Results in Mathematics最新文献

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Bounds on the Moduli of Eigenvalues of Rational Matrices 有理矩阵特征值模数的界限
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-20 DOI: 10.1007/s00025-024-02238-9
Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman
{"title":"Bounds on the Moduli of Eigenvalues of Rational Matrices","authors":"Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman","doi":"10.1007/s00025-024-02238-9","DOIUrl":"https://doi.org/10.1007/s00025-024-02238-9","url":null,"abstract":"<p>A rational matrix is a matrix-valued function <span>(R(lambda ): {mathbb {C}} rightarrow M_p)</span> such that <span>(R(lambda ) = begin{bmatrix} r_{ij}(lambda ) end{bmatrix} _{ptimes p})</span>, where <span>(r_{ij}(lambda ))</span> are scalar complex rational functions in <span>(lambda )</span> for <span>(i,j=1,2,ldots ,p)</span>. The aim of this paper is to obtain bounds on the moduli of eigenvalues of rational matrices in terms of the moduli of their poles. To a given rational matrix <span>(R(lambda ))</span> we associate a block matrix <span>({mathcal {C}}_R)</span> whose blocks consist of the coefficient matrices of <span>(R(lambda ))</span>, as well as a scalar real rational function <i>q</i>(<i>x</i>) whose coefficients consist of the norm of the coefficient matrices of <span>(R(lambda ))</span>. We prove that a zero of <i>q</i>(<i>x</i>) which is greater than the moduli of all the poles of <span>(R(lambda ))</span> will be an upper bound on the moduli of eigenvalues of <span>(R(lambda ))</span>. Moreover, by using a block matrix associated with <i>q</i>(<i>x</i>), we establish bounds on the zeros of <i>q</i>(<i>x</i>), which in turn yields bounds on the moduli of eigenvalues of <span>(R(lambda ))</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740417","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
Bialgebraic Structure on a Coder Pair of Any Weight 任意权重编码器对的双代数结构
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-20 DOI: 10.1007/s00025-024-02241-0
Mengqi Li, Tianshui Ma
{"title":"Bialgebraic Structure on a Coder Pair of Any Weight","authors":"Mengqi Li, Tianshui Ma","doi":"10.1007/s00025-024-02241-0","DOIUrl":"https://doi.org/10.1007/s00025-024-02241-0","url":null,"abstract":"<p>In this paper, we establish a bialgebraic structure on a Coder pair of any weight <span>(lambda )</span> (i.e., a coassociative coalgebra with a coderivation of weight <span>(lambda )</span>), which is consistent with the differential antisymmetric infinitesimal bialgebra in (SIGMA 19:018, 2023) when the weight <span>(lambda =0)</span>.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740418","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
Entropy of Non-autonomous Iterated Function Systems 非自主迭代函数系统的熵
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-18 DOI: 10.1007/s00025-024-02233-0
Yujun Ju, Huoxia Liu, Qigui Yang
{"title":"Entropy of Non-autonomous Iterated Function Systems","authors":"Yujun Ju, Huoxia Liu, Qigui Yang","doi":"10.1007/s00025-024-02233-0","DOIUrl":"https://doi.org/10.1007/s00025-024-02233-0","url":null,"abstract":"<p>The aim of this paper is to investigate the topological entropy for non-autonomous iterated function systems (NAIFSs) introduced by Ghane and Sarkooh. An inequality formula for two topological entropies with a factor map of NAIFSs is established. We extend the topological analogue of the Abramov–Rokhlin formula for the entropy of a skew product transformation. Finally, the partial variational principle is obtained about the measure-theoretic entropy and topological entropy for NAIFSs.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740419","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
Integral Radial m-Bakry–Émery Ricci Curvatures, Riccati Inequalities, and Ambrose-type Theorems 积分径向 m-Bakry-Émery 里奇曲率、里卡蒂不等式和安布罗斯型定理
IF 1.1 3区 数学
Results in Mathematics Pub Date : 2024-07-15 DOI: 10.1007/s00025-024-02165-9
H. Tadano
{"title":"Integral Radial m-Bakry–Émery Ricci Curvatures, Riccati Inequalities, and Ambrose-type Theorems","authors":"H. Tadano","doi":"10.1007/s00025-024-02165-9","DOIUrl":"https://doi.org/10.1007/s00025-024-02165-9","url":null,"abstract":"","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141649182","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
Congruence Solvability in Finite Moufang Loops of Order Coprime to Three 三阶共三次方有限毛方环中的同余可解性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-15 DOI: 10.1007/s00025-024-02231-2
Aleš Drápal, Petr Vojtěchovský
{"title":"Congruence Solvability in Finite Moufang Loops of Order Coprime to Three","authors":"Aleš Drápal, Petr Vojtěchovský","doi":"10.1007/s00025-024-02231-2","DOIUrl":"https://doi.org/10.1007/s00025-024-02231-2","url":null,"abstract":"<p>We prove that a normal subloop <i>X</i> of a Moufang loop <i>Q</i> induces an abelian congruence of <i>Q</i> if and only if <span>(u(xy) = (uy)x)</span> for all <span>(x,yin X)</span> and <span>(uin Q)</span>. This characterization is then used to show that classically solvable finite 3-divisible Moufang loops are congruence solvable.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717797","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
Almost Invertible Operators 几乎不可逆的算子
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-15 DOI: 10.1007/s00025-024-02226-z
Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh
{"title":"Almost Invertible Operators","authors":"Zakariae Aznay, Abdelmalek Ouahab, Hassan Zariouh","doi":"10.1007/s00025-024-02226-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02226-z","url":null,"abstract":"<p>This paper aims to provide a thorough characterization of the family of all Cantor-Bendixson derivatives of the spectrum, Browder spectrum, and the Drazin spectrum of bounded linear operators using projections and invariant subspaces. Furthermore, our findings demonstrate that if two commuting operators, <i>R</i> and <i>T</i>, satisfy the conditions that <i>R</i> is Riesz and <i>T</i> is a direct sum of an invertible operator and an operator with an at most countable spectrum, then <span>(T+R)</span> can also be represented as a direct sum of an invertible operator and an operator with an at most countable spectrum. </p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717795","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 a Characterization of the Logarithmic Mean 论对数平均数的特征
