Pub Date : 1900-01-01DOI: 10.20948/MATHMON-2019-44-8
G. Kuvyrkin, I. Y. Savelyeva, V. S. Zarubin
The use of modern polymeric materials as dielectrics makes it possible to increase operational characteristics of the elements of various electric power and electronic devices. The necessary combination of interconnected values of permissible electric field strength and maximum operating temperature is crucial when choosing a particular polymer material. The relationship of these parameters is nonlinear due to the nonlinear dependence the electrical resistivity and the thermal conductivity coefficient on temperature of the polymer material. This relationship can be represented in a closed analytical form of integral relations in which the variable limit of the integrals is the desired function describing the temperature distribution in the dielectric layer. A quantitative analysis of these ratios for five different polymeric materials with known electrothermal characteristics has been carried out. The results of calculations of the temperature state of the dielectric layer and the distribution in the layer of the absolute value of the electric field intensity are given. The presented results can be used to justify the choice of a particular polymer material as a dielectric in the designed devices.
{"title":"Mathematical modeling of the temperature state of a plane layer polymer dielectric at constant voltage","authors":"G. Kuvyrkin, I. Y. Savelyeva, V. S. Zarubin","doi":"10.20948/MATHMON-2019-44-8","DOIUrl":"https://doi.org/10.20948/MATHMON-2019-44-8","url":null,"abstract":"The use of modern polymeric materials as dielectrics makes it possible to increase operational characteristics of the elements of various electric power and electronic devices. The necessary combination of interconnected values of permissible electric field strength and maximum operating temperature is crucial when choosing a particular polymer material. The relationship of these parameters is nonlinear due to the nonlinear dependence the electrical resistivity and the thermal conductivity coefficient on temperature of the polymer material. This relationship can be represented in a closed analytical form of integral relations in which the variable limit of the integrals is the desired function describing the temperature distribution in the dielectric layer. A quantitative analysis of these ratios for five different polymeric materials with known electrothermal characteristics has been carried out. The results of calculations of the temperature state of the dielectric layer and the distribution in the layer of the absolute value of the electric field intensity are given. The presented results can be used to justify the choice of a particular polymer material as a dielectric in the designed devices.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"1075 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132911010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-53-6
A. Kolesnichenko
Taking into account the methods of thermodynamics of irreversible processes using the Onsager principle, a model of a multicomponent continuous medium is constructed, the internal energy of which is "free" of the kinetic energy of diffusion. The model is designed for an imperfect continuous medium with chemical reactions in the field of conservative external forces. Generalized StefanMaxwell relations are obtained, which represent a system of hydrodynamic equations of motion of a mixture with true inertial forces. The proposed thermodynamic technique made it possible to obtain a number of algebraic relations known from the kinetic theory of gases for the transfer coefficients, relating, in particular, the coefficients of multicomponent diffusion with binary diffusivitys, thermal diffusion ratios with thermal diffusion coefficients and multicomponent diffusion coefficients, true (molecular) thermal conductivity coefficient for multicomponent mixture with partial thermal conductivity coefficient, which indicates their versatility. The results obtained are intended for modeling not only liquid imperfect solutions, but also gas-dust mixtures with a finely dispersed dust component.
{"title":"Correct definition of internal energy at the phenomenological construction of model of multicomponent continuous medium by methods of nonequilibrium thermodynamics","authors":"A. Kolesnichenko","doi":"10.20948/mathmontis-2022-53-6","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-6","url":null,"abstract":"Taking into account the methods of thermodynamics of irreversible processes using the Onsager principle, a model of a multicomponent continuous medium is constructed, the internal energy of which is \"free\" of the kinetic energy of diffusion. The model is designed for an imperfect continuous medium with chemical reactions in the field of conservative external forces. Generalized StefanMaxwell relations are obtained, which represent a system of hydrodynamic equations of motion of a mixture with true inertial forces. The proposed thermodynamic technique made it possible to obtain a number of algebraic relations known from the kinetic theory of gases for the transfer coefficients, relating, in particular, the coefficients of multicomponent diffusion with binary diffusivitys, thermal diffusion ratios with thermal diffusion coefficients and multicomponent diffusion coefficients, true (molecular) thermal conductivity coefficient for multicomponent mixture with partial thermal conductivity coefficient, which indicates their versatility. The results obtained are intended for modeling not only liquid imperfect solutions, but also gas-dust mixtures with a finely dispersed dust component.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"118 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133684931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-5
B. Benaissa, Aissa Benguessoum
The integral inequalities concerning the inverse Hardy inequalities have been studied by a large number of authors during this century, of these articles have appeared, the work of Sulaiman in 2012, followed by Banyat Sroysang who gave an extension to these inequalities in 2013. In 2020 B. Benaissa presented a generalization of inverse Hardy inequalities. In this article, we establish a new generalization of these inequalities by introducing a weight function and a second parameter. The results will be proved using the Hölder inequality and the Jensen integral inequality. Several the reverses weighted Hardy’s type inequalities and the reverses Hardy’s type inequalities were derived from the main results.
