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Existence and Nonexistence of Global Solutions to the Parabolic Equations on Locally Finite Graphs 局部有限图上抛物方程全局解的存在与不存在
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-21 DOI: 10.1007/s00025-024-02192-6
Yang Liu
{"title":"Existence and Nonexistence of Global Solutions to the Parabolic Equations on Locally Finite Graphs","authors":"Yang Liu","doi":"10.1007/s00025-024-02192-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02192-6","url":null,"abstract":"","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Brezis–Nirenberg Problem for Fractional p-Laplacian Systems in Unbounded Domains 无界域中分数 p-Laplacian 系统的 Brezis-Nirenberg 问题
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-20 DOI: 10.1007/s00025-024-02207-2
Yansheng Shen
{"title":"The Brezis–Nirenberg Problem for Fractional p-Laplacian Systems in Unbounded Domains","authors":"Yansheng Shen","doi":"10.1007/s00025-024-02207-2","DOIUrl":"https://doi.org/10.1007/s00025-024-02207-2","url":null,"abstract":"","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Borsik’s Properties of Topological Spaces and Their Applications 博尔西克拓扑空间特性及其应用
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-18 DOI: 10.1007/s00025-024-02194-4
Tomasz Natkaniec
{"title":"Borsik’s Properties of Topological Spaces and Their Applications","authors":"Tomasz Natkaniec","doi":"10.1007/s00025-024-02194-4","DOIUrl":"https://doi.org/10.1007/s00025-024-02194-4","url":null,"abstract":"<p>Let <i>X</i> be an uncountable Polish space. L̆ubica Holá showed recently that there are <span>(2^{mathfrak {c}})</span> quasi-continuous real valued functions defined on the uncountable Polish space <i>X</i> that are not Borel measurable. Inspired by Holá’s result, we are extending it in two directions. First, we prove that if <i>X</i> is an uncountable Polish space and <i>Y</i> is any Hausdorff space with <span>(|Y|ge 2)</span> then the family of all non-Borel measurable quasi-continuous functions has cardinality <span>(ge 2^{{mathfrak {c}}})</span>. Secondly, we show that the family of quasi-continuous non Borel functions from <i>X</i> to <i>Y</i> may contain big algebraic structures.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141058995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variations of the Mutual Curvature of Two Orthogonal Non-complementary Distributions 两个正交非互补分布的互曲率变化
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-18 DOI: 10.1007/s00025-024-02185-5
Vladimir Rovenski, Tomasz Zawadzki
{"title":"Variations of the Mutual Curvature of Two Orthogonal Non-complementary Distributions","authors":"Vladimir Rovenski, Tomasz Zawadzki","doi":"10.1007/s00025-024-02185-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02185-5","url":null,"abstract":"<p>On a smooth manifold with distributions <span>(mathcal {D}_1)</span> and <span>(mathcal {D}_2)</span> having trivial intersection, we consider the integral of their mutual curvature, as a functional of Riemannian metrics that make the distributions orthogonal. The mutual curvature is defined as the sum of sectional curvatures of planes spanned by all pairs of vectors from an orthonormal basis, such that one vector of the pair belongs to <span>(mathcal {D}_1)</span> and the second vector belongs to <span>(mathcal {D}_2)</span>. As such, it interpolates between the sectional curvature of a plane field (if both distributions are one-dimensional), and the mixed scalar curvature of a Riemannian almost product structure (if both distributions together span the tangent bundle). We derive Euler–Lagrange equations for the functional, formulated in terms of extrinsic geometry of distributions, i.e., their second fundamental forms and integrability tensors. We give examples of critical metrics for distributions defined on domains of Riemannian submersions, twisted products and <i>f</i>–<i>K</i>-contact manifolds.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141064146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence Theorems for Parameter Dependent Weakly Continuous Operators with Applications 参数相关弱连续算子的存在定理及其应用
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00025-024-02189-1
Grzegorz Andrzejczak, Marek Galewski, Dumitru Motreanu
{"title":"Existence Theorems for Parameter Dependent Weakly Continuous Operators with Applications","authors":"Grzegorz Andrzejczak, Marek Galewski, Dumitru Motreanu","doi":"10.1007/s00025-024-02189-1","DOIUrl":"https://doi.org/10.1007/s00025-024-02189-1","url":null,"abstract":"<p>The paper presents results on the solvability and parameter dependence for problems driven by weakly continuous potential operators with continuously differentiable and coercive potential. We provide a parametric version on the existence result to nonlinear equations involving coercive and weakly continuous operators. Applications address a variant of elastic beam equation.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relativity of Reductive Chain Complexes of Non-abelian Simplexes 非阿贝尔简体还原链复合物的相对性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00025-024-02188-2
A. Zuevsky
{"title":"Relativity of Reductive Chain Complexes of Non-abelian Simplexes","authors":"A. Zuevsky","doi":"10.1007/s00025-024-02188-2","DOIUrl":"https://doi.org/10.1007/s00025-024-02188-2","url":null,"abstract":"<p>Chain total double complexes with reductive differentials for non-abelian simplexes with associated spaces are considered. It is conjectured that corresponding relative cohomology is equivalent to the coset space of vanishing functionals over non-vanishing functionals related to differentials of complexes. The conjecture is supported by the theorem for the case of spaces of correlation functions and generalized connections on vertex operator algebra bundles.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Directional Compactness, Approximations and Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Constraints 有约束条件的非光滑矢量均衡问题的方向紧凑性、近似性和效率条件
