Pub Date : 2020-06-21DOI: 10.17323/1609-4514-2022-22-1-1-68
G. Cotti, A. Varchenko
We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov equation and its solutions are reflected in the properties of the $*$-Markov equation and its solutions.
{"title":"The ∗-Markov Equation for Laurent Polynomials","authors":"G. Cotti, A. Varchenko","doi":"10.17323/1609-4514-2022-22-1-1-68","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-1-68","url":null,"abstract":"We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov equation and its solutions are reflected in the properties of the $*$-Markov equation and its solutions.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47362337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-16DOI: 10.17323/1609-4514-2022-22-3-393-400
R. Aliev, A. Asgarova, V. Ismailov
In this paper, we show that the pair of classes of locally Holder continuous functions (considered on $mathbb{R}$ and $mathbb{R}^{2}$, respectively) has the double difference property.
{"title":"The Double Difference Property for the Class of Locally Hölder Continuous Functions","authors":"R. Aliev, A. Asgarova, V. Ismailov","doi":"10.17323/1609-4514-2022-22-3-393-400","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-3-393-400","url":null,"abstract":"In this paper, we show that the pair of classes of locally Holder continuous functions (considered on $mathbb{R}$ and $mathbb{R}^{2}$, respectively) has the double difference property.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45166379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-14DOI: 10.17323/1609-4514-2020-20-3-531-573
Ryo Ohkawa
{"title":"Functional Equations of Nekrasov Functions Proposed by Ito, Maruyoshi, and Okuda","authors":"Ryo Ohkawa","doi":"10.17323/1609-4514-2020-20-3-531-573","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-3-531-573","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43811976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-14DOI: 10.17323/1609-4514-2020-20-3-441-451
H. Alzer, M. Kwong
{"title":"A Generalization of the Fejér–Jackson Inequality and Related Results","authors":"H. Alzer, M. Kwong","doi":"10.17323/1609-4514-2020-20-3-441-451","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-3-441-451","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43150271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-14DOI: 10.17323/1609-4514-2020-20-3-495-509
Maria Fărcăşeanu, M. Mihăilescu
{"title":"The Asymptotic Behaviour of the Sequence of Solutions for a Family of Equations Involving p ( ⋅ ) -Laplace Operators","authors":"Maria Fărcăşeanu, M. Mihăilescu","doi":"10.17323/1609-4514-2020-20-3-495-509","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-3-495-509","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48126966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-07DOI: 10.17323/1609-4514-2020-20-3-511-530
M. Kazarian, R. Uribe-Vargas
We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a closed simple expression.
{"title":"Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces","authors":"M. Kazarian, R. Uribe-Vargas","doi":"10.17323/1609-4514-2020-20-3-511-530","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-20-3-511-530","url":null,"abstract":"We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a \"fundamental cubic form\" for which we provide a closed simple expression.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44297321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-30DOI: 10.17323/1609-4514-2020-2-311-321
Jens Forsgård
{"title":"Tropical Approximation of Exponential Sums and the Multivariate Fujiwara Bound","authors":"Jens Forsgård","doi":"10.17323/1609-4514-2020-2-311-321","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-311-321","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48667992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-30DOI: 10.17323/1609-4514-2020-2-375-404
Jessica Jaurez Rosas, L. Ortiz-Bobadilla
{"title":"Orbital Chen Theorem for Germs of C∞ Vector Fields with Degenerate Singularity","authors":"Jessica Jaurez Rosas, L. Ortiz-Bobadilla","doi":"10.17323/1609-4514-2020-2-375-404","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-375-404","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48922302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-30DOI: 10.17323/1609-4514-2020-2-257-276
N. Turki, A. Pratoussevitch
{"title":"Symmetries of Tilings of Lorentz Spaces","authors":"N. Turki, A. Pratoussevitch","doi":"10.17323/1609-4514-2020-2-257-276","DOIUrl":"https://doi.org/10.17323/1609-4514-2020-2-257-276","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45448706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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