O. A. Islamova, Z. S. Chay, F. S. Rakhimova, Feruza Abdullayeva
This work belongs to the field of limit theorems for separable statistics. In particular, this paper considers the number of empty cells after placing particles in a finite number of cells, where each particle is placed in a polynomial scheme. The statistics under consideration belong to the class of separable statistics, which were previously considered in (Mirakhmedov: 1985), where necessary statements for the layout of particles in a countable number of cells were proved. The same scheme was considered in (Asimov: 1982), in which the conditions for the asymptotic normality of random variables were established. In this paper, the asymptotic normality of the statistics in question is proved and an estimate of the remainder term in the central limit theorem is obtained. In summary, the demand for separable statistics systems is growing day by day to address large-scale databases or to facilitate user access to data management. Because such systems are not only used for data entry and storage, they also describe their structure: file collection supports logical consistency; provides data processing language; restores data after various interruptions; database management systems allow multiple users.
{"title":"Calculate central limit theorem for the number of empty cells after allocation of particles","authors":"O. A. Islamova, Z. S. Chay, F. S. Rakhimova, Feruza Abdullayeva","doi":"10.21744/ijpm.v5n1.1803","DOIUrl":"https://doi.org/10.21744/ijpm.v5n1.1803","url":null,"abstract":"This work belongs to the field of limit theorems for separable statistics. In particular, this paper considers the number of empty cells after placing particles in a finite number of cells, where each particle is placed in a polynomial scheme. The statistics under consideration belong to the class of separable statistics, which were previously considered in (Mirakhmedov: 1985), where necessary statements for the layout of particles in a countable number of cells were proved. The same scheme was considered in (Asimov: 1982), in which the conditions for the asymptotic normality of random variables were established. In this paper, the asymptotic normality of the statistics in question is proved and an estimate of the remainder term in the central limit theorem is obtained. In summary, the demand for separable statistics systems is growing day by day to address large-scale databases or to facilitate user access to data management. Because such systems are not only used for data entry and storage, they also describe their structure: file collection supports logical consistency; provides data processing language; restores data after various interruptions; database management systems allow multiple users.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90213951","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.01
D. Serikbaev
In this paper, we consider an initial value problem for the Burgers’ equation with convolution type weak nonlinearity for the Sturm–Liouville operator. We prove that this problem has an explicit solution in the form of series. To achieve our goals, we use methods that correspond to various fields of mathematics, such as the theory of partial differential equations, mathematical physics, and functional analysis. In particular, we use the Fourier analysis method to establish the existence of solutions to this problem on the Sobolev space. As far as we know, it is the first result obtained for the convolution type Burgers’ equation. Since, we use the Fourier analysis method we gave the properties of Fourier transform when acting on convolution, and also gave a property of fractional order of the Sturm–Liouville operator. The generalized solutions of the convolution type weak nonlinear Burgers’ equation with the initial Cauchy condition are studied.
{"title":"Gas Dynamics type Burgers equation with convolutional nonlinearity","authors":"D. Serikbaev","doi":"10.26577/ijmph.2021.v12.i2.01","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.01","url":null,"abstract":"In this paper, we consider an initial value problem for the Burgers’ equation with convolution type weak nonlinearity for the Sturm–Liouville operator. We prove that this problem has an explicit solution in the form of series. To achieve our goals, we use methods that correspond to various fields of mathematics, such as the theory of partial differential equations, mathematical physics, and functional analysis. In particular, we use the Fourier analysis method to establish the existence of solutions to this problem on the Sobolev space. As far as we know, it is the first result obtained for the convolution type Burgers’ equation. Since, we use the Fourier analysis method we gave the properties of Fourier transform when acting on convolution, and also gave a property of fractional order of the Sturm–Liouville operator. The generalized solutions of the convolution type weak nonlinear Burgers’ equation with the initial Cauchy condition are studied.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47269265","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.03
T. Nauryz
The mathematical model of determining temperature fields in cylindrical domain with solidification process is represented. The solidification process of cylinder due to cooling is constructed by two-phase cylindrical Stefan problem for liquid and solid zones with freezing interface. Respect to strength of the heat sink at the center of cylindrical material boundary condition 1 0 0 lim[2 ] r r r is an important to determine temperature in solid domain. The analytical solution of the problem is introduced with method of similarity principle which enables us to reduce free boundary problem to ordinary differential equations. Temperature solutions of solid and liquid zones are represented by special function which called exponential integral equation. The free boundary at freezing interface and temperatures at two phases are determined. Lemmas about exponential integral functions are introduced and used to prove that obtained operator function is contraction operator. Upper boundness of the exponential integral function is checked graphically. It is shown that existence of uniqueness of solution exists.
