Open Mathematics最新文献

{"title":"Complex dynamics of a nonlinear discrete predator-prey system with Allee effect","authors":"Jing Wang, Ceyu Lei","doi":"10.1515/math-2024-0013","DOIUrl":"https://doi.org/10.1515/math-2024-0013","url":null,"abstract":"The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. In this article, we study a discrete predator-prey system with Holling type II functional response and Allee effect. First, the number of fixed points of the system, local stability, and global stability is discussed. The population changes of predator and prey under strong or weak Allee effects are proved using the nullclines and direction field, respectively. Second, using the bifurcation theory, the bifurcation conditions for the system to undergo transcritical bifurcation and Neimark-Sacker bifurcation at the equilibrium point are obtained. Finally, the dynamic behavior of the system is analyzed by numerical simulation of bifurcation diagram, phase diagram, and maximum Lyapunov exponent diagram. The results show that the system will produce complex dynamic phenomena such as periodic state, quasi-periodic state, and chaos.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529762","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":"Silting modules over a class of Morita rings","authors":"Dadi Asefa, Qingbing Xu","doi":"10.1515/math-2024-0009","DOIUrl":"https://doi.org/10.1515/math-2024-0009","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-2024-0009_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>Δ</m:mi> <m:mo>=</m:mo> <m:mfenced open=\"(\" close=\")\"> <m:mrow> <m:mtable> <m:mtr> <m:mtd> <m:mi>A</m:mi> </m:mtd> <m:mtd> <m:mmultiscripts> <m:mrow> <m:mi>N</m:mi> </m:mrow> <m:mrow> <m:mi>B</m:mi> </m:mrow> <m:none/> <m:mprescripts/> <m:mrow> <m:mi>A</m:mi> </m:mrow> <m:none/> </m:mmultiscripts> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mmultiscripts> <m:mrow> <m:mi>M</m:mi> </m:mrow> <m:mrow> <m:mi>A</m:mi> </m:mrow> <m:none/> <m:mprescripts/> <m:mrow> <m:mi>B</m:mi> </m:mrow> <m:none/> </m:mmultiscripts> </m:mtd> <m:mtd> <m:mi>B</m:mi> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mfenced> </m:math> <jats:tex-math>Delta =left(begin{array}{cc}A&amp; {}_{A}N_{B} {}_{B}M_{A}&amp; Bend{array}right)</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a Morita ring, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0009_eq_002.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>M</m:mi> <m:msub> <m:mrow> <m:mo>⊗</m:mo> </m:mrow> <m:mrow> <m:mi>A</m:mi> </m:mrow> </m:msub> <m:mi>N</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>=</m:mo> <m:mi>N</m:mi> <m:msub> <m:mrow> <m:mo>⊗</m:mo> </m:mrow> <m:mrow> <m:mi>B</m:mi> </m:mrow> </m:msub> <m:mi>M</m:mi> </m:math> <jats:tex-math>M{otimes }_{A}N=0=N{otimes }_{B}M</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0009_eq_003.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> be left <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0009_eq_004.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>A</m:mi> </m:math> <jats:tex-math>A</jats:tex-math> </jats:alternatives> </jats:inline-formula>-module and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0009_eq_005.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>Y</m:mi> </m:math> <jats:tex-math>Y</jats:tex-math> </jats:alternatives> </jats:inline-formula> be left <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0009_eq_006.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>B</m:mi> </m:math> <jats:tex-math>B</jats:tex-math> </jats:alternatives> </jats:inline-formula>-module. We prove that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"htt","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190597","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 distributionally robust reward-risk model for portfolio optimization","authors":"Yijia Zhou, Lijun Xu","doi":"10.1515/math-2024-0010","DOIUrl":"https://doi.org/10.1515/math-2024-0010","url":null,"abstract":"A new distributionally robust ratio optimization model is proposed under the known first and second moments of the uncertain distributions. In this article, both standard deviation (SD) and conditional value-at-risk (CVaR) are used to measure the risk, avoiding both fat-tail and volatility. The new model can be reduced to a simple distributionally robust model under assumptions on the measurements of reward, CVaR and SD. Furthermore, it can be rewritten as a tractable semi-definite programming problem by the duality theorem under partially known information of the uncertain parameters. Finally, the model is tested on portfolio problems and verified from numerical results that it can give a reasonable decision under only the first and second moments.