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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas最新文献

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Simple $$pmb {mathscr {B}}_{psi }$$ -groups 简单的 $$pmb {mathscr {B}}_{psi }$ 组
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-24 DOI: 10.1007/s13398-024-01631-x
Morteza Baniasad Azad
{"title":"Simple $$pmb {mathscr {B}}_{psi }$$ -groups","authors":"Morteza Baniasad Azad","doi":"10.1007/s13398-024-01631-x","DOIUrl":"https://doi.org/10.1007/s13398-024-01631-x","url":null,"abstract":"<p>In a finite group <i>G</i>, <span>( psi (G) )</span> denotes the sum of element orders of <i>G</i>. A finite group <i>G</i> is said to be a <span>(mathscr {B}_{psi })</span>-group if <span>( psi (H) &lt; |G| )</span> for any proper subgroup <i>H</i> of <i>G</i>. In Lazorec (Rev Real Acad Cienc Exact Fis Nat Ser A Mat 117:448, 2023), Lazorec put forward the following question: <b>Question.</b> What can be said about the <span>(mathscr {B}_{psi })</span> property of the finite simple groups <span>( {text {PSL}}(2, q) )</span>? In this paper, we show that if <i>S</i> is a finite simple group, such that <span>( S ne Alt(n) )</span> for any <span>( n ge 14 )</span>, then <i>S</i> is a <span>(mathscr {B}_{psi })</span>-group.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operators of the Cowen–Douglas class with strong flag structure 具有强旗结构的考文-道格拉斯类算子
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-21 DOI: 10.1007/s13398-024-01630-y
Yufang Xie, Kui Ji
{"title":"Operators of the Cowen–Douglas class with strong flag structure","authors":"Yufang Xie, Kui Ji","doi":"10.1007/s13398-024-01630-y","DOIUrl":"https://doi.org/10.1007/s13398-024-01630-y","url":null,"abstract":"<p>Let <span>(mathcal{F}mathcal{B}_{n}(Omega ))</span> denote operators in the Cowen–Douglas class <span>(mathcal {B}_{n}(Omega ))</span> possessing a flag structure. All the irreducible homogeneous operators in <span>(mathcal {B}_{n}(Omega ))</span> belong to this class. The unitary invariants of this class of operators include the curvature and the second fundamental form of the corresponding line bundle. In this paper, we introduce a subclass of <span>(mathcal{F}mathcal{B}_{n}(Omega ))</span> which possesses a “strong\" flag structure, and for which the curvature and the second fundamental form of the associated line bundle is a complete set of unitary invariants. We prove that this new class of operators is norm dense in <span>(mathcal {B}_{n}(Omega ))</span> up to similarity. We obtain a classification modulo conjugation by an invertible operator for a large class of operators possessing a strong flag structure. Along the way, it is shown that the number of the similarity invariants found recently can be reduced from <span>(frac{n(n-1)}{2}+1)</span> to <i>n</i>. Moreover, we obtain a complete characterization of weakly homogeneous operators with large index and flag structure.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Darboux theorems for geometric structures induced by closed forms 论封闭形式诱导的几何结构的达尔布定理
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-20 DOI: 10.1007/s13398-024-01632-w
Xavier Gràcia, Javier de Lucas, Xavier Rivas, Narciso Román-Roy
{"title":"On Darboux theorems for geometric structures induced by closed forms","authors":"Xavier Gràcia, Javier de Lucas, Xavier Rivas, Narciso Román-Roy","doi":"10.1007/s13398-024-01632-w","DOIUrl":"https://doi.org/10.1007/s13398-024-01632-w","url":null,"abstract":"<p>This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe mechanical systems), as well as certain cases of multisymplectic manifolds, while extends the Darboux theorem in new ways to <i>k</i>-symplectic and <i>k</i>-cosymplectic manifolds (all these structures appear in the geometric formulation of first-order classical field theories). Moreover, we discuss the existence of Darboux theorems for classes of precosymplectic, <i>k</i>-presymplectic, <i>k</i>-precosymplectic, and premultisymplectic manifolds, which are the geometrical structures underlying some kinds of singular field theories, i.e. with locally non-invertible Legendre maps. Approaches to Darboux theorems based on flat connections associated with geometric structures are given, while new results on polarisations for (<i>k</i>-)(pre)(co)symplectic structures arise.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence results of $$text {Spin}(2, n - 1)_0$$ -pseudo-Riemannian cobordisms $$text {Spin}(2, n - 1)_0$$ -伪黎曼共线性的存在性结果
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-18 DOI: 10.1007/s13398-024-01634-8
Valentina Bais, Victor Gustavo May Custodio, Rafael Torres
{"title":"Existence results of $$text {Spin}(2, n - 1)_0$$ -pseudo-Riemannian cobordisms","authors":"Valentina Bais, Victor Gustavo May Custodio, Rafael Torres","doi":"10.1007/s13398-024-01634-8","DOIUrl":"https://doi.org/10.1007/s13398-024-01634-8","url":null,"abstract":"<p>In this note, we study necessary and sufficient conditions for the existence of a Spin<span>((n + 1))</span>-dimensional cobordism that supports a non-singular and non-degenerate pseudo-Riemannian metric of signature <span>((2, n - 1))</span>, which restricts to a non-singular time-orientable Lorentzian metric on its boundary. The corresponding cobordism groups are computed.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Refining the integral Jensen inequality for finite signed measures using majorization 利用大化法完善有限符号度量的积分詹森不等式