建立了凝固过程中柱面温度场确定的数学模型。采用两相圆柱形Stefan问题，构建了具有冻结界面的液固两区圆柱体冷却凝固过程。对散热器的圆柱的中心物质边界条件1 0 0 lim [2] r r r温度是一个重要的决定在固体域。用相似原理的方法给出了该问题的解析解，使我们能够将自由边界问题化为常微分方程。固体和液体区域的温度解用指数积分方程表示。确定了冻结界面的自由边界和两相温度。引入指数积分函数的引理，并利用引理证明所得到的算子函数是收缩算子。用图形法检验了指数积分函数的上界。证明了解的唯一性的存在性。
{"title":"Similarity solution of two-phase cylindrical Stefan solidification problem","authors":"T. Nauryz","doi":"10.26577/ijmph.2021.v12.i2.03","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.03","url":null,"abstract":"The mathematical model of determining temperature fields in cylindrical domain with solidification process is represented. The solidification process of cylinder due to cooling is constructed by two-phase cylindrical Stefan problem for liquid and solid zones with freezing interface. Respect to strength of the heat sink at the center of cylindrical material boundary condition 1 0 0 lim[2 ] r r r is an important to determine temperature in solid domain. The analytical solution of the problem is introduced with method of similarity principle which enables us to reduce free boundary problem to ordinary differential equations. Temperature solutions of solid and liquid zones are represented by special function which called exponential integral equation. The free boundary at freezing interface and temperatures at two phases are determined. Lemmas about exponential integral functions are introduced and used to prove that obtained operator function is contraction operator. Upper boundness of the exponential integral function is checked graphically. It is shown that existence of uniqueness of solution exists.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69016695","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.09
K. Boshkayev, T. Konysbayev, E. Kurmanov, O. Luongo, M. Muccino, H. Quevedo, A. Taukenova, A. Urazalina, G. Zhumakhanova
{"title":"Motion of stars near the galactic center","authors":"K. Boshkayev, T. Konysbayev, E. Kurmanov, O. Luongo, M. Muccino, H. Quevedo, A. Taukenova, A. Urazalina, G. Zhumakhanova","doi":"10.26577/ijmph.2021.v12.i2.09","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.09","url":null,"abstract":"","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46969056","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.08
V. Kidalov, N. Sosnytska, A. Dyadenchuk, R. Oleksenko
This work is focused on the creation and study of photosensitive structures based on zinc oxide nanofibers, which are promising for solar energy. Zinc oxide nanowires were obtained on the porous zinc selenide surface. The porous substrate was obtained by electrochemical etching of a low-resistance n-ZnSe plate (110) with a polished surface. Nanowires were deposited by radical-beam epitaxy. The annealing temperature was varied from 400° C to 500° C. The oxygen radical flux was 1.5∙1017 cm-2s-1. The process duration was 50 minutes. According to the scanning electron microscopy results, the nanowires length reaches 10 μm, the nanowires diameter is ~1 μm. The predominant X-ray diffraction reflex at 2θ=34.44° indicates the polycrystalline nature of the manufactured ZnO coatings with a wurtzite-type hexagonal lattice. The study of nanowires ZnO luminescence at room temperature contains an ultraviolet peak around 385 nm. This peak is related to the zinc oxide edge luminescence. Based on the fabricated structure, the design of the photoconverter was developed. The upper contact of the fabricated photoelectric converter was created by vacuum thermal sputtering of aluminum through a mask. The deposition was carried out at a substrate temperature of 200° C. Ohmic contacts were made using conductive silver paste. The reverse ohmic contact was formed by applying Al paste to the entire reverse side of the surface. The upper layer of the structure is an array of ZnO nanowires. The active base layer is ZnSe. The light volt-ampere characteristics of the obtained structure were measured in the AM 1.5 illumination mode. No-load voltage Uxx, short-circuit current Isc and the fill factor of the current-voltage characteristic FF of the solar element were measured. The efficiency of the manufactured photoconverter was 13.7 %.
