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Projections in the J-sums of Banach spaces 巴拿赫空间 J 和中的投影
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-17 DOI: 10.1007/s13398-024-01654-4
Manuel González, Javier Pello
{"title":"Projections in the J-sums of Banach spaces","authors":"Manuel González, Javier Pello","doi":"10.1007/s13398-024-01654-4","DOIUrl":"https://doi.org/10.1007/s13398-024-01654-4","url":null,"abstract":"<p>We study some families of projections in the <i>J</i>-sums of Banach spaces <span>(J(Phi ))</span> and <span>({hat{J}}(Phi ))</span> introduced by Bellenot. As an application, we show that, under some conditions, <span>(J(Phi ))</span> and <span>({hat{J}}(Phi ))</span> are subprojective, i.e., every closed infinite-dimensional subspace of either of them contains a complemented infinite-dimensional subspace.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261165","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
New bounds on the cardinality of n-Hausdorff and n-Urysohn spaces n-Hausdorff 和 n-Urysohn 空间心性的新界限
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-17 DOI: 10.1007/s13398-024-01660-6
Maddalena Bonanzinga, Nathan Carlson, Davide Giacopello
{"title":"New bounds on the cardinality of n-Hausdorff and n-Urysohn spaces","authors":"Maddalena Bonanzinga, Nathan Carlson, Davide Giacopello","doi":"10.1007/s13398-024-01660-6","DOIUrl":"https://doi.org/10.1007/s13398-024-01660-6","url":null,"abstract":"<p>Two new cardinal functions defined in the class of <i>n</i>-Hausdorff and <i>n</i>-Urysohn spaces that extend pseudocharacter and closed pseudocharacter respectively are introduced. Through these new functions bounds on the cardinality of <i>n</i>-Urysohn spaces that represent variations of known results are given. Also properties of <i>n</i>-Urysohn <i>n</i>-H-closed spaces are proved.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261167","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
Semitoric systems of non-simple type 非简单类型的半串系统
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-16 DOI: 10.1007/s13398-024-01656-2
Joseph Palmer, Álvaro Pelayo, Xiudi Tang
{"title":"Semitoric systems of non-simple type","authors":"Joseph Palmer, Álvaro Pelayo, Xiudi Tang","doi":"10.1007/s13398-024-01656-2","DOIUrl":"https://doi.org/10.1007/s13398-024-01656-2","url":null,"abstract":"<p>Within integrable systems, the class of so called “semitoric” integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental examples from classical and quantum mechanics have been identified as semitoric by different groups of researchers. Several of these examples, however, show a particular trait not included in the original theory, that is, the presence of multiple (i.e. two or more) rank zero isolated singularities in the same energy-momentum level sets. Systems with this property are called non-simple. This paper extends the original theory of Pelayo and Vũ Ngọc to non-simple systems.\u0000</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261172","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
Control problems in the coefficients and the domain for linear elliptic equations 线性椭圆方程系数和域的控制问题
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-14 DOI: 10.1007/s13398-024-01662-4
Juan Casado-Díaz, Manuel Luna-Laynez, Faustino Maestre
{"title":"Control problems in the coefficients and the domain for linear elliptic equations","authors":"Juan Casado-Díaz, Manuel Luna-Laynez, Faustino Maestre","doi":"10.1007/s13398-024-01662-4","DOIUrl":"https://doi.org/10.1007/s13398-024-01662-4","url":null,"abstract":"<p>In the present work we are interested in an optimal design problem for a linear elliptic state equation with a homogeneous boundary Dirichlet condition. The control variables correspond to the coefficients of the diffusion term and the open set where the equation is posed. From the application point of view these variables represent the layout of the materials composing the corresponding domain and its shape. We obtain a relaxed formulation of the problem, the optimality conditions, and we provide a numerical algorithm to solve it. Some numerical simulations are also carried out.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261170","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
Power-partible reduction and congruences for Schröder polynomials 施罗德多项式的幂可平减和同余式
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-06 DOI: 10.1007/s13398-024-01659-z
