Open Mathematics最新文献

{"title":"Average value of the divisor class numbers of real cubic function fields","authors":"Yoonjin Lee, Jungyun Lee, Jinjoo Yoo","doi":"10.1515/math-2023-0160","DOIUrl":"https://doi.org/10.1515/math-2023-0160","url":null,"abstract":"We compute an asymptotic formula for the divisor class numbers of <jats:italic>real</jats:italic> cubic function fields <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>K</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mi>k</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mroot> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:mroot> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{K}_{m}=kleft(sqrt[3]{m})</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi mathvariant=\"double-struck\">F</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> </m:msub> </m:math> <jats:tex-math>{{mathbb{F}}}_{q}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a finite field with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> </m:math> <jats:tex-math>q</jats:tex-math> </jats:alternatives> </jats:inline-formula> elements, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>≡</m:mo> <m:mn>1</m:mn> <m:mspace width=\"0.3em\" /> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mrow> <m:mi>mod</m:mi> </m:mrow> <m:mspace width=\"0.3em\" /> <m:mn>3</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>qequiv 1hspace{0.3em}left(mathrm{mod}hspace{0.3em}3)</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>k</m:mi> <m:mo>≔</m:mo> <m:msub> <m:mrow> <m:mi mathvariant=\"double-struck\">F</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </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:math> <jats:tex-math>k:= {{mathbb{F}}}_{q}left(T)</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the rational function field, and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0160_eq_006.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>m</m:mi> <m:mo>∈</m:mo> <m:msub> <m:mrow> <m:mi mathvariant=\"double-struck\">F</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411275","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 quasi-boundary value regularization method for the spherically symmetric backward heat conduction problem","authors":"Wei Cheng, Yi-Liang Liu","doi":"10.1515/math-2023-0171","DOIUrl":"https://doi.org/10.1515/math-2023-0171","url":null,"abstract":"In this article, we investigate a spherically symmetric backward heat conduction problem, starting from the final temperature. This problem is severely ill posed: the solution (if it exists) does not depend continuously on the final data. A conditional stability result of its solution is given. Further, we propose a quasi-boundary value regularization method to solve this ill-posed problem. Two Hölder type error estimates between the approximate solution and its exact solution are obtained under an <jats:italic>a priori</jats:italic> and an <jats:italic>a posteriori</jats:italic> regularization parameter choice rule, respectively.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411677","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":"Some estimates for commutators of sharp maximal function on the p-adic Lebesgue spaces","authors":"Jianglong Wu, Yunpeng Chang","doi":"10.1515/math-2023-0168","DOIUrl":"https://doi.org/10.1515/math-2023-0168","url":null,"abstract":"In this article, the main aim is to consider the boundedness of the nonlinear commutator of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic sharp maximal operator <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mrow> <m:mi mathvariant=\"script\">ℳ</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mi>♯</m:mi> </m:mrow> </m:msubsup> </m:math> <jats:tex-math>{{mathcal{ {mathcal M} }}}_{p}^{sharp }</jats:tex-math> </jats:alternatives> </jats:inline-formula> with symbols belonging to the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_003.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic Lipschitz spaces in the context of the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic version of (variable) Lebesgue spaces, by which some new characterizations of the Lipschitz spaces are obtained in the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0168_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-adic field context.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411718","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 structure fault tolerance of burnt pancake networks","authors":"Huifen Ge, Chengfu Ye, Shumin Zhang","doi":"10.1515/math-2023-0154","DOIUrl":"https://doi.org/10.1515/math-2023-0154","url":null,"abstract":"One of the symbolic parameters to measure the fault tolerance of a network is its connectivity. The <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> <jats:tex-math>H</jats:tex-math> </jats:alternatives> </jats:inline-formula>-structure connectivity and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> <jats:tex-math>H</jats:tex-math> </jats:alternatives> </jats:inline-formula>-substructure connectivity extend the classical connectivity and are more practical. For a graph <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_003.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> and its connected subgraph <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_004.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> <jats:tex-math>H</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_005.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> <jats:tex-math>H</jats:tex-math> </jats:alternatives> </jats:inline-formula>-structure connectivity <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_006.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>κ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>G</m:mi> <m:mo>;</m:mo> <m:mspace width=\"0.33em\" /> <m:mi>H</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>kappa left(G;hspace{0.33em}H)</jats:tex-math> </jats:alternatives> </jats:inline-formula> (resp. <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_007.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> <jats:tex-math>H</jats:tex-math> </jats:alternatives> </jats:inline-formula>-substructure connectivity <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0154_eq_008.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo>","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411278","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 digital Jordan surface theorem with respect to a graph connectedness","authors":"Josef Šlapal","doi":"10.1515/math-2023-0172","DOIUrl":"https://doi.org/10.1515/math-2023-0172","url":null,"abstract":"After introducing a graph connectedness induced by a given set of paths of the same length, we focus on the 2-adjacency graph on the digital line <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0172_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"double-struck\">Z</m:mi> </m:math> <jats:tex-math>{mathbb{Z}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> with a certain set of paths of length <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0172_eq_002.