article describes and proposes a solution to the oil flow problem in a pipeline using two methods: with preheating and using a Laval nozzle at the inlet of the pipeline. Mathematical models of the flow of highviscosity oil in the main oil pipeline for the two named pumping methods have been compiled. An algorithm has been developed for calculating temperature, viscosity and pressure along the length of the Uzen-Atyrau pipeline at various oil flow rates. The results of temperature and pressure distribution are analyzed and compared at different oil flow rates along the length of the pipeline for two pumping methods. It is shown that the use of cavitation improves the rheological properties of oil and can significantly reduce the cost of pumping. The research results can be used to predict the operation of main oil pipelines pumping oil both in a heated state and in isothermal mode with a Laval nozzle.

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 13-19; doi:10.26577/ijmph.2020.v11.i1.02

**Abstract:**

The paper is concerned with the derivation of the hyperbolic-elliptic asymptotic model for surface wave in a pre-stressed, compressible, elastic half-space, within the framework of plane-strain assumption. The consideration extends the existing methodology of asymptotic theories for Rayleigh and Rayleigh-type waves induced by surface/edge loading, and oriented to extraction of the contribution of studied waves to the overall dynamic response. The methodology relies on the slow-time perturbation around the eigensolution, or, equivalently, accounting for the contribution of the poles of the studied wave. As a result, the vector problem of elasticity is reduced to a scalar one for the scaled Laplace equation in terms of the auxiliary function, with the boundary condition is formulated as a hyperbolic equation with the forcing terms. Moreover, hyperbolic equations for surface displacements are also presented. Scalar hyperbolic equations for surface displacements could potentially be beneficial for further development of methods of non-destructive evaluation. The paper is concerned with the derivation of the hyperbolic-elliptic asymptotic model for surface wave in a pre-stressed, compressible, elastic half-space, within the framework of plane-strain assumption. The consideration extends the existing methodology of asymptotic theories for Rayleigh and Rayleigh-type waves induced by surface/edge loading, and oriented to extraction of the contribution of studied waves to the overall dynamic response. The methodology relies on the slow-time perturbation around the eigensolution, or, equivalently, accounting for the contribution of the poles of the studied wave. As a result, the vector problem of elasticity is reduced to a scalar one for the scaled Laplace equation in terms of the auxiliary function, with the boundary condition is formulated as a hyperbolic equation with the forcing terms. Moreover, hyperbolic equations for surface displacements are also presented. Scalar hyperbolic equations for surface displacements could potentially be beneficial for further development of methods of non-destructive evaluation.

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 14-19; doi:10.26577/ijmph.2020.v11.i2.02

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 32-40; doi:10.26577/ijmph.2020.v11.i2.05

Published: 1 January 2020

International Journal of Mathematics and Physics, Volume 11, pp 20-26; doi:10.26577/ijmph.2020.v11.i2.03