Chen-Bo Jia, Rong-Hua Wang, Michael X. X. Zhong
{"title":"Power-partible reduction and congruences for Schröder polynomials","authors":"Chen-Bo Jia, Rong-Hua Wang, Michael X. X. Zhong","doi":"10.1007/s13398-024-01659-z","DOIUrl":"https://doi.org/10.1007/s13398-024-01659-z","url":null,"abstract":"<p>In this paper, we apply the power-partible reduction to show the following arithmetic properties of large Schröder polynomials <span>(S_n(z))</span> and little Schröder polynomials <span>(s_n(z))</span>: for any odd prime <i>p</i>, nonnegative integer <span>(rin {mathbb {N}})</span>, <span>(varepsilon in {-1,1})</span> and <span>(zin {mathbb {Z}})</span> with <span>(gcd (p,z(z+1))=1)</span>, we have </p><span>$$begin{aligned} sum _{k=0}^{p-1}(2k+1)^{2r+1}varepsilon ^k S_k(z)equiv 1pmod {p}quad text {and} quad sum _{k=0}^{p-1}(2k+1)^{2r+1}varepsilon ^k s_k(z)equiv 0pmod {p}. end{aligned}$$</span>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202817","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
Composition operators on the algebra of Dirichlet series 狄利克列代数上的合成算子
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-03 DOI: 10.1007/s13398-024-01646-4
Manuel D. Contreras, Carlos Gómez-Cabello, Luis Rodríguez-Piazza
{"title":"Composition operators on the algebra of Dirichlet series","authors":"Manuel D. Contreras, Carlos Gómez-Cabello, Luis Rodríguez-Piazza","doi":"10.1007/s13398-024-01646-4","DOIUrl":"https://doi.org/10.1007/s13398-024-01646-4","url":null,"abstract":"<p>The algebra of Dirichlet series <span>(mathcal {A}({{mathbb {C}}}_+))</span> consists on those Dirichlet series convergent in the right half-plane <span>({{mathbb {C}}}_+)</span> and which are also uniformly continuous there. This algebra was recently introduced by Aron, Bayart, Gauthier, Maestre, and Nestoridis. We describe the symbols <span>(Phi :{{mathbb {C}}}_+rightarrow {{mathbb {C}}}_+)</span> giving rise to bounded composition operators <span>(C_{Phi })</span> in <span>(mathcal {A}({{mathbb {C}}}_+))</span> and denote this class by <span>(mathcal {G}_{mathcal {A}})</span>. We also characterise when the operator <span>(C_{Phi })</span> is compact in <span>(mathcal {A}({{mathbb {C}}}_+))</span>. As a byproduct, we show that the weak compactness is equivalent to the compactness for <span>(C_{Phi })</span>. Next, the closure under the local uniform convergence of several classes of symbols of composition operators in Banach spaces of Dirichlet series is discussed. We also establish a one-to-one correspondence between continuous semigroups of analytic functions <span>({Phi _t})</span> in the class <span>(mathcal {G}_{mathcal {A}})</span> and strongly continuous semigroups of composition operators <span>({T_t})</span>, <span>(T_tf=fcirc Phi _t)</span>, <span>(fin mathcal {A}({{mathbb {C}}}_+))</span>. We conclude providing examples showing the differences between the symbols of bounded composition operators in <span>(mathcal {A}({{mathbb {C}}}_+))</span> and the Hardy spaces of Dirichlet series <span>(mathcal {H}^p)</span> and <span>(mathcal {H}^{infty })</span>.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202818","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
Topological prevalence of variable speed of convergence in the deterministic chaos game 确定性混沌博弈中收敛速度可变的拓扑普遍性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-08-30 DOI: 10.1007/s13398-024-01658-0
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
{"title":"Topological prevalence of variable speed of convergence in the deterministic chaos game","authors":"Krzysztof Leśniak, Nina Snigireva, Filip Strobin","doi":"10.1007/s13398-024-01658-0","DOIUrl":"https://doi.org/10.1007/s13398-024-01658-0","url":null,"abstract":"<p>Let <i>A</i> be the attractor of a Banach contractive iterated function system (IFS) on a complete space. We prove that the orbit generated by a typical (in the sense of Baire category) driver recovers <i>A</i> with every possible speed. Our result extends the one from the paper: Leśniak et al. (Chaos 32(1):013110, 2022). We also show that our result is optimal from a certain point of view.</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":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202819","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 entire solutions for several systems of quadratic trinomial Fermat type functional equations in $${mathbb {C}}^2$$ 论 $${{mathbb {C}}^2$ 中若干二次三项式费马型函数方程组的全解
