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

{"title":"The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets","authors":"Dirceu Bagio, Cristóbal Gil Canto, Daniel Gonçalves, Danilo Royer","doi":"10.1007/s13398-024-01576-1","DOIUrl":"https://doi.org/10.1007/s13398-024-01576-1","url":null,"abstract":"<p>Let <i>R</i> be a commutative unital ring, <span>({ textsf {X}})</span> a subshift, and <span>({widetilde{{mathcal {A}}}}_R({ textsf {X}}))</span> the corresponding unital subshift algebra. We establish the reduction theorem for <span>({widetilde{{mathcal {A}}}}_R({ textsf {X}}))</span>. As a consequence, we obtain a Cuntz–Krieger uniqueness theorem for <span>({widetilde{{mathcal {A}}}}_R({ textsf {X}}))</span> and we show that <span>({widetilde{{mathcal {A}}}}_R({ textsf {X}}))</span> is semiprimitive (resp. semiprime) whenever <i>R</i> is a field (resp. a domain).</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"133 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199599","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}

{"title":"Weakly web-compact Banach spaces C(X), and $$Lip_0(M)$$ , $$mathcal {F}(M)$$ over metric spaces M","authors":"Jerzy Ka̧kol","doi":"10.1007/s13398-024-01567-2","DOIUrl":"https://doi.org/10.1007/s13398-024-01567-2","url":null,"abstract":"<p>The class of web-compact spaces (in sense of Orihuela), which encompasses a number of spaces, like Lindelöf <span>(Sigma )</span>-spaces (called also countably determined), Quasi-Suslin spaces, separable spaces, etc., applies to distinguish a class of weakly web-compact Banach spaces <i>E</i> whose dual unit ball is weak<span>(^{*})</span>-sequentially compact, consequently Banach spaces without quotients isomorphic to <span>(ell _{infty }.)</span> We prove however that for a Banach space <i>E</i> the space <span>(E_w)</span> (i.e. <i>E</i> with the weak topology) is web-compact if and only if <span>(E_w)</span> is a Lindelöf <span>(Sigma )</span>-space if and only if <span>(E_w)</span> contains a web-compact total subset. Consequently, for compact <i>X</i> the space <span>(C(X)_w)</span> is web-compact if and only if <i>X</i> is Gul’ko compact if and only if <span>(C(X)_w)</span> is a Lindelöf <span>(Sigma )</span>-space if and only if <span>(C_p(X))</span> contains a web-compact total subset. If <i>X</i> is compact and <span>(C(X)_w)</span> is web-compact, then <span>(C_p(X))</span> contains a complemented copy of the space <span>((c_{0})_p={(x_{n})in mathbb R^{omega }: x_{n}rightarrow 0})</span> with the topology of <span>(mathbb {R}^{omega })</span> but does not admit quotients isomorphic to <span>((ell _{infty })_{p}={(x_{n})in mathbb R^{omega }: sup _n|x_{n}|&lt;infty })</span>. We characterize weakly web-compact Banach spaces <span>(Lip_0(M))</span> of Lipschitz functions on metric spaces <i>M</i> and their predual <span>(mathcal {F}(M))</span>. In fact, <span>(Lip_0(M)_w)</span> is web-compact if and only if <i>M</i> is separable. Illustrating examples are provided.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199545","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}

{"title":"Cofiniteness of top local cohomology modules","authors":"","doi":"10.1007/s13398-024-01568-1","DOIUrl":"https://doi.org/10.1007/s13398-024-01568-1","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>R</em> be a commutative Noetherian ring with non-zero identity, <span> <span>(mathfrak {a})</span> </span> an ideal of <em>R</em>, <em>M</em> a finitely generated <em>R</em>-module with finite Krull dimension <em>d</em>, and <em>n</em> a non-negative integer. In this paper, we prove that the top local cohomology module <span> <span>({text {H}}^{d-n}_{mathfrak {a}}(M))</span> </span> is an <span> <span>(({text {FD}}_{&lt;n},mathfrak {a}))</span> </span>-cofinite <em>R</em>-module and <span> <span>({mathfrak {p}in {{text {Ass}}_R({text {H}}^{d-n}_{mathfrak {a}}(M))}:dim (R/mathfrak {p})ge {n}})</span> </span> is a finite set. As a consequence, we observe that <span> <span>({text {Supp}}_R({text {H}}^{d-1}_{mathfrak {a}}(M)))</span> </span> is a finite set when <em>R</em> is a semi-local ring.</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":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128066","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}

{"title":"Ellis enveloping semigroups in real closed fields","authors":"Elías Baro, Daniel Palacín","doi":"10.1007/s13398-024-01562-7","DOIUrl":"https://doi.org/10.1007/s13398-024-01562-7","url":null,"abstract":"<p>We introduce the Boolean algebra of <i>d</i>-semialgebraic (more generally, <i>d</i>-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless, we prove that in general these two families differ, even in the semialgebraic case over the real algebraic numbers. On the other hand, in the semialgebraic case we characterise real semialgebraic functions representing Boolean combinations of <i>d</i>-semialgebraic sets.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140117479","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}

{"title":"A geometric Jordan decomposition theorem","authors":"","doi":"10.1007/s13398-024-01569-0","DOIUrl":"https://doi.org/10.1007/s13398-024-01569-0","url":null,"abstract":"<h3>Abstract</h3> <p>For a compact convex set <em>K</em>, let <em>A</em>(<em>K</em>) denote the space of real-valued affine continuous functions, equipped with the supremum norm. For a closed subspace <span> <span>(X subset A(K))</span> </span> we give sufficient conditions, so that the weak<span> <span>(^*)</span> </span> closure of the set of extreme points of the dual unit ball has a decomposition in terms of ‘positive’ and ‘negative’ parts. We give several applications of these ideas to convexity and positivity. When <em>K</em> is a Choquet simplex, we show that the dual unit ball of such an <em>X</em>, inherits nice facial structure. We also use this to partly solve the open problem of exhibiting faces that are Choquet simplexes in the dual unit ball of a Banach space.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140100166","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}

