{"title":"A Fixed Point Theorem for a Pair of Generalized Nonexpansive Mappings in Uniformly Convex Metric Spaces","authors":"Chao Wang null, H. Fan","doi":"10.4208/jms.v55n4.22.06","DOIUrl":"https://doi.org/10.4208/jms.v55n4.22.06","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44335588","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}
. By analyzing Lie symmetric algebra of the hyperbolic geometric flow, the one-dimensional optimal system of the symmetries to the equation is obtained, and we use similarity reduction to find the reduced equation. By solving the reduced equations, the invariant solutions of the hyperbolic geometric flow are finally obtained.
{"title":"Optimal System and Invariant Solutions of the Hyperbolic Geometric Flow","authors":"Han Zhang null, Zenggui Wang","doi":"10.4208/jms.v55n3.22.04","DOIUrl":"https://doi.org/10.4208/jms.v55n3.22.04","url":null,"abstract":". By analyzing Lie symmetric algebra of the hyperbolic geometric flow, the one-dimensional optimal system of the symmetries to the equation is obtained, and we use similarity reduction to find the reduced equation. By solving the reduced equations, the invariant solutions of the hyperbolic geometric flow are finally obtained.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44750518","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}
. We analyze complete manifolds with boundary which admit solutions to Obata type equations ∇ 2 f − f g = 0 and ∇ 2 f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.
． 我们分析了在不同边界条件下Obata型方程∇2f−f g = 0和∇2f = g有边界的完全流形。在给定内临界点存在的情况下，这种流形分别是双曲空间和欧几里德空间中的域。
{"title":"A Note on Obata Equations on Manifolds with Boundary","authors":"Mijia Lai null, Hui Zhou","doi":"10.4208/jms.v55n3.22.02","DOIUrl":"https://doi.org/10.4208/jms.v55n3.22.02","url":null,"abstract":". We analyze complete manifolds with boundary which admit solutions to Obata type equations ∇ 2 f − f g = 0 and ∇ 2 f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46562354","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}
{"title":"Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay","authors":"Qiang Li null, H. Qiao","doi":"10.4208/jms.v55n4.22.03","DOIUrl":"https://doi.org/10.4208/jms.v55n4.22.03","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48506708","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}
. In this paper we establish a mathematical model for two-sided matching swaption problems in real world. We find a necessary matching condition of the two-sided swaption and deduce analytical formulations of the swaptions in virtue of pricing kernel methods. Also we explore the optimal exercise boundary and properties of the swaptions for investment decision making.
{"title":"The Value of a Two-Sided Real Swaption","authors":"Nengsheng Fang null, C. Liao","doi":"10.4208/jms.v55n3.22.06","DOIUrl":"https://doi.org/10.4208/jms.v55n3.22.06","url":null,"abstract":". In this paper we establish a mathematical model for two-sided matching swaption problems in real world. We find a necessary matching condition of the two-sided swaption and deduce analytical formulations of the swaptions in virtue of pricing kernel methods. Also we explore the optimal exercise boundary and properties of the swaptions for investment decision making.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45493662","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}
. We consider the equivalent conditions with W − m , p ( · ) -version of the J. L. Lions Lemma, where p ( · ) is a variable exponent satisfying some condition. As applications with m = 0, we first derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.
． 我们考虑了J. L. Lions引理的W−m, p(·)版本的等价条件，其中p(·)是满足某些条件的可变指数。作为m = 0的应用，我们首先推导了Korn不等式，并进一步考虑了它与其他基本结果的关系。本文的目的之一是应用于麦克斯韦-斯托克斯型问题弱解的存在性。
{"title":"Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications","authors":"J. Aramaki","doi":"10.4208/jms.v55n3.22.05","DOIUrl":"https://doi.org/10.4208/jms.v55n3.22.05","url":null,"abstract":". We consider the equivalent conditions with W − m , p ( · ) -version of the J. L. Lions Lemma, where p ( · ) is a variable exponent satisfying some condition. As applications with m = 0, we first derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47580257","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}
. Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.
{"title":"Zeros of Primitive Characters","authors":"Wenyang Wang null, N. Du","doi":"10.4208/jms.v55n1.22.05","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.05","url":null,"abstract":". Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48487177","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}
. Let µ M , D be a self-affine measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an infinite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.
． 设µM, D是由展开实矩阵M = (cid:18) a e f b (cid:19)和数字集D = {(0,0) t， (1,0) t， (0,1) t， (1,1) t}生成的自仿射测度。在本文中，我们考虑l2(µM, D)在什么情况下允许一个指数函数的无限正交集?进一步得到，当e = f = 0，且a, b∈{pq, p, q∈2z + 1}，则l2(µM, D)中最多存在4个相互正交的指数函数，且4是最优值。
{"title":"Orthogonal Exponentials of Planar Self-Affine Measures with Four-Element Digit Set","authors":"Hong Li","doi":"10.4208/jms.v55n3.22.07","DOIUrl":"https://doi.org/10.4208/jms.v55n3.22.07","url":null,"abstract":". Let µ M , D be a self-affine measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an infinite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43990058","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}
{"title":"On a Coupled Cahn–Hilliard System for Copolymer/Homopolymer Mixtures","authors":"Laurence Cherfil null, A. Miranville","doi":"10.4208/jms.v55n1.22.02","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.02","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526741","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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