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148598","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":"Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results","authors":"Adel M. Al-Mahdi","doi":"10.1515/math-2024-0011","DOIUrl":"https://doi.org/10.1515/math-2024-0011","url":null,"abstract":"In this study, we consider a viscoelastic Shear beam model with no rotary inertia. Specifically, we study <jats:disp-formula> <jats:alternatives> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0011_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:mtable displaystyle=\"true\" columnspacing=\"0.33em\"> <m:mtr> <m:mtd columnalign=\"right\"> <m:msub> <m:mrow> <m:mi>ρ</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>φ</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> <m:mi>t</m:mi> </m:mrow> </m:msub> <m:mo>−</m:mo> <m:mi>κ</m:mi> <m:msub> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>φ</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>g</m:mi> <m:mo>∗</m:mo> <m:msub> <m:mrow> <m:mi>φ</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mi>x</m:mi> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mtd> <m:mtd columnalign=\"center\"> <m:mo>=</m:mo> </m:mtd> <m:mtd columnalign=\"left\"> <m:mn>0</m:mn> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=\"right\"> <m:mo>−</m:mo> <m:mi>b</m:mi> <m:msub> <m:mrow> <m:mi>ψ</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mi>κ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>φ</m:mi> </m:mrow> <m:mrow> <m:mi>x</m:mi> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mtd> <m:mtd columnalign=\"center\"> <m:mo>=</m:mo> </m:mtd> <m:mtd columnalign=\"left\"> <m:mn>0</m:mn> <m:mo>,</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:math> <jats:tex-math>begin{array}{rcl}{rho }_{1}{varphi }_{tt}-kappa {left({varphi }_{x}+psi )}_{x}+left(gast {varphi }_{xx})left(t)&amp; =&amp; 0, -b{psi }_{xx}+kappa left({varphi }_{x}+psi )&amp; =&amp; 0,end{array}</jats:tex-math> </jats:alternatives> </jats:disp-formula> where the convolution memory function <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0011_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> belongs to a class of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0011_eq_003.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>∞</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>{L}^{1}left(0,infty )</jats:tex-math> </jats:alternati","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153925","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":"Almost periodic dynamics for a delayed differential neoclassical growth model with discontinuous control strategy","authors":"Qian Wang, Wei Wang, Qian Zhan","doi":"10.1515/math-2024-0006","DOIUrl":"https://doi.org/10.1515/math-2024-0006","url":null,"abstract":"In this study, we are concerned with the existence and exponential stability issue of a delayed differential neoclassical growth model with discontinuous control strategy. By employing the Filippov’s theory and dichotomy theory, together with the Lyapunov functional method, novel criteria on existence and exponential stability are established for the addressed model. The established theoretical results extend and supplement the related results in the existing literature. Moreover, a simulation example is presented to verify the practicability of the proposed results.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148553","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":"Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model","authors":"Wenjing Hu, Wei Wang, Yi Wu","doi":"10.1515/math-2024-0003","DOIUrl":"https://doi.org/10.1515/math-2024-0003","url":null,"abstract":"In this article, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0003_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>α</m:mi> <m:mo>,</m:mo> <m:mi>β</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(alpha ,beta )</jats:tex-math> </jats:alternatives> </jats:inline-formula>-mixing random variables are presented. An application to simple linear errors-in-variables model is provided. Simulation studies are also carried out to support the theoretical results.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148554","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 distribution of powered numbers","authors":"Jörg Brüdern, Olivier Robert","doi":"10.1515/math-2024-0007","DOIUrl":"https://doi.org/10.1515/math-2024-0007","url":null,"abstract":"Asymptotic formulae are established for the number of natural numbers <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0007_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>m</m:mi> </m:math> <jats:tex-math>m</jats:tex-math> </jats:alternatives> </jats:inline-formula> with largest square-free divisor not exceeding <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0007_eq_002.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:mi mathvariant=\"italic\">ϑ</m:mi> </m:mrow> </m:msup> </m:math> <jats:tex-math>{m}^{{vartheta }}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, for any fixed positive parameter <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0007_eq_003.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"italic\">ϑ</m:mi> </m:math> <jats:tex-math>{vartheta }</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Related counting functions are also considered.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148604","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":"(p, q)-Compactness in spaces of holomorphic mappings","authors":"Antonio Jiménez-Vargas, David Ruiz-Casternado","doi":"10.1515/math-2023-0183","DOIUrl":"https://doi.org/10.1515/math-2023-0183","url":null,"abstract":"Based on the concept of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0183_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(p,q)</jats:tex-math> </jats:alternatives> </jats:inline-formula>-compact operator for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0183_eq_002.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mi>∞</m:mi> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:math> <jats:tex-math>pin left[1,infty ]</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-2023-0183_eq_003.