{"title":"ZnO nanowires for photoelectric converter applications","authors":"V. Kidalov, N. Sosnytska, A. Dyadenchuk, R. Oleksenko","doi":"10.26577/ijmph.2021.v12.i2.08","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.08","url":null,"abstract":"This work is focused on the creation and study of photosensitive structures based on zinc oxide nanofibers, which are promising for solar energy. Zinc oxide nanowires were obtained on the porous zinc selenide surface. The porous substrate was obtained by electrochemical etching of a low-resistance n-ZnSe plate (110) with a polished surface. Nanowires were deposited by radical-beam epitaxy. The annealing temperature was varied from 400° C to 500° C. The oxygen radical flux was 1.5∙1017 cm-2s-1. The process duration was 50 minutes. According to the scanning electron microscopy results, the nanowires length reaches 10 μm, the nanowires diameter is ~1 μm. The predominant X-ray diffraction reflex at 2θ=34.44° indicates the polycrystalline nature of the manufactured ZnO coatings with a wurtzite-type hexagonal lattice. The study of nanowires ZnO luminescence at room temperature contains an ultraviolet peak around 385 nm. This peak is related to the zinc oxide edge luminescence. Based on the fabricated structure, the design of the photoconverter was developed. The upper contact of the fabricated photoelectric converter was created by vacuum thermal sputtering of aluminum through a mask. The deposition was carried out at a substrate temperature of 200° C. Ohmic contacts were made using conductive silver paste. The reverse ohmic contact was formed by applying Al paste to the entire reverse side of the surface. The upper layer of the structure is an array of ZnO nanowires. The active base layer is ZnSe. The light volt-ampere characteristics of the obtained structure were measured in the AM 1.5 illumination mode. No-load voltage Uxx, short-circuit current Isc and the fill factor of the current-voltage characteristic FF of the solar element were measured. The efficiency of the manufactured photoconverter was 13.7 %.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42126158","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.06
D. Zhakebayev, A. Zhumali, B. Satenova
In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.
{"title":"An Interpolated Bounce Back Thermable Method for Simulating Solid Particles Dynamics in a Viscous Medium","authors":"D. Zhakebayev, A. Zhumali, B. Satenova","doi":"10.26577/ijmph.2021.v12.i2.06","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.06","url":null,"abstract":"In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46812356","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.010
K. Myrzakulov, D. Kenzhalin, T. Myrzakul
. The study of the origin and evolution of our Universe is one of the interesting and actual directions in modern physics and astrophysics. This paper considers the cosmological model of the Universe in the Einstein's theory of gravity and k -essence, where the gravitational field interacts in a non-minimal way with the scalar field φ . That is, in action, in the role of the matter field, we consider the special case of the Lagrange function for the essence. The corresponding field equations of the considered model are obtained. Also, particular solutions for the scale factor a ( t ) were obtained in the form of de Sitter's solution. Two solutions were found, for the potential energy V ( t ) and the scalar field φ ( t ), and their graphical solutions were also built. The analytical solutions obtained in this work are solutions of the considered integrable systems. These solutions are in good agreement with the available observational data and are able to describe the modern dynamics of the expansion of the Universe.
{"title":"On one integrable cosmological model of the flat universe in k-essence","authors":"K. Myrzakulov, D. Kenzhalin, T. Myrzakul","doi":"10.26577/ijmph.2021.v12.i2.010","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.010","url":null,"abstract":". The study of the origin and evolution of our Universe is one of the interesting and actual directions in modern physics and astrophysics. This paper considers the cosmological model of the Universe in the Einstein's theory of gravity and k -essence, where the gravitational field interacts in a non-minimal way with the scalar field φ . That is, in action, in the role of the matter field, we consider the special case of the Lagrange function for the essence. The corresponding field equations of the considered model are obtained. Also, particular solutions for the scale factor a ( t ) were obtained in the form of de Sitter's solution. Two solutions were found, for the potential energy V ( t ) and the scalar field φ ( t ), and their graphical solutions were also built. The analytical solutions obtained in this work are solutions of the considered integrable systems. These solutions are in good agreement with the available observational data and are able to describe the modern dynamics of the expansion of the Universe.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":"18 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41265703","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.05
D. Nurakhmetov, S. Jumabayev, A. Aniyarov
In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary variable coefficient of foundation on a finite segment. The variable of foundation corresponds to the Winkler model. The control problem the first eigenvalues of the beam vibration is investigated. Two types of fastenings at the ends are considered: clamped-clamped and hinged-hinged. The control is based on the Kanguzhin algorithm through integral perturbations of one of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found. First, a result is formulated regarding the control of the first eigenvalue of the oscillation of the Euler-Bernoulli beam with hinge fastening at both ends. The result is then extended to control with several eigenvalues for this beam, which are important from the point of view of the application. Such questions are especially relevant when studying the resonant natural frequencies of a mechanical system. A similar result was obtained for a Euler-Bernoulli beam with clamped fastening at both ends. Such results of eigenvalue control of a mechanical system contribute to the creation of various non-destructive testing devices that are widely used in technical acoustics.
