发布求助
文献互助 智能选刊 最新文献

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

筛选
英文 中文
Khovanov homology, wedges of spheres and complexity 霍瓦诺夫同源性、球楔和复杂性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-02 DOI: 10.1007/s13398-024-01594-z
Jozef H. Przytycki, Marithania Silvero
{"title":"Khovanov homology, wedges of spheres and complexity","authors":"Jozef H. Przytycki, Marithania Silvero","doi":"10.1007/s13398-024-01594-z","DOIUrl":"https://doi.org/10.1007/s13398-024-01594-z","url":null,"abstract":"<p>Our main result has topological, combinatorial and computational flavor. It is motivated by a fundamental conjecture stating that computing Khovanov homology of a closed braid of fixed number of strands has polynomial time complexity. We show that the independence simplicial complex <i>I</i>(<i>w</i>) associated to the 4-braid diagram <i>w</i> (and therefore its Khovanov spectrum at extreme quantum degree) is contractible or homotopy equivalent to either a sphere, or a wedge of two spheres (possibly of different dimensions), or a wedge of three spheres (at least two of them of the same dimension), or a wedge of four spheres (at least three of them of the same dimension). On the algorithmic side we prove that finding the homotopy type of <i>I</i>(<i>w</i>) can be done in polynomial time with respect to the number of crossings in <i>w</i>. In particular, we prove the wedge of spheres conjecture for circle graphs obtained from 4-braid diagrams. We also introduce the concept of Khovanov adequate diagram and discuss criteria for a link to have a Khovanov adequate braid diagram with at most 4 strands.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883708","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
Diffusion approximation of critical controlled multi-type branching processes 临界受控多类型分支过程的扩散近似值
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-29 DOI: 10.1007/s13398-024-01593-0
Mátyás Barczy, Miguel González, Pedro Martín-Chávez, Inés del Puerto
{"title":"Diffusion approximation of critical controlled multi-type branching processes","authors":"Mátyás Barczy, Miguel González, Pedro Martín-Chávez, Inés del Puerto","doi":"10.1007/s13398-024-01593-0","DOIUrl":"https://doi.org/10.1007/s13398-024-01593-0","url":null,"abstract":"<p>Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion approximation is derived for some critical CMBPs. Namely, we consider a sequence of appropriately scaled random step functions formed from a critical CMBP with control distributions having expectations that satisfy a kind of linearity assumption. It is proved that such a sequence converges weakly toward a squared Bessel process supported by a ray determined by an eigenvector of a matrix related to the offspring mean matrix and the control distributions of the branching process in question. As applications, among others, we derive Feller-type diffusion approximations of critical, primitive multi-type branching processes with immigration and some two-sex branching processes. We also describe the asymptotic behaviour of the relative frequencies of distinct types of individuals for critical CMBPs.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809257","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
Modular differential equations and algebraic systems 模微分方程和代数系统
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-28 DOI: 10.1007/s13398-024-01602-2
Hicham Saber, Abdellah Sebbar
{"title":"Modular differential equations and algebraic systems","authors":"Hicham Saber, Abdellah Sebbar","doi":"10.1007/s13398-024-01602-2","DOIUrl":"https://doi.org/10.1007/s13398-024-01602-2","url":null,"abstract":"<p>This paper investigates the modular differential equation <span>(y''+sE_4y=0)</span> on the upper half-plane <span>({{mathbb {H}}})</span>, where <span>(E_4)</span> is the weight 4 Eisenstein series and <i>s</i> is a complex parameter. This is equivalent to studying the Schwarz differential equation <span>({h,tau }=2sE_4)</span>, where the unknown <i>h</i> is a meromorphic function on <span>({{mathbb {H}}})</span>. On the other hand, such a solution <i>h</i> must satisfy <span>(h(gamma tau )=varrho (gamma )h(tau ))</span> for <span>(tau in {{mathbb {H}}})</span>, <span>(gamma in {text{ SL}_2({{mathbb {Z}}})})</span> and <span>(varrho )</span> being a <span>(2-)</span>dimensional complex representation of <span>({text{ SL}_2({{mathbb {Z}}})})</span>. Moreover, in order for <i>h</i> to be meromorphic or to have logarithmic singularities at the <span>({text{ SL}_2({{mathbb {Z}}})})</span>-cusps of <span>({{mathbb {H}}})</span>, it is necessary to have <span>(s=pi ^2r^2)</span> with <i>r</i> being a rational number. For <span>(r=m/n)</span> in reduced form, it turns out that <span>(varrho )</span> is irreducible with finite image if and only if <span>(2le nle 5)</span> and in this case <i>h</i> is a modular function for the genus zero torsion-free principal congruence group <span>({Gamma }(n))</span>, while<span>(varrho )</span> is reducible if and only if <span>(n=6)</span>. By Solving an explicit algebraic system, we prove that solutions for any <span>(r=m/n)</span> can be built from a solution corresponding to <span>(r=1/n)</span>, for <span>(2le nle 6)</span>, by integrating certain weight 2 meromorphic modular forms. Together with the earlier work by the authors for <i>r</i> being an integer [20], this provides the solutions to the above-mentioned differential equations for all <span>(r=m/n)</span> with <span>(1le nle 6)</span>.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"127 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809247","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
Convergence of operators based on some special functions 基于某些特殊函数的算子收敛性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-26 DOI: 10.1007/s13398-024-01597-w
Vijay Gupta
{"title":"Convergence of operators based on some special functions","authors":"Vijay Gupta","doi":"10.1007/s13398-024-01597-w","DOIUrl":"https://doi.org/10.1007/s13398-024-01597-w","url":null,"abstract":"<p>The present article is in continuation of our previous paper by Gupta (Rev Real Acad Cienc Exactas Fis Nat Ser A-Mat 118:19, 2024, https://doi.org/10.1007/s13398-023-01521-8), we consider the operators, which are connected to the solutions of differential equations. The differential equations considered here are Hermite and Laguerre differential equations. We discuss here the new operators constructed by the solutions of these differential equations. We also provide only the basic convergence properties. As other can be done by researchers in different settings. In the last section, we provide higher order self composition operators and observe that the convergence takes place for all finite higher order composition operators but worse convergence is achieved in case of higher order finite self composition of operators.</p>","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":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806311","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 strong algebrability of families of non-measurable functions of two variables 论二变量不可量函数族的强可并性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-25 DOI: 10.1007/s13398-024-01601-3
Szymon Głąb, Mateusz Lichman, Michał Pawlikowski
{"title":"On strong algebrability of families of non-measurable functions of two variables","authors":"Szymon Głąb, Mateusz Lichman, Michał Pawlikowski","doi":"10.1007/s13398-024-01601-3","DOIUrl":"https://doi.org/10.1007/s13398-024-01601-3","url":null,"abstract":"<p>Recently Tomasz Natkaniec in (Natkaniec in Rev R Acad Cenc Exactas Fís Nat Ser A Mat RACSAM, 115(1):10, 2021) studied the lineability problem for several classes of non-measurable functions in two variables. In this note we improve his results in the direction of algebrability. In particular, we show that most of the classes considered by Natkaniec contain free algebras with <span>(2^mathfrak c)</span> many generators.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806410","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
Refined Kato inequality and applications to norm and numerical radius inequalities 改进的加藤不等式及其在规范和数值半径不等式中的应用
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-24 DOI: 10.1007/s13398-024-01600-4
F. Kittaneh, H. Moradi, M. Sababheh
{"title":"Refined Kato inequality and applications to norm and numerical radius inequalities","authors":"F. Kittaneh, H. Moradi, M. Sababheh","doi":"10.1007/s13398-024-01600-4","DOIUrl":"https://doi.org/10.1007/s13398-024-01600-4","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"68 49","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664222","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
Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and $$Delta $$-points 具有单位球的弱开放小子集以及道加维特和 $$Delta $$ 点的大规模集合的巴拿赫空间
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-22 DOI: 10.1007/s13398-024-01596-x
Christian Cobollo, Daniel Isert, Ginés López-Pérez, Miguel Martín, Yoel Perreau, Alicia Quero, Andrés Quilis, Daniel L. Rodriguez-Vidanes, Abraham Rueda Zoca
{"title":"Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and $$Delta $$-points","authors":"Christian Cobollo, Daniel Isert, Ginés López-Pérez, Miguel Martín, Yoel Perreau, Alicia Quero, Andrés Quilis, Daniel L. Rodriguez-Vidanes, Abraham Rueda Zoca","doi":"10.1007/s13398-024-01596-x","DOIUrl":"https://doi.org/10.1007/s13398-024-01596-x","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"75 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140676907","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