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-08-23 DOI: 10.1007/s13398-024-01655-3
Zhuying Tai, Jianren Long, Xuxu Xiang
{"title":"On entire solutions for several systems of quadratic trinomial Fermat type functional equations in $${mathbb {C}}^2$$","authors":"Zhuying Tai, Jianren Long, Xuxu Xiang","doi":"10.1007/s13398-024-01655-3","DOIUrl":"https://doi.org/10.1007/s13398-024-01655-3","url":null,"abstract":"<p>The precise forms of finite order transcendental entire solutions for three kinds of systems of quadratic trinomial Fermat type difference equations, Fermat type partial differential equations and Fermat type partial differential-difference equations in <span>({mathbb {C}}^2)</span> are described by applying the Nevanlinna theory, which improves and generalizes previous results in Luo et al. (Open Math 19(1):1018–1028, 2021) and Xu and Jiang (Rev Real Acad Cienc Exactas Fís Nat Ser A Mat 116:1–19, 2022). Some examples are given to show these results.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202820","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 the sum of annihilators in Monoid rings 论类单元环中的湮没者之和
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-08-19 DOI: 10.1007/s13398-024-01657-1
Ebrahim Hashemi, Mahsa Paykanian
{"title":"On the sum of annihilators in Monoid rings","authors":"Ebrahim Hashemi, Mahsa Paykanian","doi":"10.1007/s13398-024-01657-1","DOIUrl":"https://doi.org/10.1007/s13398-024-01657-1","url":null,"abstract":"<p>A given ring <i>R</i>, is called a left IN-ring if the right annihilator of the intersection of any two left ideals is equal to the sum of their right annihilators. Also, <i>R</i> is said to be a right SA-ring if the sum of the right annihilators of any two ideals forms a right annihilator of an ideal itself. For example, a domain is left Ore if and only if it is left IN. In this paper, our investigation focuses on understanding how the behavior of left IN-rings or right SA-rings relates to monoid rings, and whether these properties transfer between the base ring <i>R</i> and its monoid ring <i>R</i>[<i>M</i>]. Among various findings, for instance, we show that if <i>R</i>[<i>M</i>] is a right SA-ring, then <i>R</i> is also a right SA-ring, and conversely holds true for a semiprime ring <i>R</i> and a unique product monoid <i>M</i>. Additionally, we examine and clarify the connections between these classes of rings and well-known classes of rings.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202821","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
Some inequalities and equalities on Lin–Peng–Toh’s partition statistic for k-colored partitions 关于 k 色分区的林鹏-陶氏分区统计的一些不等式和等式
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-08-12 DOI: 10.1007/s13398-024-01653-5
Yueya Hu, Eric H. Liu, Olivia X. M. Yao
{"title":"Some inequalities and equalities on Lin–Peng–Toh’s partition statistic for k-colored partitions","authors":"Yueya Hu, Eric H. Liu, Olivia X. M. Yao","doi":"10.1007/s13398-024-01653-5","DOIUrl":"https://doi.org/10.1007/s13398-024-01653-5","url":null,"abstract":"<p>A <i>k</i>-colored partition <span>(pi )</span> of a positive integer <i>n</i> is a <i>k</i>-tuple of partitions <span>(pi =(pi ^{(1)},ldots , pi ^{(k)}))</span> such that <span>(|pi ^{(1)}| +cdots +|pi ^{(k)}|=n)</span>. Recently, Fu and Tang defined a generalized crank for <i>k</i>-colored partitions by <span>( textrm{crank}_k(pi ) =#(pi ^{(1)})-#(pi ^{(2)}) )</span>, where <span>(#(pi ^{(i)}))</span> denotes the number of parts in <span>(pi ^{(i)})</span>. They also proved some inequalities and equalities for <span>(M_k(m,j,n))</span> which counts the number of <i>k</i>-colored partitions of <i>n</i> with generalized crank congruent to <i>m</i> modulo <i>j</i>. Very recently, Lin, Peng and Toh established some new Andrews–Beck type congruences on <span>(NB_k(m,j,n))</span> which denotes the total number of parts of <span>(pi ^{(1)})</span> in each <i>k</i>-colored partition <span>(pi )</span> of <i>n</i> with <span>( textrm{crank}_k(pi ))</span> congruent to <i>m</i> modulo <i>j</i>. In this paper, motivated by the work of Fu–Tang and Lin–Peng–Toh, we establish the generating functions for <span>(NB_k(m,j,n))</span> when <span>(j=2,3,4)</span> and deduce some new inequalities and equalities for <span>(NB_k(m,j,n))</span>.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937346","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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