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Bulletin of the Brazilian Mathematical Society, New Series最新文献

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The Twisted Partial Group Algebra and (Co)homology of Partial Crossed Products 部分交叉积的扭曲部分群代数和（同）同源性
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-06-21 DOI: 10.1007/s00574-024-00408-5
Mikhailo Dokuchaev, Emmanuel Jerez
{"title":"The Twisted Partial Group Algebra and (Co)homology of Partial Crossed Products","authors":"Mikhailo Dokuchaev, Emmanuel Jerez","doi":"10.1007/s00574-024-00408-5","DOIUrl":"https://doi.org/10.1007/s00574-024-00408-5","url":null,"abstract":"<p>Given a group <i>G</i> and a partial factor set <span>(sigma )</span> of <i>G</i>, we introduce the twisted partial group algebra <span>({kappa }_{textrm{par}}^sigma G,)</span> which governs the partial projective <span>(sigma )</span>-representations of <i>G</i> into algebras over a field <span>(kappa .)</span> Using the relation between partial projective representations and twisted partial actions we endow <span>({kappa }_{textrm{par}}^sigma G)</span> with the structure of a crossed product by a twisted partial action of <i>G</i> on a commutative subalgebra of <span>({kappa }_{textrm{par}}^sigma G.)</span> Then, we use twisted partial group algebras to obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the crossed product <span>(A*_{Theta } G,)</span> involving the Hochschild homology of <i>A</i> and the partial homology of <i>G</i>, where <span>({Theta })</span> is a unital twisted partial action of <i>G</i> on a <span>(kappa )</span>-algebra <i>A</i> with a <span>(kappa )</span>-based twist. An analogous third quadrant cohomological spectral sequence is also obtained.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529777","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
Star Flows: A Characterization Via Lyapunov Functions 星体流动：通过 Lyapunov 函数进行表征
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-06-10 DOI: 10.1007/s00574-024-00403-w
Luciana Salgado
{"title":"Star Flows: A Characterization Via Lyapunov Functions","authors":"Luciana Salgado","doi":"10.1007/s00574-024-00403-w","DOIUrl":"https://doi.org/10.1007/s00574-024-00403-w","url":null,"abstract":"<p>In this work, it is presented a characterization of star property for a <span>(C^1)</span> vector field based on Lyapunov functions. It is also obtained conditions to strong homogeneity for singular sets by using the notion of infinitesimal Lyapunov functions. As an application, we obtain some results related to singular hyperbolic sets for flows.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509014","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 New Approach to Solving the Split Common Solution Problem for Monotone Operator Equations in Hilbert Spaces 解决希尔伯特空间中单调算子方程的分割共解问题的新方法
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-06-04 DOI: 10.1007/s00574-024-00405-8
Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen
{"title":"A New Approach to Solving the Split Common Solution Problem for Monotone Operator Equations in Hilbert Spaces","authors":"Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen","doi":"10.1007/s00574-024-00405-8","DOIUrl":"https://doi.org/10.1007/s00574-024-00405-8","url":null,"abstract":"<p>In the present paper, we propose a new approach to solving a class of generalized split problems. This approach will open some new directions for research to solve the other split problems, for instance, the split common zero point problem and the split common fixed point problem. More precisely, we study the split common solution problem for monotone operator equations in real Hilbert spaces. To find a solution to this problem, we propose and establish the strong convergence of the two new iterative methods by using the Tikhonov regularization method. Meantime, we also study the stability of the iterative methods. Finally, two numerical examples are also given to illustrate the effectiveness of the proposed methods.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251977","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
Phase Transitions for Surface Diffeomorphisms 曲面衍射的相变
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-06-03 DOI: 10.1007/s00574-024-00404-9
Thiago Bomfim, Paulo Varandas
{"title":"Phase Transitions for Surface Diffeomorphisms","authors":"Thiago Bomfim, Paulo Varandas","doi":"10.1007/s00574-024-00404-9","DOIUrl":"https://doi.org/10.1007/s00574-024-00404-9","url":null,"abstract":"<p>In this paper we consider <span>(C^1)</span> surface diffeomorphisms and study the existence of phase transitions, here expressed by the non-analiticity of the pressure function associated to smooth and geometric-type potentials. We prove that the space of <span>(C^1)</span>-surface diffeomorphisms admitting phase transitions is a <span>(C^1)</span>-Baire generic subset of the space of non-Anosov diffeomorphisms. In particular, if <i>S</i> is a compact surface which is not homeomorphic to the 2-torus then a <span>(C^1)</span>-generic diffeomorphism on <i>S</i> has phase transitions. We obtain similar statements in the context of <span>(C^1)</span>-volume preserving diffeomorphisms. Finally, we prove that a <span>(C^2)</span>-surface diffeomorphism exhibiting a dominated splitting admits phase transitions if and only if has some non-hyperbolic periodic point.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141251984","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
Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps 广义马蹄图的绝对连续不变度量
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-05-31 DOI: 10.1007/s00574-024-00402-x
Abbas Fakhari, Maryam Khalaj, Mohammad Soufi
{"title":"Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps","authors":"Abbas Fakhari, Maryam Khalaj, Mohammad Soufi","doi":"10.1007/s00574-024-00402-x","DOIUrl":"https://doi.org/10.1007/s00574-024-00402-x","url":null,"abstract":"<p>In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and fatness, the SRB measure is indeed absolutely continuous with respect to the Lebesgue measure.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188885","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
Quasi-Lie Bialgebroids, Dirac Structures, and Deformations of Poisson Quasi-Nijenhuis Manifolds 准里氏比尔格布鲁克、狄拉克结构和泊松准尼雅赫伊斯流形的变形
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-05-24 DOI: 10.1007/s00574-024-00400-z
M. do Nascimento Luiz, I. Mencattini, M. Pedroni
{"title":"Quasi-Lie Bialgebroids, Dirac Structures, and Deformations of Poisson Quasi-Nijenhuis Manifolds","authors":"M. do Nascimento Luiz, I. Mencattini, M. Pedroni","doi":"10.1007/s00574-024-00400-z","DOIUrl":"https://doi.org/10.1007/s00574-024-00400-z","url":null,"abstract":"<p>We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147103","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
Multiplicities in the Length Spectrum and Growth Rate of Salem Numbers 萨林数长度谱中的倍数和增长率
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-05-18 DOI: 10.1007/s00574-024-00398-4
Alexandr Grebennikov
{"title":"Multiplicities in the Length Spectrum and Growth Rate of Salem Numbers","authors":"Alexandr Grebennikov","doi":"10.1007/s00574-024-00398-4","DOIUrl":"https://doi.org/10.1007/s00574-024-00398-4","url":null,"abstract":"<p>We prove that mean multiplicities in the length spectrum of a non-compact arithmetic hyperbolic orbifold of dimension <span>(n geqslant 4)</span> have exponential growth rate </p><span>$$begin{aligned} langle g(L) rangle geqslant c frac{e^{([n/2] - 1)L}}{L^{1 + delta _{5, 7}(n) }}, end{aligned}$$</span><p>extending the analogous result for even dimensions of Belolipetsky, Lalín, Murillo and Thompson. Our proof is based on the study of (square-rootable) Salem numbers. As a counterpart, we also prove an asymptotic formula for the distribution of square-rootable Salem numbers by adapting the argument of Götze and Gusakova. It shows that one can not obtain a better estimate on mean multiplicities using our approach.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"220 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061918","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
Constant Components of the Mertens Function and Its Connections with Tschebyschef’s Theory for Counting Prime Numbers II 梅腾斯函数的常数成分及其与舍比雪夫质数计数理论 II 的联系
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-05-16 DOI: 10.1007/s00574-024-00399-3
André Pierro de Camargo, P. A. Martin
{"title":"Constant Components of the Mertens Function and Its Connections with Tschebyschef’s Theory for Counting Prime Numbers II","authors":"André Pierro de Camargo, P. A. Martin","doi":"10.1007/s00574-024-00399-3","DOIUrl":"https://doi.org/10.1007/s00574-024-00399-3","url":null,"abstract":"","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"49 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140970407","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
Triviality Results and Conjugate Radius Estimation of Ricci Solitons 利玛窦孤子的琐碎性结果和共轭半径估计
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-04-25 DOI: 10.1007/s00574-024-00396-6
Absos Ali Shaikh, Prosenjit Mandal, V. Amarendra Babu
{"title":"Triviality Results and Conjugate Radius Estimation of Ricci Solitons","authors":"Absos Ali Shaikh, Prosenjit Mandal, V. Amarendra Babu","doi":"10.1007/s00574-024-00396-6","DOIUrl":"https://doi.org/10.1007/s00574-024-00396-6","url":null,"abstract":"<p>The investigation of Ricci solitons is the focus of this work. We have proved triviality results for compact gradient Ricci soliton under certain restriction. Later, a rigidity result is derived for a compact gradient shrinking Ricci soliton. Also, we have estimated the conjugate radius for non-compact gradient shrinking Ricci soliton with superharmonic potential. Moreover, an upper bound for the conjugate radius of Ricci soliton with concircular potential vector field is determined. Finally, it is proved that a non-compact gradient Ricci soliton with a pole and non-negative Ricci curvature is non-shrinking.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799651","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
An Explicit Croot-Łaba-Sisask Lemma Free of Probabilistic Language 不含概率语言的显式克罗-罗巴-西萨斯克定理
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-04-25 DOI: 10.1007/s00574-024-00397-5
Olivier Ramaré
{"title":"An Explicit Croot-Łaba-Sisask Lemma Free of Probabilistic Language","authors":"Olivier Ramaré","doi":"10.1007/s00574-024-00397-5","DOIUrl":"https://doi.org/10.1007/s00574-024-00397-5","url":null,"abstract":"","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"45 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140655574","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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