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Energy analysis of magnetic structural states of the Potts model 波茨模型磁结构状态的能量分析
Daghestan Electronic Mathematical Reports Pub Date : 2022-06-01 DOI: 10.31029/demr.17.4
M. Ramazanov, A. Murtazaev, M. Magomedov, D. Kurbanova, K. Ramazanov, M. Hizriev
{"title":"Energy analysis of magnetic structural states of the Potts model","authors":"M. Ramazanov, A. Murtazaev, M. Magomedov, D. Kurbanova, K. Ramazanov, M. Hizriev","doi":"10.31029/demr.17.4","DOIUrl":"https://doi.org/10.31029/demr.17.4","url":null,"abstract":"Based on the Wang-Landau algorithm, the Monte Carlo method was used to perform an energy analysis of the magnetic structures of the ground state of the two-dimensional Potts model with the number of spin states $q=4$ on a triangular lattice, taking into account the exchange interactions of the first $J_1$ and second $J_2$ nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval $-2.0 leq J_2 leq 0.0$. The magnetic structures of the ground state are determined for different values of the interaction of the second nearest neighbors. It is found that a change in the magnitude of the interaction of the second nearest neighbors in this model leads to a change in the magnetic ordering.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116246250","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}
引用次数: 0
A mixed problem for a multidimensional integro-differential equation in partial derivatives of the fourth order 一个四阶偏导数的多维积分微分方程的混合问题
Daghestan Electronic Mathematical Reports Pub Date : 2022-06-01 DOI: 10.31029/demr.17.1
T. Yuldashev, S. Rasulova
{"title":"A mixed problem for a multidimensional integro-differential equation in partial derivatives of the fourth order","authors":"T. Yuldashev, S. Rasulova","doi":"10.31029/demr.17.1","DOIUrl":"https://doi.org/10.31029/demr.17.1","url":null,"abstract":"The problems of the unique classical solvability and the construction of a solution of a multidimensional mixed problem for a homogeneous fourth order partial integro-differential equations with a degenerate kernel are studied. The multidimensional Fourier series method, based on the separation of many variables, is used. A system of countable systems of algebraic equations is derived. Iteration process of solving the problem is constructed. Sufficient coefficient conditions for the unique classical solvability of the mixed problem are established.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133553889","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}
引用次数: 0
Inversion of the Radon V-transform with a power-law weight on the plane 在平面上用幂律权的Radon v变换的反演
Daghestan Electronic Mathematical Reports Pub Date : 2022-06-01 DOI: 10.31029/demr.17.3
Ziaudin Medzhidov
{"title":"Inversion of the Radon V-transform with a power-law weight on the plane","authors":"Ziaudin Medzhidov","doi":"10.31029/demr.17.3","DOIUrl":"https://doi.org/10.31029/demr.17.3","url":null,"abstract":"A formula for inverting an integral transformation on one family of polylines on the plane is obtained. It generalizes the known formulas to the case of a weighted power function.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114238097","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}
引用次数: 0
Phase diagram and structure of the ground state of the three-vertex Potts model on the Kagome lattice Kagome晶格上三顶点Potts模型基态的相图和结构
Daghestan Electronic Mathematical Reports Pub Date : 2022-06-01 DOI: 10.31029/demr.17.5
M. Magomedov, A. Murtazaev, Madina Isaeva
{"title":"Phase diagram and structure of the ground state of the three-vertex Potts model on the Kagome lattice","authors":"M. Magomedov, A. Murtazaev, Madina Isaeva","doi":"10.31029/demr.17.5","DOIUrl":"https://doi.org/10.31029/demr.17.5","url":null,"abstract":"The high-efficient Wang-Landau algorithm of the Monte-Carlo entropic method has used for studies the three-state Potts model on the Kagome lattice, taking into account the ferromagnetic exchange interaction between the nearest neighbors and the competing antiferromagnetic interaction between the next nearest neighbors. The density of states are calculated, the magnetic structures of the ground state are determined and the temperature dependences of various thermodynamic parameters are calculated. It is shown that depending on the ratio of interactions between the nearest and next nearest neighbors, the ground state of the system can be ferromagnetic, highly degenerated frustrated or have a special type of triplet antiferromagnetic ordering. It was established that the phase transition from the ferromagnetic phase to the paramagnetic is the phase transition of the second order, while the transition from the triplet antiferromagnetic phase is the first order. At the frustration point, which divides both regions, the phase transitions does not occur (the system does not go to ordered phase for any temperature close to zero). The critical temperature of the phase transitions calculated and phase diagram of the system are determined.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116076006","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}
引用次数: 0
On the approximate solution of the Fredholm's integral equations by the method of collocation rational spline functions 用配置有理样条函数法近似解Fredholm积分方程
Daghestan Electronic Mathematical Reports Pub Date : 2022-06-01 DOI: 10.31029/demr.17.2
A. Ramazanov, V. Magomedova
{"title":"On the approximate solution of the Fredholm's integral equations by the method of collocation rational spline functions","authors":"A. Ramazanov, V. Magomedova","doi":"10.31029/demr.17.2","DOIUrl":"https://doi.org/10.31029/demr.17.2","url":null,"abstract":"For arbitrary grids of nodes, an approximate solution of the integral equation Fredholm of the second kind in the form of a collocation rational spline function is obtained. Estimates of the rate of uniform convergence of approximate solutions to the exact solution from the smoothness class $C^r$ for $r=0,1,2$ are presented.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124925801","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}