{"title":"Control of Vibrations of a Beam with Nonlocal Boundary Conditions","authors":"D. Nurakhmetov, S. Jumabayev, A. Aniyarov","doi":"10.26577/ijmph.2021.v12.i2.05","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.05","url":null,"abstract":"In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary variable coefficient of foundation on a finite segment. The variable of foundation corresponds to the Winkler model. The control problem the first eigenvalues of the beam vibration is investigated. Two types of fastenings at the ends are considered: clamped-clamped and hinged-hinged. The control is based on the Kanguzhin algorithm through integral perturbations of one of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found. First, a result is formulated regarding the control of the first eigenvalue of the oscillation of the Euler-Bernoulli beam with hinge fastening at both ends. The result is then extended to control with several eigenvalues for this beam, which are important from the point of view of the application. Such questions are especially relevant when studying the resonant natural frequencies of a mechanical system. A similar result was obtained for a Euler-Bernoulli beam with clamped fastening at both ends. Such results of eigenvalue control of a mechanical system contribute to the creation of various non-destructive testing devices that are widely used in technical acoustics.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44557554","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.04
Kimbugwe Nasser, Tingrui Pei
{"title":"An Efficient Privacy and Integrity-Preserving Range Query Scheme over Unsorted Data in IoT Two-tiered Wireless Sensor Networks","authors":"Kimbugwe Nasser, Tingrui Pei","doi":"10.26577/ijmph.2021.v12.i2.04","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.04","url":null,"abstract":"","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45053164","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 : 2021-12-01DOI: 10.26577/ijmph.2021.v12.i2.07
K. Boshkayev, O. Luongo, M. Muccino, H. Quevedo
. Static and rotating, cold and hot white dwarf stars are investigated both in Newtonian gravity and general theory of relativity, employing the well-established Chandrasekhar equation of state. The Hartle formalism is involved to construct and study uniformly rotating configurations of white dwarfs. The mass-radius, mass-central density, radius-central density and other basic relations of stable white dwarfs, consisting of pure helium and iron, are constructed for different temperatures at mass shedding limit. Stability of white dwarfs is analyzed with respect to the inverse beta decay process, pycnonuclear reactions and instabilities of general relativity. It is found that for a fixed mass hot white dwarfs consisting of pure iron are smaller in size, correspondingly denser with respect to the ones composed of light elements. In addition, it is shown that near the Chandrasekhar mass limit the mass of hot rotating white dwarfs is slightly less than for cold ones, though for low mass rotating white dwarfs and static ones in all mass range the situation is opposite.
{"title":"Static and rotating white dwarf stars at finite temperatures","authors":"K. Boshkayev, O. Luongo, M. Muccino, H. Quevedo","doi":"10.26577/ijmph.2021.v12.i2.07","DOIUrl":"https://doi.org/10.26577/ijmph.2021.v12.i2.07","url":null,"abstract":". Static and rotating, cold and hot white dwarf stars are investigated both in Newtonian gravity and general theory of relativity, employing the well-established Chandrasekhar equation of state. The Hartle formalism is involved to construct and study uniformly rotating configurations of white dwarfs. The mass-radius, mass-central density, radius-central density and other basic relations of stable white dwarfs, consisting of pure helium and iron, are constructed for different temperatures at mass shedding limit. Stability of white dwarfs is analyzed with respect to the inverse beta decay process, pycnonuclear reactions and instabilities of general relativity. It is found that for a fixed mass hot white dwarfs consisting of pure iron are smaller in size, correspondingly denser with respect to the ones composed of light elements. In addition, it is shown that near the Chandrasekhar mass limit the mass of hot rotating white dwarfs is slightly less than for cold ones, though for low mass rotating white dwarfs and static ones in all mass range the situation is opposite.","PeriodicalId":40756,"journal":{"name":"International Journal of Mathematics and Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46781302","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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