{"title":"Reverses Hardy-type inequalities via Jensen integral inequality","authors":"B. Benaissa, Aissa Benguessoum","doi":"10.20948/mathmontis-2021-52-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-5","url":null,"abstract":"The integral inequalities concerning the inverse Hardy inequalities have been studied by a large number of authors during this century, of these articles have appeared, the work of Sulaiman in 2012, followed by Banyat Sroysang who gave an extension to these inequalities in 2013. In 2020 B. Benaissa presented a generalization of inverse Hardy inequalities. In this article, we establish a new generalization of these inequalities by introducing a weight function and a second parameter. The results will be proved using the Hölder inequality and the Jensen integral inequality. Several the reverses weighted Hardy’s type inequalities and the reverses Hardy’s type inequalities were derived from the main results.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132311586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/MATHMONTIS-2019-46-1
D. Jokanović
{"title":"A breaf survey on Armendariz and central Armendariz rings","authors":"D. Jokanović","doi":"10.20948/MATHMONTIS-2019-46-1","DOIUrl":"https://doi.org/10.20948/MATHMONTIS-2019-46-1","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"23 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125843324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-2
Engin Özkan, M. Uysal
We introduce Mersenne-Lucas hybrid numbers. We give the Binet formula, the generating function, the sum, the character, the norm and the vector representation of these numbers. We find some relations among Mersenne-Lucas hybrid numbers, Jacopsthal hybrid numbers, Jacopsthal-Lucas hybrid numbers and Mersenne hybrid numbers. Then we present some important identities such as Cassini identities for Mersenne-Lucas hybrid numbers
{"title":"Mersenne-Lucas hybrid numbers","authors":"Engin Özkan, M. Uysal","doi":"10.20948/mathmontis-2021-52-2","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-2","url":null,"abstract":"We introduce Mersenne-Lucas hybrid numbers. We give the Binet formula, the generating function, the sum, the character, the norm and the vector representation of these numbers. We find some relations among Mersenne-Lucas hybrid numbers, Jacopsthal hybrid numbers, Jacopsthal-Lucas hybrid numbers and Mersenne hybrid numbers. Then we present some important identities such as Cassini identities for Mersenne-Lucas hybrid numbers","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130084689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-53-8
V. Mazhukin, O. Koroleva, A. V. Shapranov, A. A. Aleksashkina, M. Demin
By constructing the thermal hysteresis of the enthalpy and density of the noble metals of gold (Au) and copper (Cu), non-equilibrium processes are investigated during the melting – crystallization phase transformations, i.e. during the solid–liquid transition. Thermal hysteresis is obtained from the atomistic modeling. The limiting temperatures of superheating of the solid phase during melting and undercooling of the liquid phase during crystallization of gold and copper are obtained. The possibility of the formation of highly superheated-undercooled metastable states of solid and liquid phases with rapid heating-cooling of the studied metals has been confirmed. The results obtained are compared with the results of alternative calculations.
{"title":"Molecular dynamics study of thermal hysteresis during melting-crystallization of noble metals","authors":"V. Mazhukin, O. Koroleva, A. V. Shapranov, A. A. Aleksashkina, M. Demin","doi":"10.20948/mathmontis-2022-53-8","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-8","url":null,"abstract":"By constructing the thermal hysteresis of the enthalpy and density of the noble metals of gold (Au) and copper (Cu), non-equilibrium processes are investigated during the melting – crystallization phase transformations, i.e. during the solid–liquid transition. Thermal hysteresis is obtained from the atomistic modeling. The limiting temperatures of superheating of the solid phase during melting and undercooling of the liquid phase during crystallization of gold and copper are obtained. The possibility of the formation of highly superheated-undercooled metastable states of solid and liquid phases with rapid heating-cooling of the studied metals has been confirmed. The results obtained are compared with the results of alternative calculations.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"5 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120978240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2019-45-10
Lazar Obradović
The value and the optimal exercise time of the perpetual American straddle is characterized by the unique solution of a single non-linear equation with one unknown variable.
