Open Mathematics最新文献

{"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}

{"title":"On Bohr's inequality for special subclasses of stable starlike harmonic mappings","authors":"Wei Jin, Zhihong Liu, Qian Hu, Wenbo Zhang","doi":"10.1515/math-2023-0141","DOIUrl":"https://doi.org/10.1515/math-2023-0141","url":null,"abstract":"The focus of this article is to explore the Bohr inequality for a specific subset of harmonic starlike mappings introduced by Ghosh and Vasudevarao (&lt;jats:italic&gt;Some basic properties of certain subclass of harmonic univalent functions&lt;/jats:italic&gt;, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1687–1703.). This set is denoted as &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0141_eq_001.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msubsup&gt; &lt;m:mrow&gt; &lt;m:mi mathvariant=\"script\"&gt;ℬ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;H&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msubsup&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;M&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;≔&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;{&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;f&lt;/m:mi&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mi&gt;h&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mover accent=\"true\"&gt; &lt;m:mrow&gt; &lt;m:mi&gt;g&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"true\"&gt;¯&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mover&gt; &lt;m:mo&gt;∈&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi mathvariant=\"script\"&gt;ℋ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;:&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;∣&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mi&gt;h&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo accent=\"true\"&gt;″&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;∣&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mi&gt;M&lt;/m:mi&gt; &lt;m:mo&gt;−&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;∣&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mi&gt;g&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo accent=\"true\"&gt;″&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;∣&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;}&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;{{mathcal{ {mathcal B} }}}_{H}^{0}left(M):= {f=h+overline{g}in {{mathcal{ {mathcal H} }}}_{0}:| z{h}^{^{primeprime} }left(z)| le M-| z{g}^{^{primeprime} }left(z)| }&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; for &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0141_eq_002.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:mo&gt;∈&lt;/m:mo&gt; &lt;m:mi mathvariant=\"double-struck\"&gt;D&lt;/m:mi&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;zin {mathbb{D}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, where &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0141_eq_003.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mo&gt;&lt;&lt;/m:mo&gt; &lt;m:mi&gt;M&lt;/m:mi&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;0lt Mle 1&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. It is worth mentioning that the functions belonging to the class &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;ja","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"731 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527075","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":"Properties of meromorphic solutions of first-order differential-difference equations","authors":"Lihao Wu, Baoqin Chen, Sheng Li","doi":"10.1515/math-2023-0147","DOIUrl":"https://doi.org/10.1515/math-2023-0147","url":null,"abstract":"For the first-order differential-difference equations of the form &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0147_eq_001.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mi&gt;f&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mi&gt;f&lt;/m:mi&gt; &lt;m:mo accent=\"false\"&gt;′&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mi&gt;C&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mi&gt;f&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mi&gt;F&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;Aleft(z)fleft(z+1)+Bleft(z)f^{prime} left(z)+Cleft(z)fleft(z)=Fleft(z),&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:disp-formula&gt; where &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0147_eq_002.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;m:mi&gt;C&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;Aleft(z),Bleft(z),Cleft(z)&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0147_eq_003.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mi&gt;F&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;Fleft(z)&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; are polynomials, the existence, growth, zeros, poles, and fixed points of their nonconstant meromorphic solutions are investigated. It is shown that all nonconstant meromorphic solutions are transcendental when &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0147_eq_004.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mi mathvariant=\"normal\"&gt;deg&lt;/m:mi&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;&lt;&lt;/m:mo&gt; &lt;m:mi mathvariant=\"normal\"&gt;deg&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;{&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:m","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"38 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527073","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":"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"title":"Transcendental entire solutions of several complex product-type nonlinear partial differential equations in ℂ2","authors":"Yi Hui Xu, Yan Fang Li, Xiao Lan Liu, Hong Yan Xu","doi":"10.1515/math-2023-0151","DOIUrl":"https://doi.org/10.1515/math-2023-0151","url":null,"abstract":"Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0151_eq_001.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;a&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;b&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;c&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;a&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;b&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;c&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;/m:math&gt; &lt;jats:tex-math&gt;left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})left({a}_{2}u+{b}_{2}{u}_{{z}_{1}}+{c}_{2}{u}_{{z}_{2}})=1,&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:disp-formula&gt; and &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0151_eq_002.png\" /&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;a&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;b&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;c&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;u&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;z&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mrow&gt; &lt;m:mi&gt;a&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt;","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"70 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527107","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}