In this article, the notions of ∼ sim admissible congruences and ∼ sim normal congruences on a weakly type B semigroup are characterized and the relationship between ∼ sim admissible congruences and ∼ sim normal congruences is investigated. In particular, some properties of such congruences on a weakly type B semigroup are given using an approach of kernel-trace. Finally, we extend the congruence pair on an inverse semigroup to the case of a weakly type B semigroup and obtain some results.
{"title":"A characterization of a ∼ admissible congruence on a weakly type B semigroup","authors":"Chunhua Li, Jieying Fang, Lingxiang Meng, Huawei Huang","doi":"10.1515/math-2023-0152","DOIUrl":"https://doi.org/10.1515/math-2023-0152","url":null,"abstract":"In this article, the notions of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0152_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:tex-math> sim </jats:tex-math> </jats:alternatives> </jats:inline-formula> admissible congruences and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0152_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:tex-math> sim </jats:tex-math> </jats:alternatives> </jats:inline-formula> normal congruences on a weakly type B semigroup are characterized and the relationship between <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0152_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:tex-math> sim </jats:tex-math> </jats:alternatives> </jats:inline-formula> admissible congruences and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0152_eq_006.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>∼</m:mo> </m:math> <jats:tex-math> sim </jats:tex-math> </jats:alternatives> </jats:inline-formula> normal congruences is investigated. In particular, some properties of such congruences on a weakly type B semigroup are given using an approach of kernel-trace. Finally, we extend the congruence pair on an inverse semigroup to the case of a weakly type B semigroup and obtain some results.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542986","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}
对于形式为A (z) f (z + 1) + B (z) f ' (z) + C (z) f (z) = f (z)的一阶微分差分方程，Aleft(z)fleft(z+1)+Bleft(z)f^{prime} left(z)+Cleft(z)fleft(z)=Fleft(z)其中A (z) B (z) C (z) Aleft选BleftC .正确答案left(z) F (z) Fleft(z)是多项式，研究了它们的非常亚纯解的存在性、生长、零点、极点和不动点。证明当deg B (z) ＆lt时，所有非常亚纯解都是超越的;度 { A (z) + C (z) } + 1 {rm{deg }}bleft(z)lt {rm{deg }}left｛aleft(z)+Cleft(z)right｝+1并且所有超越解的阶数至少为1。对于有限阶超越解f (z) fleft(z) ρ (f)的关系 rho (f)和Max { λ (f)， λ(1∕f) } max left｛lambda (f);lambda left(1/f)right｝进行了讨论。给出了一些结果清晰度的例子。
In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binary means as a practical application.
{"title":"Schur-power convexity of integral mean for convex functions on the coordinates","authors":"Huannan Shi, Jing Zhang","doi":"10.1515/math-2023-0157","DOIUrl":"https://doi.org/10.1515/math-2023-0157","url":null,"abstract":"In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore, we introduce novel and fascinating inequalities for binary means as a practical application.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"44 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527074","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 M3{M}^{3} be a strictly almost cosymplectic three-manifold whose Ricci operator is weakly ϕphi -invariant. In this article, it is proved that Ricci curvatures of M3{M}^{3} are invariant along the Reeb flow if and only if M3{M}^{3} is locally isometric to the Lie group E(1,1)Eleft(1,1) of rigid motions of the Minkowski 2-space equipped with a left-invariant almost cosymplectic structure.