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-13 DOI: 10.1007/s00025-024-02182-8
Tran Van Su
{"title":"Directional Compactness, Approximations and Efficiency Conditions for Nonsmooth Vector Equilibrium Problems with Constraints","authors":"Tran Van Su","doi":"10.1007/s00025-024-02182-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02182-8","url":null,"abstract":"<p>In this article, we introduce and study a natural version of the directional compactness, which can be viewed as one of the effective tools for constructing sufficient conditions in nonsmooth vector equilibrium problems. We also provide the generalized Hadamard directional derivative notion which is closely related to a version of contingent derivative. The relation among the first-order approximations/the Clarke generalized Jacobian and the generalized Hadamard directional differentiability is formulated. Using the tool of approximations, a new version of the constraint qualification of the (CQ) type is proposed for establishing KT-type necessary nonsmooth optimality conditions via the generalized Hadamard directional derivatives for the weak/and strict efficiency of constrained nonsmooth vector equilibrium problems. As applications, we study a nonsmooth vector equilibrium problem with set, cone constraints using approximations and the constraint qualification (CQ).</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Left T-Nilpotent Rings 论左 T 无蕴环
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-11 DOI: 10.1007/s00025-024-02187-3
Ryszard R. Andruszkiewicz, Marek Kȩpczyk
{"title":"On Left T-Nilpotent Rings","authors":"Ryszard R. Andruszkiewicz, Marek Kȩpczyk","doi":"10.1007/s00025-024-02187-3","DOIUrl":"https://doi.org/10.1007/s00025-024-02187-3","url":null,"abstract":"<p>It is shown that any ring being a sum of two left <i>T</i>-nilpotent subrings is left <i>T</i>-nilpotent. The paper contains the description of all the semigroups <i>S</i> such that an <i>S</i>-graded ring <span>(R=bigoplus _{sin S}A_s)</span> has the property that the left <i>T</i>-nilpotency of all subrings among the subgroups <span>(A_s)</span> of the additive group of <i>R</i> implies the left <i>T</i>-nilpotency of <i>R</i>. Furthermore, this result is extended to rings <i>R</i> being <i>S</i>-sums.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upper Triangular Operator Matrices and Stability of Their Various Spectra 上三角算子矩阵及其各种谱的稳定性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-11 DOI: 10.1007/s00025-024-02181-9
Nikola Sarajlija
{"title":"Upper Triangular Operator Matrices and Stability of Their Various Spectra","authors":"Nikola Sarajlija","doi":"10.1007/s00025-024-02181-9","DOIUrl":"https://doi.org/10.1007/s00025-024-02181-9","url":null,"abstract":"<p>Denote by <span>(T_n^d(A))</span> an upper triangular operator matrix of dimension <span>(nin mathbb {N})</span> whose diagonal entries <span>(D_i, 1le ile n)</span>, are known, and <span>(A=(A_{ij})_{1le i&lt;jle n})</span> is an unknown tuple of operators. This article is aimed at investigation of defect spectrum <span>(mathcal {D}^{sigma _*}=bigcup _{i=1}^nsigma _*(D_i){setminus }sigma _*(T_n^d(A)))</span>, where <span>(sigma _*)</span> is a spectrum corresponding to various types of invertibility: (left, right) invertibility, (left, right) Fredholm invertibility, left/right Weyl invertibility. We give characterizations for each of the previous types, and provide some sufficent conditions for the stability of certain spectrum (the case <span>(mathcal {D}^{sigma _*}=emptyset )</span>). The results are proved for all matrix dimensions <span>(nge 2)</span>, and they hold in arbitrary Hilbert spaces without assuming separability, thus generalizing results from Wu and Huang (Ann Funct Anal 11(3):780–798, 2020; Acta Math Sin 36(7):783–796, 2020). We also retrieve a result from Bai et al. (J Math Anal Appl 434(2):1065–1076, 2016) in the case <span>(n=2)</span>, and we provide a precise form of the well known ‘filling in holes’ result from Han et al. (Proc Am Math Soc 128(1):119–123, 2000).</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric Methodology for Analyzing Timelike Curve Flows in Minkowski Space 分析闵科夫斯基空间中 Timelike 曲线流的几何方法论
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-05-11 DOI: 10.1007/s00025-024-02178-4
Mehmet Bektaş, Dae Won Yoon, Zühal Küçükarslan Yüzbaşı
{"title":"Geometric Methodology for Analyzing Timelike Curve Flows in Minkowski Space","authors":"Mehmet Bektaş, Dae Won Yoon, Zühal Küçükarslan Yüzbaşı","doi":"10.1007/s00025-024-02178-4","DOIUrl":"https://doi.org/10.1007/s00025-024-02178-4","url":null,"abstract":"<p>The present study introduces an innovative link between integrable equations and the motion of timelike curves within a three-dimensional Minkowski space. This study aims to establish an anology between the modified generalizations of the Heisenberg spin chain model equation, a complex Korteweg–de Vries equation, and the Ablowitz–Kaup–Newell–Segur hierarchy systems of real type, respectively. This is accomplished through the application of specific functions, which are derived based on the curvatures and torsions of three distinct curves and their corresponding Frenet frames in a 3-dimensional Minkowski space. Making use of this method, the geometric derivation of the integrable equation has been demonstrated with success.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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