永久美式跨骑运动的数值和最佳运动时间具有一个单一未知变量非线性方程的唯一解的特点。
{"title":"A note on the perpetual American straddle","authors":"Lazar Obradović","doi":"10.20948/mathmontis-2019-45-10","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-45-10","url":null,"abstract":"The value and the optimal exercise time of the perpetual American straddle is characterized by the unique solution of a single non-linear equation with one unknown variable.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122936146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-7
A. Kroshilin, Mikhail Evgenievich Kroshilin
At present, to describe the two-velocity flow of a dispersed mixture, as a rule, a two-fluid model is used with equal pressure of the phases of the medium and different velocities of the phases. The corresponding system of equations without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. Recently, it has been proposed to use similar models more widely, but with different pressures of the phases of the medium. Such models allow one to take into account new physical effects associated with different phase pressures and often provide hyperbolicity of the corresponding system of equations. This article analyzes the influence of the difference in the pressure of the phases of the medium on the properties of the system: the importance of the corresponding new effects, the hyperbolicity of the system of equations, the stability of its stationary solutions, and the correctness of the corresponding Cauchy problem are investigated. Three systems are considered. The first, simplest model system is based on the well-known non-hyperbolic system, which has been modernized. It is shown that the Cauchy problem for the modified system is formally correct, but the practical possibility of using the calculation results obtained from the solution of this system should be investigated in each specific case, and depends on the calculated step and duration of the process under study. The techniques worked out to solve the first simplest system were used for other systems. As the second system, a model of the flow of a two-phase medium with different phase pressures and two momentum equations is considered. We will assume the phases are barotropic. Let us postulate an equation relating the pressure in the phases. It is proved that this system is always hyperbolic. The stability of its stationary solutions is investigated. Relationships are derived that make it possible to determine under what conditions, due to instability, the obtained solutions are unreliable. The properties of this system are compared with the system of two-speed flow of a dispersed mixture with equal pressure of the phases of the medium. As a third system, a two-pressure model describing bubble pulsations is considered. We will assume the phases are barotropic. Conditions are determined when the system is non-hyperbolic and the Cauchy problem is incorrect. It is investigated for what conditions the ill-posedness of the Cauchy problem leads to the unreliability of the solution, and under what conditions the ill-posedness of the Cauchy problem does not lead to the unreliability of the solution.
{"title":"Flow stability and correctness of the Cauchy problem for a two-speed medium model with different phase pressures","authors":"A. Kroshilin, Mikhail Evgenievich Kroshilin","doi":"10.20948/mathmontis-2021-52-7","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-7","url":null,"abstract":"At present, to describe the two-velocity flow of a dispersed mixture, as a rule, a two-fluid model is used with equal pressure of the phases of the medium and different velocities of the phases. The corresponding system of equations without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. \u0000Recently, it has been proposed to use similar models more widely, but with different pressures of the phases of the medium. Such models allow one to take into account new physical effects associated with different phase pressures and often provide hyperbolicity of the corresponding system of equations. This article analyzes the influence of the difference in the pressure of the phases of the medium on the properties of the system: the importance of the corresponding new effects, the hyperbolicity of the system of equations, the stability of its stationary solutions, and the correctness of the corresponding Cauchy problem are investigated. Three systems are considered. The first, simplest model system is based on the well-known non-hyperbolic system, which has been modernized. It is shown that the Cauchy problem for the modified system is formally correct, but the practical possibility of using the calculation results obtained from the solution of this system should be investigated in each specific case, and depends on the calculated step and duration of the process under study. The techniques worked out to solve the first simplest system were used for other systems. As the second system, a model of the flow of a two-phase medium with different phase pressures and two momentum equations is considered. We will assume the phases are barotropic. Let us postulate an equation relating the pressure in the phases. It is proved that this system is always hyperbolic. The stability of its stationary solutions is investigated. Relationships are derived that make it possible to determine under what conditions, due to instability, the obtained solutions are unreliable. The properties of this system are compared with the system of two-speed flow of a dispersed mixture with equal pressure of the phases of the medium. As a third system, a two-pressure model describing bubble pulsations is considered. We will assume the phases are barotropic. Conditions are determined when the system is non-hyperbolic and the Cauchy problem is incorrect. It is investigated for what conditions the ill-posedness of the Cauchy problem leads to the unreliability of the solution, and under what conditions the ill-posedness of the Cauchy problem does not lead to the unreliability of the solution.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129408783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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