设M³{M}³{是一个严格概余辛三流形，其Ricci算子弱φ }phi不变。本文证明了m3m ^{3}的Ricci曲率沿Reeb流是不变的，当且仅当m3m ^{3}局部等距于具有左不变几乎余弦结构的Minkowski 2-空间刚性运动的Lie群E (1,1) E {}{}left(1,1)。
{"title":"Ricci ϕ-invariance on almost cosymplectic three-manifolds","authors":"Quanxiang Pan","doi":"10.1515/math-2023-0156","DOIUrl":"https://doi.org/10.1515/math-2023-0156","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0156_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>M</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math>{M}^{3}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a strictly almost cosymplectic three-manifold whose Ricci operator is weakly <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0156_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ϕ</m:mi> </m:math> <jats:tex-math>phi </jats:tex-math> </jats:alternatives> </jats:inline-formula>-invariant. In this article, it is proved that Ricci curvatures of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0156_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>M</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math>{M}^{3}</jats:tex-math> </jats:alternatives> </jats:inline-formula> are invariant along the Reeb flow if and only if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0156_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>M</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math>{M}^{3}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is locally isometric to the Lie group <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0156_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>E</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>Eleft(1,1)</jats:tex-math> </jats:alternatives> </jats:inline-formula> of rigid motions of the Minkowski 2-space equipped with a left-invariant almost cosymplectic structure.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527058","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}
This study investigates some topological properties of locally semi-compact Ir-topological groups and establishes the relationship between Ir-topological groups and semi-compact spaces. The proved theorems generalize the corresponding results of Ir-topological group. Finally, we define a quotient topology on the Ir-topological group and study some topological properties of the space.
{"title":"Properties of locally semi-compact Ir-topological groups","authors":"ZhongLi Wang, Wen Chean Teh","doi":"10.1515/math-2023-0144","DOIUrl":"https://doi.org/10.1515/math-2023-0144","url":null,"abstract":"This study investigates some topological properties of locally semi-compact Ir-topological groups and establishes the relationship between Ir-topological groups and semi-compact spaces. The proved theorems generalize the corresponding results of Ir-topological group. Finally, we define a quotient topology on the Ir-topological group and study some topological properties of the space.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"66 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527076","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}
David J. López, Jose A. Padilla, Juan Ruiz, Carlos Tapia, Juan C. Trillo
In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval [a,b].left[a,b]. These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.
{"title":"About a dubious proof of a correct result about closed Newton Cotes error formulas","authors":"David J. López, Jose A. Padilla, Juan Ruiz, Carlos Tapia, Juan C. Trillo","doi":"10.1515/math-2023-0150","DOIUrl":"https://doi.org/10.1515/math-2023-0150","url":null,"abstract":"In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0150_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mi>a</m:mi> <m:mo>,</m:mo> <m:mi>b</m:mi> </m:mrow> <m:mo>]</m:mo> </m:mrow> <m:mo>.</m:mo> </m:math> <jats:tex-math>left[a,b].</jats:tex-math> </jats:alternatives> </jats:inline-formula> These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527060","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 article, a new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order is obtained, by using the weight functions, the mid-value theorem, and the techniques of real analysis. A few equivalent statements of the best possible constant factor related to several parameters are considered. As applications, the equivalent forms and some particular inequalities are provided.
{"title":"A new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order","authors":"Jianquan Liao, Bicheng Yang","doi":"10.1515/math-2023-0139","DOIUrl":"https://doi.org/10.1515/math-2023-0139","url":null,"abstract":"In this article, a new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order is obtained, by using the weight functions, the mid-value theorem, and the techniques of real analysis. A few equivalent statements of the best possible constant factor related to several parameters are considered. As applications, the equivalent forms and some particular inequalities are provided.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"12 6","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527108","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}
This study is concerned with the stability of Nash equilibria for a class of nn-person noncooperative differential games. More precisely, due to a preorder induced by a convex cone on a real linear normed space, we define a new concept called ordering stability of equilibria against the perturbation of the right-hand side functions of state equations for the differential game. Moreover, using the set-valued analysis theory, we present the sufficient conditions of the ordering stability for such differential games.
{"title":"Ordering stability of Nash equilibria for a class of differential games","authors":"Keke Jia, Shihuang Hong, Jieqing Yue","doi":"10.1515/math-2023-0132","DOIUrl":"https://doi.org/10.1515/math-2023-0132","url":null,"abstract":"This study is concerned with the stability of Nash equilibria for a class of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0132_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>n</m:mi> </m:math> <jats:tex-math>n</jats:tex-math> </jats:alternatives> </jats:inline-formula>-person noncooperative differential games. More precisely, due to a preorder induced by a convex cone on a real linear normed space, we define a new concept called ordering stability of equilibria against the perturbation of the right-hand side functions of state equations for the differential game. Moreover, using the set-valued analysis theory, we present the sufficient conditions of the ordering stability for such differential games.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"16 5","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527059","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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