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-13 DOI: 10.1007/s00025-024-02230-3
Timothy Nadhomi, Maciej Sablik, Justyna Sikorska
{"title":"On a Characterization of the Logarithmic Mean","authors":"Timothy Nadhomi, Maciej Sablik, Justyna Sikorska","doi":"10.1007/s00025-024-02230-3","DOIUrl":"https://doi.org/10.1007/s00025-024-02230-3","url":null,"abstract":"<p>In the present note we are interested in proving the counterpart of the (right-hand side of the) celebrated Hermite–Hadamard inequality for <span>(varphi )</span>-convex functions. In particular, we prove that the only <span>(varphi )</span>-convex function for which the Hermite–Hadamard inequality holds with the Lagrangian mean on the right-hand side is (up to an affine transformation) the <span>(log )</span>-convex function.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610859","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 the Dynamics of a Three-dimensional Differential System Related to the Normalized Ricci Flow on Generalized Wallach Spaces 论广义瓦拉几空间上与归一化利玛窦流相关的三维微分系统动力学
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-12 DOI: 10.1007/s00025-024-02229-w
Nurlan Abiev
{"title":"On the Dynamics of a Three-dimensional Differential System Related to the Normalized Ricci Flow on Generalized Wallach Spaces","authors":"Nurlan Abiev","doi":"10.1007/s00025-024-02229-w","DOIUrl":"https://doi.org/10.1007/s00025-024-02229-w","url":null,"abstract":"<p>We study the behavior of a three-dimensional dynamical system with respect to some set <span>(textbf{S})</span> given in 3-dimensional euclidean space. Geometrically such a system arises from the normalized Ricci flow on some class of generalized Wallach spaces that can be described by a real parameter <span>(ain (0,1/2))</span>, as for <span>(textbf{S})</span> it represents the set of invariant Riemannian metrics of positive sectional curvature on the Wallach spaces. Establishing that <span>(textbf{S})</span> is bounded by three conic surfaces and regarding the normalized Ricci flow as an abstract dynamical system we find out the character of interrelations between that system and <span>(textbf{S})</span> for all <span>(ain (0,1/2))</span>. These results can cover some well-known results, in particular, they can imply that the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curvature into metrics with mixed sectional curvature on the Wallach spaces corresponding to the cases <span>(ain {1/9, 1/8, 1/6})</span> of generalized Wallach spaces.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610853","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
Inequalities for Maximal Operators Associated with a Family of General Sets 与一般集合族相关的最大算子不等式
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-12 DOI: 10.1007/s00025-024-02224-1
Biswaranjan Behera, Md. Nurul Molla
{"title":"Inequalities for Maximal Operators Associated with a Family of General Sets","authors":"Biswaranjan Behera, Md. Nurul Molla","doi":"10.1007/s00025-024-02224-1","DOIUrl":"https://doi.org/10.1007/s00025-024-02224-1","url":null,"abstract":"<p>Let <span>({mathbb {E}}={E_r(x):r&gt;0,xin X})</span> be a family of open subsets of a topological space <i>X</i> equipped with a nonnegative Borel measure <span>(mu )</span> satisfying some basic properties. We establish sharp quantitative weighted norm inequalities for the Hardy–Littlewood maximal operator <span>(M_{{mathbb {E}}})</span> associated with <span>({mathbb {E}})</span> in terms of mixed <span>(A_p)</span>–<span>(A_infty )</span> constants. The main ingredient to prove this result is a sharp form of a weak reverse Hölder inequality for the <span>(A_{infty ,{mathbb {E}}})</span> weights. As an application of this inequality, we also provide a quantitative version of the open property for <span>(A_{p,{mathbb {E}}})</span> weights. Next, we prove a covering lemma in this setting and using this lemma establish the endpoint Fefferman–Stein weighted inequality for the maximal operator <span>(M_{{mathbb {E}}})</span>. Moreover, vector-valued extensions for maximal inequalities are also obtained in this context.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610863","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 Automorphisms of Differential Extensions of Characteristic p 特征 p 的微分扩展的自动形
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-07-09 DOI: 10.1007/s00025-024-02234-z
S. Pumplün
{"title":"The Automorphisms of Differential Extensions of Characteristic p","authors":"S. Pumplün","doi":"10.1007/s00025-024-02234-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02234-z","url":null,"abstract":"<p>Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension <i>K</i> of exponent one of a field <i>F</i>, <i>F</i> of characteristic <i>p</i>, or of a central division algebra over a purely inseparable field extension of <i>F</i>. Associative differential extensions are well known central simple algebras first defined by Amitsur and Jacobson. We explicitly compute the automorphisms of nonassociative differential extensions. These are canonically obtained by restricting automorphisms of the differential polynomial ring used in the construction of the algebra. In particular, we obtain descriptions for the automorphisms of associative differential extensions of <i>D</i> and <i>K</i>, which are known to be inner.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141586098","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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