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:msup> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mo>*</m:mo> </m:mrow> </m:msup> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:math> <jats:tex-math>qin left[1,{p}^{* }]</jats:tex-math> </jats:alternatives> </jats:inline-formula>, we introduce and study the notion of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0183_eq_004.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(p,q)</jats:tex-math> </jats:alternatives> </jats:inline-formula>-compact holomorphic mapping between Banach spaces. We prove that the space formed by such mappings is a surjective <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0183_eq_005.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> <m:mi>q</m:mi> <m:mo>∕</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>+</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>pq/left(p+q)</jats:tex-math> </jats:alternatives> </jats:inline-formula>-Banach bounded-holomorphic ideal that can be generated by composition with the ideal of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0183_eq_006.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> <jats:tex-math>left(p,q)</jats:tex-math> </jats:alternatives> </jats:inline-formu","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058719","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 j{mathscr{j}}-Noetherian rings","authors":"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Najib Mahdou, El Houssaine Oubouhou","doi":"10.1515/math-2024-0014","DOIUrl":"https://doi.org/10.1515/math-2024-0014","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-2024-0014_eq_003.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>R</m:mi> </m:math> <jats:tex-math>R</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a commutative ring with identity and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_004.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">j</m:mi> </m:math> <jats:tex-math>{mathscr{j}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> an ideal of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_005.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>R</m:mi> </m:math> <jats:tex-math>R</jats:tex-math> </jats:alternatives> </jats:inline-formula>. An ideal <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_006.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>I</m:mi> </m:math> <jats:tex-math>I</jats:tex-math> </jats:alternatives> </jats:inline-formula> of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_007.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>R</m:mi> </m:math> <jats:tex-math>R</jats:tex-math> </jats:alternatives> </jats:inline-formula> is said to be a <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_008.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">j</m:mi> </m:math> <jats:tex-math>{mathscr{j}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-ideal if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_009.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>I</m:mi> <m:mspace width=\"0.33em\"/> <m:mo>⊈</m:mo> <m:mspace width=\"0.33em\"/> <m:mi mathvariant=\"script\">j</m:mi> </m:math> <jats:tex-math>Ihspace{0.33em} nsubseteq hspace{0.33em}{mathscr{j}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We define <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_010.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>R</m:mi> </m:math> <jats:tex-math>R</jats:tex-math> </jats:alternatives> </jats:inline-formula> to be a <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2024-0014_eq_011.png\"/> <m:mat","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058614","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 deferred f-statistical convergence for double sequences","authors":"Yahui Zhu, Ang Shen, Zhongzhi Wang, Weicai Peng","doi":"10.1515/math-2023-0174","DOIUrl":"https://doi.org/10.1515/math-2023-0174","url":null,"abstract":"In this article, we first put forward the concept of deferred <jats:italic>f</jats:italic>-double natural density for double sequences, where <jats:italic>f</jats:italic> is an unbounded modulus. Then, we combine <jats:italic>f</jats:italic>-density with deferred statistical convergence for double sequences and investigate deferred <jats:italic>f</jats:italic>-statistical convergence and strongly deferred <jats:italic>Cesàro</jats:italic> summability with respect to modulus <jats:italic>f</jats:italic>. Moreover, we extend these concepts to deferred <jats:italic>f</jats:italic>-statistical convergence for double sequences of random variables in the Wijsman sense and prove some inclusions. Finally, we consider the concepts of deferred <jats:italic>f</jats:italic>-statistical convergence of order <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0174_eq_001.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>α</m:mi> </m:math> <jats:tex-math>alpha </jats:tex-math> </jats:alternatives> </jats:inline-formula> and strongly deferred <jats:italic>f</jats:italic>-summability of order <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2023-0174_eq_002.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>α</m:mi> </m:math> <jats:tex-math>alpha </jats:tex-math> </jats:alternatives> </jats:inline-formula> for double sequences and obtain some conclusions.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801293","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}