Open Mathematics最新文献

{"title":"On pomonoid of partial transformations of a poset","authors":"Bana Al Subaiei","doi":"10.1515/math-2023-0161","DOIUrl":"https://doi.org/10.1515/math-2023-0161","url":null,"abstract":"The main objective of this article is to study the ordered partial transformations <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">PO</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{mathcal{PO}}left(X)</jats:tex-math> </jats:alternatives> </jats:inline-formula> of a poset <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>X</m:mi> </m:math> <jats:tex-math>X</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The findings show that the set of all partial transformations of a poset with a pointwise order is not necessarily a pomonoid. Some conditions are implemented to guarantee that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">PO</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{mathcal{PO}}left(X)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a pomonoid and this pomonoid is denoted by <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"script\">PO</m:mi> </m:mrow> <m:mrow> <m:mi>↑</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{{mathcal{PO}}}^{uparrow }left(X)</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Moreover, we determine the necessary conditions in order that the partial order-embedding transformations define the ordered version of the symmetric inverse monoid. The findings show that this set is an inverse pomonoid and we will denote it by <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"script\">ℐPO</m:mi> </m:mrow> <m:mrow> <m:mi>↑</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{{mathcal{ {mathcal I} PO}}}^{uparrow }left(X)</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In case the order on the poset <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0161_eq_006.png","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138687900","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":"Global well-posedness of initial-boundary value problem of fifth-order KdV equation posed on finite interval","authors":"Xiangqing Zhao, Chengqiang Wang, Jifeng Bao","doi":"10.1515/math-2023-0158","DOIUrl":"https://doi.org/10.1515/math-2023-0158","url":null,"abstract":"We have established the existence and uniqueness of the local solution for <jats:disp-formula> <jats:label>(0.1)</jats:label> <jats:alternatives> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0158_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:mfenced open=\"{\" close=\"\"> <m:mrow> <m:mtable displaystyle=\"true\"> <m:mtr> <m:mtd columnalign=\"left\"> <m:msub> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:msubsup> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>5</m:mn> </m:mrow> </m:msubsup> <m:mi>u</m:mi> <m:mo>−</m:mo> <m:mi>u</m:mi> <m:msub> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> </m:mtd> <m:mtd columnalign=\"left\"> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>x</m:mi> <m:mo>&lt;</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mspace width=\"1.0em\" /> <m:mi>t</m:mi> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=\"left\"> <m:mi>u</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mn>0</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mi>φ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mtd> <m:mtd columnalign=\"left\"> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>x</m:mi> <m:mo>&lt;</m:mo> <m:mn>1</m:mn> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=\"left\"> <m:mi>u</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>h</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>h</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:mspace width=\"0.33em\" /> <m:msub> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>h</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mtd> <m:mtd columnalign=\"left\" /> </m:mtr> <m:mtr> <m:mtd columnalign=\"left\"> <m:msub> <m:mrow> <m:mo>∂</m:mo> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138687816","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":"Approximate solvability method for nonlocal impulsive evolution equation","authors":"Weifeng Ma, Yongxiang Li","doi":"10.1515/math-2023-0155","DOIUrl":"https://doi.org/10.1515/math-2023-0155","url":null,"abstract":"In this article, without assuming the compactness of semigroup, we deal with the existence and uniqueness of a mild solution for semilinear impulsive evolution equation with nonlocal condition in a reflexive Banach space by applying the approximate solvability method and Yosida approximations of the infinitesimal generator of <jats:italic>C</jats:italic> <jats:sub>0</jats:sub>-semigroup.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138687482","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":"Construction of a functional by a given second-order Ito stochastic equation","authors":"Marat Tleubergenov, Gulmira Vassilina, Shakhmira Ismailova","doi":"10.1515/math-2023-0148","DOIUrl":"https://doi.org/10.1515/math-2023-0148","url":null,"abstract":"In this article, we consider the problem of extending Hamilton’s principle to the class of natural mechanical systems with random perturbing forces of white noise type. By the method of moment functions, we construct the functionals taking a stationary value on the solutions of a given stochastic equation of Lagrangian structure.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138575883","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":"The 𝔪-WG° inverse in the Minkowski space","authors":"Xiaoji Liu, Kaiyue Zhang, Hongwei Jin","doi":"10.1515/math-2023-0145","DOIUrl":"https://doi.org/10.1515/math-2023-0145","url":null,"abstract":"In this article, we study the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0145_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"fraktur\">m</m:mi> </m:math> <jats:tex-math>{mathfrak{m}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-WG<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0145_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow /> <m:mrow> <m:mrow> <m:mo>∘</m:mo> </m:mrow> </m:mrow> </m:msup> </m:math> <jats:tex-math>{}^{circ }</jats:tex-math> </jats:alternatives> </jats:inline-formula> inverse which presents a generalization of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0145_eq_999.