{"title":"Computer simulation of a two-dimensional Potts model with competing exchange interactions","authors":"M. Ramazanov, A. Murtazaev","doi":"10.31029/demr.16.2","DOIUrl":"https://doi.org/10.31029/demr.16.2","url":null,"abstract":"The phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states $q = 4$ on a hexagonal lattice with competing exchange interactions have been investigated on the basis of the Wang-Landau algorithm by the Monte Carlo method. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to a violation of the magnetic ordering and to the appearance of frustration.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"1 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":"125857587","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}
{"title":"On uniform convergence of Fourier-Sobolev series","authors":"T. Shakh-Emirov","doi":"10.31029/demr.12.5","DOIUrl":"https://doi.org/10.31029/demr.12.5","url":null,"abstract":"Let ${varphi_{k}}_{k=0}^infty$ be a system of functions defined on $ [a, b] $ and orthonormal in $ L ^ 2_ rho = L ^ 2_rho ( a, b) $ with respect to the usual inner product.\u0000For a given positive integer $ r $, by ${varphi_{r,k}}_{k=0}^infty$ we denote the system of functions orthonormal with respect to the Sobolev-type inner product and generated by the system ${varphi_{k}}_{k=0}^infty$.\u0000In this paper, we study the question of the uniform convergence of the Fourier series by the system of functions ${varphi_{r,k}}_{k=0}^infty$ to the functions $fin W^r_{L^p_rho}$ in the case when the original system ${varphi_{k}}_{k=0}^infty$ forms a basis in the space $L^p_rho=L^p_rho(a,b)$ ($1le p$, $pneq2$).","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133723931","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}
{"title":"Inverse of the conic transformation of a function with a power weight","authors":"Z. Medzhidov","doi":"10.31029/demr.12.4","DOIUrl":"https://doi.org/10.31029/demr.12.4","url":null,"abstract":"We consider the Radon transformation defined on circular cones called the conical Radon transform. In the three-dimensional space $R^{3}$, it maps the functions to its surface integrals over a circular cone, and in $R^{2}$ to its integrals over two rays with a common vertex. In this paper, we present new formulas for inversion of k-weighted conical and X-ray Radon transformations under complete and incomplete data in $R^{2}$ and $R^{3}$.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"31 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":"121191639","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}
{"title":"On Bergman-type spaces in tubular domains over symmetric cones","authors":"R. Shamoyan","doi":"10.31029/DEMR.14.2","DOIUrl":"https://doi.org/10.31029/DEMR.14.2","url":null,"abstract":"Some properties of new Bergman-type integral operators on product of the tube domains are obtained.\u0000An integral condition in tube to get atomic-type decomposition in multifunctional analytic Bergman spaces in tube domains over symmetric cones are provided.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"22 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":"114315553","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}
{"title":"Some aspects of familiarization with binomial coefficients","authors":"A. Magomedov, S. Lavrenchenko","doi":"10.31029/demr.11.6","DOIUrl":"https://doi.org/10.31029/demr.11.6","url":null,"abstract":"New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"50 2 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":"123561216","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}
{"title":"Analogs of the Liouville property for Bessel function series","authors":"N. Volchkova, V. Volchkov","doi":"10.31029/demr.11.1","DOIUrl":"https://doi.org/10.31029/demr.11.1","url":null,"abstract":"We study functions given in the form of a series in Bessel's functions of the first kind. The admissible asymptotic behavior of such functions at infinity is founded. As a consequence we obtain an analog of Liouville's theorem for the Fourier-Bessel and Dini developments.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"26 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":"128767742","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}
{"title":"Titchmarsh's theorem of Hankel transform","authors":"Mohamed-Ahmed Boudref","doi":"10.31029/demr.11.2","DOIUrl":"https://doi.org/10.31029/demr.11.2","url":null,"abstract":"Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc.\u0000 In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"27 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":"115430010","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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