引用次数: 0
Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms 从矢量场的纵向和横向射线变换数据重建矢量场
Daghestan Electronic Mathematical Reports Pub Date : 2021-12-01 DOI: 10.31029/demr.16.5
Z. Medzhidov
{"title":"Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms","authors":"Z. Medzhidov","doi":"10.31029/demr.16.5","DOIUrl":"https://doi.org/10.31029/demr.16.5","url":null,"abstract":"An algorithm for the complete reconstruction of a vector field in three-dimensional Euclidean space based on incomplete integral data of a longitudinal and a transverse ray transforms is constructed. From of data of a longitudinal ray transform given on the family of straight lines intersecting a piecewise smooth curve, the solenoidal part of the vector field is constructed, and from of data of a transverse ray transform, the potential of an unknown field is constructed. The problem of reconstruction is also solved in the case of a family of lines intersecting a curve at infinity.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129300715","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}
引用次数: 0
Operator estimates for the averaging of the Riemann-Hilbert problem for the Beltrami equation with a locally periodic coefficient 具有局部周期系数的Beltrami方程的Riemann-Hilbert问题的平均算子估计
Daghestan Electronic Mathematical Reports Pub Date : 2021-12-01 DOI: 10.31029/demr.16.4
M. Sirazhudinov, L. Dzhabrailova
{"title":"Operator estimates for the averaging of the Riemann-Hilbert problem for the Beltrami equation with a locally periodic coefficient","authors":"M. Sirazhudinov, L. Dzhabrailova","doi":"10.31029/demr.16.4","DOIUrl":"https://doi.org/10.31029/demr.16.4","url":null,"abstract":"Local characteristics of mathematical models of strongly inhomogeneous media are usually described by functions of the form $a(varepsilon^{-1} x)$, $b(x,varepsilon^{-1} x)$, $c(varepsilon^{-1} x,delta^{-1} x)$, $d(varepsilon^{-1} x,delta^{-1} x,gamma^{-1} x)$, etc., where $varepsilon$, $delta$, $gamma,ldots>0$ --- small parameters, while functions $a$, $b$, $c$, $d$, $ldots$ have an ordered structure (for example, they are periodic in variables $y=varepsilon^{-1} x$, $z=delta^{-1} x$, etc.). Consequently, the corresponding mathematical models are differential equations with rapidly oscillating coefficients. This work is devoted to estimates of the averaging error. We study the generalized Beltrami equation with a locally periodic coefficient $mu(x,varepsilon^{-1} x)$.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"179 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133410188","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}
引用次数: 0
Representation of the solution of the Cauchy problem for a difference equation by a Fourier series in Meixner - Sobolev polynomials 差分方程的柯西问题解的傅里叶级数在梅克纳-索博列夫多项式中的表示
Daghestan Electronic Mathematical Reports Pub Date : 2021-12-01 DOI: 10.31029/demr.16.6
R. Gadzhimirzaev, M. Sultanakhmedov
{"title":"Representation of the solution of the Cauchy problem for a difference equation by a Fourier series in Meixner - Sobolev polynomials","authors":"R. Gadzhimirzaev, M. Sultanakhmedov","doi":"10.31029/demr.16.6","DOIUrl":"https://doi.org/10.31029/demr.16.6","url":null,"abstract":"We obtain a representation of the solution to the Cauchy problem for the $r$-th order difference equation with constant coefficients and given initial conditions at the point $x=0$. This representation is based on the expansion of the solution in the Fourier series by polynomials that are orthogonal in the sense of Sobolev on the grid ${0, 1, ldots}$ and generated by the classical Meixner polynomials. In addition, an algorithm for numerical finding of the unknown coefficients in this expansion has been developed.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126400452","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}
引用次数: 0
Computational algorithm for enumerating graphs of a given order 列举给定顺序的图的计算算法
Daghestan Electronic Mathematical Reports Pub Date : 2021-12-01 DOI: 10.31029/demr.16.1
A. Magomedov, S. Lavrenchenko
{"title":"Computational algorithm for enumerating graphs of a given order","authors":"A. Magomedov, S. Lavrenchenko","doi":"10.31029/demr.16.1","DOIUrl":"https://doi.org/10.31029/demr.16.1","url":null,"abstract":"For a given set $M$ of bigraphs of a given order, an algorithm is developed for constructing a set of representatives of the isomorphism classes of $M$. \u0000The algorithm is designed as a function defined in terms of nested loops; each set of values of the cycle counters (\"indexer\") defines an isomorphism class whose representative is assigned to the indexer.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132691279","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}
引用次数: 0
Stability of systems of Ito linear differential equations with delays 具有时滞的Ito线性微分方程系统的稳定性
Daghestan Electronic Mathematical Reports Pub Date : 2021-12-01 DOI: 10.31029/demr.16.3
R. Kadiev
{"title":"Stability of systems of Ito linear differential equations with delays","authors":"R. Kadiev","doi":"10.31029/demr.16.3","DOIUrl":"https://doi.org/10.31029/demr.16.3","url":null,"abstract":"The questions of instant stability of systems of linear differential equations Ito with delays based on the theory of positively reversible matrices are investigated. The ideas and methods developed by N. V. Azbelev and his students to investigate the sustainability of deterministic linear functional--differential equations are used for this. Are brought sufficient conditions $2p$--stability $(1le p <infty)$ systems of linear differential Ito equations with delays in terms of positive reversibility of the matrices, built according to the parameters of the source system. The fulfillment of these conditions for specific equations is checked.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115001930","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}
引用次数: 0
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