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"fraktur\">m</m:mi> </m:math> <jats:tex-math>{mathfrak{m}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-WG inverse in the Minkowski space. We first show the existence and the uniqueness of the generalized inverse. Then, we discuss several properties and characterizations of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0145_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"fraktur\">m</m:mi> </m:math> <jats:tex-math>{mathfrak{m}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-WG<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0145_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow /> <m:mrow> <m:mrow> <m:mo>∘</m:mo> </m:mrow> </m:mrow> </m:msup> </m:math> <jats:tex-math>{}^{circ }</jats:tex-math> </jats:alternatives> </jats:inline-formula> inverse by using the core-EP decomposition. Applying the generalized inverse, we obtain the solutions of some matrix equations in Minkowski space.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560953","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 series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine","authors":"Yan-Fang Li, Feng Qi","doi":"10.1515/math-2023-0159","DOIUrl":"https://doi.org/10.1515/math-2023-0159","url":null,"abstract":"In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of specific determinants and prove a decreasing property of the ratio of two logarithmic expressions containing the cosine function.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560775","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":"Stability result for Lord Shulman swelling porous thermo-elastic soils with distributed delay term","authors":"Abdelbaki Choucha, Salah Mahmoud Boulaaras, Rashid Jan","doi":"10.1515/math-2023-0165","DOIUrl":"https://doi.org/10.1515/math-2023-0165","url":null,"abstract":"The Lord Shulman swelling porous thermo-elastic soil system with the presence of a distributed delay term is studied in this work. We will establish the well-posedness of the system and the exponential stability of the system is derived.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560947","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 double-phase eigenvalue problem with large exponents","authors":"Lujuan Yu","doi":"10.1515/math-2023-0138","DOIUrl":"https://doi.org/10.1515/math-2023-0138","url":null,"abstract":"In the present article, we consider a double-phase eigenvalue problem with large exponents. Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mrow> <m:mi>λ</m:mi> </m:mrow> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msubsup> </m:math> <jats:tex-math>{lambda }_{left({p}_{n},{q}_{n})}^{1}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the first eigenvalues and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:math> <jats:tex-math>{u}_{n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the first eigenfunctions, normalized by <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mo>‖</m:mo> <m:msub> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:mo>‖</m:mo> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi mathvariant=\"script\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> <jats:tex-math>Vert {u}_{n}{Vert }_{{{mathcal{ {mathcal H} }}}_{n}}=1</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Under some assumptions on the exponents <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:math> <jats:tex-math>{p}_{n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>q</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:math> <jats:tex-math>{q}_{n}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, we show that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0138_eq_006.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mr","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547194","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":"Evolutoids and pedaloids of frontals on timelike surfaces","authors":"Yongqiao Wang, Lin Yang, Yuan Chang, Haiming Liu","doi":"10.1515/math-2023-0149","DOIUrl":"https://doi.org/10.1515/math-2023-0149","url":null,"abstract":"In this article, we define evolutoids and pedaloids of frontals on timelike surfaces in Minkowski 3-space. The evolutoids of frontals on timelike surfaces are not only the generalization of evolutoids of curves in the Minkowski plane but also the generalization of caustics in Minkowski 3-space. As an application of the singularity theory, we classify the singularities of evolutoids and reveal the relationships between the singularities and geometric invariants of frontals. Furthermore, we find that there exists a close connection between the pedaloids of frontals and the pedal surfaces of evolutoids. Finally, we give some examples to demonstrate the results.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547139","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 the number of perfect matchings in random polygonal chains","authors":"Shouliu Wei, Yongde Feng, Xiaoling Ke, Jianwu Huang","doi":"10.1515/math-2023-0146","DOIUrl":"https://doi.org/10.1515/math-2023-0146","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-2023-0146_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> <jats:tex-math>G</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a graph. A perfect matching of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0146_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:math> <jats:tex-math>G</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics. But the enumeration problem of perfect matchings for general graphs (even in bipartite graphs) is non-deterministic polynomial (NP)-hard. Xiao et al. [C. Xiao, H. Chen, L. Liu, <jats:italic>Perfect matchings in random pentagonal chains</jats:italic>, J. Math. Chem. 55 (2017), 1878–1886] have studied the problem of perfect matchings for random odd-polygonal chain (i.e., with odd polygons). In this article, we further present simple counting formulae for the expected value of the number of perfect matchings in random even-polygonal chains (i.e., with even polygons). Based on these formulae, we obtain the average values of the number for perfect matchings with respect to the set of all even-polygonal chains with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0146_eq_003.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> polygons.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138548569","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}