Optimality conditions and Lipschitz stability for non-smooth semilinear elliptic optimal control problems with sparse controls 具有稀疏控制的非光滑半线性椭圆最优控制问题的最优性条件和 Lipschitz 稳定性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-21 DOI: 10.1007/s13398-024-01595-y
Vu Huu Nhu, Phan Quang Sang
{"title":"Optimality conditions and Lipschitz stability for non-smooth semilinear elliptic optimal control problems with sparse controls","authors":"Vu Huu Nhu, Phan Quang Sang","doi":"10.1007/s13398-024-01595-y","DOIUrl":"https://doi.org/10.1007/s13398-024-01595-y","url":null,"abstract":"<p>This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the <span>(L^1)</span>-norm of the control in the cost functional. In addition to the appearance of the <span>(L^1)</span>-norm leading to the non-differentiability of the objective and promoting the sparsity of the optimal controls, the non-smoothness of the nonlinear coefficient in the state equation causes the same property of the control-to-state operator. Exploiting a regularization scheme, we derive <i>C</i>-stationarity conditions for any local optimal control. Under a structural assumption on the associated state, we define the curvature functional for the part not including the <span>(L^1)</span>-norm of controls of the objective for which the second-order necessary and sufficient optimality conditions with minimal gap are shown. Furthermore, under a more restrictive structural assumption imposed on the mentioned state, an explicit formula for the curvature is established and thus the explicit second-order optimality conditions are stated. Finally, the Lipschitz stability of local solutions with respect to the sparsity parameter is shown.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628573","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
Conformally flat centroaffine Tchebychev hypersurfaces 共形平坦的向心轴切比切夫超曲面
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-18 DOI: 10.1007/s13398-024-01598-9
Cece Li, Huiyang Xu
{"title":"Conformally flat centroaffine Tchebychev hypersurfaces","authors":"Cece Li, Huiyang Xu","doi":"10.1007/s13398-024-01598-9","DOIUrl":"https://doi.org/10.1007/s13398-024-01598-9","url":null,"abstract":"<p>In this paper, we study locally strongly convex, conformally flat centroaffine hypersurfaces. The key step is to obtain some relations between the Schouten operator <i>P</i>, the difference tensor and its traceless tensor, which is achieved by applying the Tsinghua principle for two related symmetric Codazzi tensors of (1, 2)-form on a conformally flat manifold. As the main results, (1) such hypersurfaces are proved to be of constant sectional curvature if <i>P</i> has no eigenvalues of multiplicity one; (2) such Tchebychev hypersurfaces are classified if <i>P</i> has exactly one eigenvalue of multiplicity one. As a byproduct, we obtain the classification of conformally flat proper affine hyperspheres whose Schouten operator admits at most one eigenvalue of multiplicity one.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614413","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 full range of Zippin and inclusion indices of rearrangement-invariant spaces 论重排不变空间的全部齐平指数和包含指数
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-04-17 DOI: 10.1007/s13398-024-01599-8
Guillermo P. Curbera, Oleksiy Karlovych, Eugene Shargorodsky
{"title":"On the full range of Zippin and inclusion indices of rearrangement-invariant spaces","authors":"Guillermo P. Curbera, Oleksiy Karlovych, Eugene Shargorodsky","doi":"10.1007/s13398-024-01599-8","DOIUrl":"https://doi.org/10.1007/s13398-024-01599-8","url":null,"abstract":"<p>Let <i>X</i> be a rearrangement-invariant space on [0, 1]. It is known that its Zippin indices <span>(underline{beta }{}_X,overline{beta }{}_X)</span> and its inclusion indices <span>(gamma _X,delta _X)</span> are related as follows: <span>(0le underline{beta }{}_Xle 1/gamma _X le 1/delta _Xle overline{beta }{}_Xle 1)</span>. We show that given <span>(underline{beta },overline{beta }in [0,1])</span> and <span>(gamma ,delta in [1,infty ])</span> satisfying <span>(underline{beta }le 1/gamma le 1/delta le overline{beta })</span>, there exists a rearrangement-invariant space <i>X</i> such that <span>(underline{beta }{}_X=underline{beta })</span>, <span>(overline{beta }{}_X=overline{beta })</span> and <span>(gamma _X=gamma )</span>, <span>(delta _X=delta )</span>.</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":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140614049","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书