{"title":"New bounds for a generalized logarithmic mean and Heinz mean","authors":"Jiahua Ding, Ling Zhu","doi":"10.1007/s13398-024-01566-3","DOIUrl":"https://doi.org/10.1007/s13398-024-01566-3","url":null,"abstract":"<p>In this paper, by using the monotone form of L’Hospital’s rule and a criterion for the monotonicity of quotient of two power series we present some sharp bounds for a generalized logarithmic mean and Heinz mean by weighted means of harmonic mean, geometric mean, arithmetic mean, two power means <span>(M_{1/2}(a,b))</span> and <span>(M_{2}(a,b))</span>. Operator versions of these inequalities are obtained except for those related to the quadratic mean <span>( M_{2}(a,b))</span>.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098790","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}

{"title":"$$L^infty $$ a-priori estimates for subcritical p-laplacian equations with a Carathéodory non-linearity","authors":"","doi":"10.1007/s13398-024-01565-4","DOIUrl":"https://doi.org/10.1007/s13398-024-01565-4","url":null,"abstract":"<h3>Abstract</h3> <p>Let us consider a quasi-linear boundary value problem <span> <span>( -Delta _p u= f(x,u),)</span> </span> in <span> <span>(Omega ,)</span> </span> with Dirichlet boundary conditions, where <span> <span>(Omega subset mathbb {R}^N )</span> </span>, with <span> <span>(p&lt;N,)</span> </span> is a bounded smooth domain strictly convex, and the non-linearity <em>f</em> is a Carathéodory function <em>p</em>-super-linear and subcritical. We provide <span> <span>(L^infty )</span> </span> a priori estimates for weak solutions, in terms of their <span> <span>(L^{p^*})</span> </span>-norm, where <span> <span>(p^*= frac{Np}{N-p} )</span> </span> is the critical Sobolev exponent. No hypotheses on the sign of the solutions, neither of the non-linearities are required. This method is based in elliptic regularity for the <em>p</em>-Laplacian combined either with Gagliardo–Nirenberg or with Caffarelli–Kohn–Nirenberg interpolation inequalities. By a subcritical non-linearity we mean, for instance, <span> <span>(|f(x,s)|le |x|^{-mu }, tilde{f}(s),)</span> </span> where <span> <span>(mu in (0,p),)</span> </span> and <span> <span>(tilde{f}(s)/|s|^{p_{mu }^*-1}rightarrow 0)</span> </span> as <span> <span>(|s|rightarrow infty )</span> </span>, here <span> <span>(p^*_{mu }:=frac{p(N-mu )}{N-p})</span> </span> is the critical Hardy–Sobolev exponent. Our non-linearities includes non-power non-linearities. In particular we prove that when <span> <span>(f(x,s)=|x|^{-mu },frac{|s|^{p^*_{mu }-2}s}{big [log (e+|s|)big ]^alpha },)</span> </span> with <span> <span>(mu in [1,p),)</span> </span> then, for any <span> <span>(varepsilon &gt;0)</span> </span> there exists a constant <span> <span>(C_varepsilon &gt;0)</span> </span> such that for any solution <span> <span>(uin H^1_0(Omega ))</span> </span>, the following holds <span> <span>$$begin{aligned} Big [log big (e+Vert uVert _{infty }big )Big ]^alpha le C_varepsilon , Big (1+Vert uVert _{p^*}Big )^{, (p^*_{mu }-p)(1+varepsilon )},, end{aligned}$$</span> </span>where <span> <span>(C_varepsilon )</span> </span> is independent of the solution <em>u</em>.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140100175","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}

{"title":"A Reilly type integral inequality for the p-Laplacian and applications to submanifolds of the unit sphere","authors":"Fábio R. dos Santos, Matheus N. Soares","doi":"10.1007/s13398-024-01563-6","DOIUrl":"https://doi.org/10.1007/s13398-024-01563-6","url":null,"abstract":"<p>An integral inequality for the compact (with or without boundary) submanifolds in the unit sphere with constant scalar curvature is established. Through this result, a characterization of totally geodesic spheres is obtained.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071161","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}

{"title":"Correction to: A note on the hit problem for the polynomial algebra in the case of odd primes and its application","authors":"Ɖặng Võ Phúc","doi":"10.1007/s13398-024-01564-5","DOIUrl":"https://doi.org/10.1007/s13398-024-01564-5","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"71 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140266659","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}

{"title":"Modes of convergence of random variables and algebraic genericity","authors":"G. Araújo, M. Fenoy, J. Fernández-Sánchez, J. López-Salazar, J. B. Seoane-Sepúlveda, J. M. Vecina","doi":"10.1007/s13398-024-01561-8","DOIUrl":"https://doi.org/10.1007/s13398-024-01561-8","url":null,"abstract":"<p>Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways and various kinds of convergence can be defined. Among the many types of convergence of sequences of random variables, we can highlight, for example, that convergence in <span>(L^p)</span>-sense implies convergence in probability, which, in turn, implies convergence in distribution, besides that all these implications are strict. In this paper, the relationship between several types of convergence of sequences of random variables will be analyzed from the perspective of lineability theory.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139954436","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}