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> for every positive integer <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0172_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>. The connectedness in the strong product of three copies of the graph is used to define digital Jordan surfaces. These are obtained as polyhedral surfaces bounding the polyhedra that can be face-to-face tiled with digital tetrahedra.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375970","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 preconditioned iterative method for coupled fractional partial differential equation in European option pricing","authors":"Shuang Wu, Lot-Kei Chou, Xu Chen, Siu-Long Lei","doi":"10.1515/math-2023-0169","DOIUrl":"https://doi.org/10.1515/math-2023-0169","url":null,"abstract":"Recently, regime-switching option pricing based on fractional diffusion models has been used, which explains many significant empirical facts about financial markets better. There are many methods to solve the problem, but to the best of our knowledge, effective preconditioners for the second-order schemes have not been proposed. Thus, in this article, an implicit numerical scheme is developed for a regime-switching European option pricing problem under a multi-state tempered fractional model. The scheme is proven to be unconditionally stable and converges quadratically in space and linearly in time. Besides, the resulting linear system is solved using an iterative method, and a preconditioner is proposed to accelerate the rate of convergence. The preconditioner is constructed through circulant approximations to the Toeplitz blocks due to the coefficient matrix, which is is a block matrix with Toeplitz blocks. The spectral analysis of the preconditioned matrix is given, which demonstrates that the spectrum of the preconditioned matrix is clustered around 1. Numerical examples show the efficiency of the proposed method, and an empirical study is also provided.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095254","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 blow-up criterion for solution of 3D fractional Navier-Stokes-Coriolis equations in Lei-Lin-Gevrey spaces","authors":"Xiaochun Sun, Gaoting Xu, Yulian Wu","doi":"10.1515/math-2023-0170","DOIUrl":"https://doi.org/10.1515/math-2023-0170","url":null,"abstract":"In this article, we researched the existence of the solution to the fractional Navier-Stokes equations with the Coriolis force under initial data, which belong to the Lei-Lin-Gevrey spaces. Moreover, we showed a blow-up criterion, i.e., when the maximal time of existence <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0170_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>T</m:mi> </m:mrow> <m:mrow> <m:mo>*</m:mo> </m:mrow> </m:msup> </m:math> <jats:tex-math>{T}^{* }</jats:tex-math> </jats:alternatives> </jats:inline-formula> is finite, we proved that the norm of this same solution, in a specific Lei-Lin-Gevrey space, goes to infinity, as time tends to the maximal time of its existence.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139083696","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":"Eigenfunctions in Finsler Gaussian solitons","authors":"Caiyun Liu, Songting Yin","doi":"10.1515/math-2023-0167","DOIUrl":"https://doi.org/10.1515/math-2023-0167","url":null,"abstract":"Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate function, other first eigenfunctions must involve exponential functions and the so-called error functions. Moreover, the second eigenfunctions are also described. In the second part, we discuss the corresponding issues in Finsler Gaussian shrinking solitons, which is a natural generalization of Gaussian shrinking solitons. For the first eigenfunction, we complement an example to show that if a coordinate function is a first eigenfunction, then the Finsler Gaussian shrinking soliton must be a Euclidean measure space. For the second eigenfunction, we give some necessary and sufficient conditions for these spaces to be Euclidean measure spaces.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139083705","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":"An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition","authors":"Shuimu Zou, Jun Zhang","doi":"10.1515/math-2023-0128","DOIUrl":"https://doi.org/10.1515/math-2023-0128","url":null,"abstract":"In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce the equivalent reduced-dimension scheme and essential pole condition associated with the original problem, based on which a class of weighted Sobolev spaces are defined and a weak formulation and its discrete scheme are also established for each reduced one-dimensional problem. Second, the existence and uniqueness of the weak solution and the approximation solutions are given using the Lax-Milgram theorem. Then, we construct a class of projection operators, give their approximation properties, and then prove the error estimates of the approximation solutions. In addition, we construct a set of effective basis functions in approximate space using orthogonal property of Legendre polynomials and derive the equivalent matrix form of the discrete scheme. Finally, a large number of numerical examples are performed, and the numerical results illustrate the validity and high accuracy of our algorithm.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027937","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":"New fractional integral inequalities via Euler's beta function","authors":"Ohud Bulayhan Almutairi","doi":"10.1515/math-2023-0163","DOIUrl":"https://doi.org/10.1515/math-2023-0163","url":null,"abstract":"In this article, we present new fractional integral inequalities via Euler’s beta function in terms of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0163_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>s</m:mi> </m:math> <jats:tex-math>s</jats:tex-math> </jats:alternatives> </jats:inline-formula>-convex mappings. We develop some new generalizations of fractional trapezoid- and midpoint-type inequalities using the class of differentiable <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0163_eq_002.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>s</m:mi> </m:math> <jats:tex-math>s</jats:tex-math> </jats:alternatives> </jats:inline-formula>-convexity. The results obtained in this study extended other related results reported in the literature.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027992","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}