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-18 DOI: 10.1007/s13398-024-01627-7
László Horváth
{"title":"Refining the integral Jensen inequality for finite signed measures using majorization","authors":"László Horváth","doi":"10.1007/s13398-024-01627-7","DOIUrl":"https://doi.org/10.1007/s13398-024-01627-7","url":null,"abstract":"<p>Among inequalities that use the concept of convexity, Jensen-type inequalities and majorization-type inequalities are significant and fundamental. An important and widely researched area in the study of Jensen-type inequalities is the refinement of such inequalities. In this paper, we provide a general method for refining the integral Jensen inequality for finite signed measures using integral majorization inequalities. Under the conditions considered in the paper, the results are unique, and even for measures, they give a new approach. We also provide interesting specific refinements, some of which relate to Jensen–Steffensen’s inequality. A new and extended version of this inequality is also obtained in the paper.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"168 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A mean field type equation on vector bundles 向量束上的均场型方程
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-17 DOI: 10.1007/s13398-024-01622-y
Jie Yang
{"title":"A mean field type equation on vector bundles","authors":"Jie Yang","doi":"10.1007/s13398-024-01622-y","DOIUrl":"https://doi.org/10.1007/s13398-024-01622-y","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"12 29","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141335102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpreting systems of continuity equations in spaces of probability measures through PDE duality 通过 PDE 对偶解释概率计量空间中的连续性方程组
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-17 DOI: 10.1007/s13398-024-01628-6
José A. Carrillo, David Gómez-Castro
{"title":"Interpreting systems of continuity equations in spaces of probability measures through PDE duality","authors":"José A. Carrillo, David Gómez-Castro","doi":"10.1007/s13398-024-01628-6","DOIUrl":"https://doi.org/10.1007/s13398-024-01628-6","url":null,"abstract":"<p>We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality is, under suitable assumptions, equivalent to gradient flow solutions in case the single/system of equations has this structure. In contrast, we can deal with a quite general system of nonlinear non-local, diffusive or not, system of PDEs without any variational structure.\u0000</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Common properties of elements in a ring and a Banach algebra and application to the $$nu $$ ν -convergence 环和巴拿赫代数中元素的共同性质及其在 $$nu $$ ν - 收敛中的应用
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-14 DOI: 10.1007/s13398-024-01629-5
Soufiane Hadji, H. Zguitti
{"title":"Common properties of elements in a ring and a Banach algebra and application to the \u0000 \u0000 \u0000 \u0000 $$nu $$\u0000 \u0000 ν\u0000 \u0000 -convergence","authors":"Soufiane Hadji, H. Zguitti","doi":"10.1007/s13398-024-01629-5","DOIUrl":"https://doi.org/10.1007/s13398-024-01629-5","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"76 18","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141338012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher analogues of discrete topological complexity 离散拓扑复杂性的高级类似物
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-13 DOI: 10.1007/s13398-024-01623-x
Hilal Alabay, Ayşe Borat, Esra Cihangirli, Esma Dirican Erdal
{"title":"Higher analogues of discrete topological complexity","authors":"Hilal Alabay, Ayşe Borat, Esra Cihangirli, Esma Dirican Erdal","doi":"10.1007/s13398-024-01623-x","DOIUrl":"https://doi.org/10.1007/s13398-024-01623-x","url":null,"abstract":"<p>In this paper, we introduce the <i>n</i>th discrete topological complexity and study its properties such as its relation with simplicial Lusternik–Schnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of <i>n</i>-th discrete topological complexity which is given by the <i>n</i>th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction: Injective dimension of cofinite modules and local cohomology 更正：共穷模块的注入维度与局部同调
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-06-12 DOI: 10.1007/s13398-024-01621-z
Fardin Asghari, R. Naghipour, M. Sedghi
{"title":"Correction: Injective dimension of cofinite modules and local cohomology","authors":"Fardin Asghari, R. Naghipour, M. Sedghi","doi":"10.1007/s13398-024-01621-z","DOIUrl":"https://doi.org/10.1007/s13398-024-01621-z","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"140 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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