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Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows 环流平滑时间变化的正交幂和Möbius猜想
Electronic Research Announcements in Mathematical Sciences Pub Date : 2018-11-12 DOI: 10.3934/ERA.2019.26.002
L. Flaminio, G. Forni
{"title":"Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows","authors":"L. Flaminio, G. Forni","doi":"10.3934/ERA.2019.26.002","DOIUrl":"https://doi.org/10.3934/ERA.2019.26.002","url":null,"abstract":"We derive, from the work of M. Ratner on joinings of time-changes of horocycle flows and from the result of the authors on its cohomology, the property of orthogonality of powers for non-trivial smooth time-changes of horocycle flows on compact quotients. Such a property is known to imply P. Sarnak's Mobius orthogonality conjecture, already known for horocycle flows by the work of J. Bourgain, P. Sarnak and T. Ziegler.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86541287","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: 11
Fractal Weyl bounds and Hecke triangle groups 分形Weyl界与Hecke三角群
Electronic Research Announcements in Mathematical Sciences Pub Date : 2018-10-10 DOI: 10.3934/ERA.2019.26.003
Fr'ed'eric Naud, A. Pohl, Louis Soares
{"title":"Fractal Weyl bounds and Hecke triangle groups","authors":"Fr'ed'eric Naud, A. Pohl, Louis Soares","doi":"10.3934/ERA.2019.26.003","DOIUrl":"https://doi.org/10.3934/ERA.2019.26.003","url":null,"abstract":"Let $Gamma_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$ and let $varrhocolonGamma_wto U(V)$ be a finite-dimensional unitary representation of $Gamma_w$. In this note we announce a new fractal upper bound for the Selberg zeta function of $Gamma_{w}$ twisted by $varrho$. In strips parallel to the imaginary axis and bounded away from the real axis, the Selberg zeta function is bounded by $expleft( C_{varepsilon} vert svert^{delta + varepsilon} right)$, where $delta = delta_{w}$ denotes the Hausdorff dimension of the limit set of $Gamma_{w}$. This bound implies fractal Weyl bounds on the resonances of the Laplacian for all geometrically finite surfaces $X=widetilde{Gamma}backslashmathbb{H}$ where $widetilde{Gamma}$ is a finite index, torsion-free subgroup of $Gamma_w$.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89596400","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: 6
Cluster algebras with Grassmann variables 具有Grassmann变量的簇代数
Electronic Research Announcements in Mathematical Sciences Pub Date : 2018-09-06 DOI: 10.3934/ERA.2019.26.001
V. Ovsienko, M. Shapiro
{"title":"Cluster algebras with Grassmann variables","authors":"V. Ovsienko, M. Shapiro","doi":"10.3934/ERA.2019.26.001","DOIUrl":"https://doi.org/10.3934/ERA.2019.26.001","url":null,"abstract":"We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of \"extended quivers,\" which are oriented hypergraphs. We describe mutations of such objects and define a corresponding commutative superalgebra. Our construction includes the notion of weighted quivers that has already appeared in different contexts. This paper is a step towards understanding the notion of cluster superalgebra.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87493893","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: 21
On matrix wreath products of algebras 关于代数的矩阵环积
Electronic Research Announcements in Mathematical Sciences Pub Date : 2017-08-01 DOI: 10.3934/ERA.2017.24.009
A. Alahmadi, H. Alsulami, S. Jain, E. Zelmanov
{"title":"On matrix wreath products of algebras","authors":"A. Alahmadi, H. Alsulami, S. Jain, E. Zelmanov","doi":"10.3934/ERA.2017.24.009","DOIUrl":"https://doi.org/10.3934/ERA.2017.24.009","url":null,"abstract":"We introduce a new construction of matrix wreath products of algebras that is similar to the construction of wreath products of groups introduced by L. Kaloujnine and M. Krasner [ 17 ]. We then illustrate its usefulness by proving embedding theorems into finitely generated algebras and constructing nil algebras with prescribed Gelfand-Kirillov dimension.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"24 1","pages":"78-86"},"PeriodicalIF":0.0,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41623969","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: 5
A note on parallelizable dynamical systems 关于可并行动力系统的一个注记
Electronic Research Announcements in Mathematical Sciences Pub Date : 2017-06-01 DOI: 10.3934/ERA.2017.24.007
J. Souza, T. A. Pacifico, Hélio V. M. Tozatti
{"title":"A note on parallelizable dynamical systems","authors":"J. Souza, T. A. Pacifico, Hélio V. M. Tozatti","doi":"10.3934/ERA.2017.24.007","DOIUrl":"https://doi.org/10.3934/ERA.2017.24.007","url":null,"abstract":"Hajek [ 3 ] showed that a dynamical system on a Tychonoff space with paracompact orbit space is parallelizable if and only if its corresponding bundle is a locally trivial fiber bundle with fiber begin{document}$mathbb{R}$end{document} . The present paper provides an enhancement for this classical theorem by omitting all topological hypotheses.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"24 1","pages":"64-67"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47813337","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: 2
The orbifold Langer-Miyaoka-Yau Inequality and Hirzebruch-type inequalities 轨道Langer-Miyaoka-Yau不等式与hirzebruch型不等式
Electronic Research Announcements in Mathematical Sciences Pub Date : 2016-12-15 DOI: 10.3934/era.2017.24.003
Piotr Pokora
{"title":"The orbifold Langer-Miyaoka-Yau Inequality and Hirzebruch-type inequalities","authors":"Piotr Pokora","doi":"10.3934/era.2017.24.003","DOIUrl":"https://doi.org/10.3934/era.2017.24.003","url":null,"abstract":"Using Langer's variation on the Bogomolov-Miyaoka-Yau inequality, we provide some Hirzebruch-type inequalities for curve arrangements in the complex projective plane.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"24 1","pages":"21-27"},"PeriodicalIF":0.0,"publicationDate":"2016-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233690","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: 12
Banach limit in convexity and geometric means for convex bodies 凸性的Banach极限与凸体的几何均值
Electronic Research Announcements in Mathematical Sciences Pub Date : 2016-11-01 DOI: 10.3934/ERA.2016.23.005
Liran Rotem
{"title":"Banach limit in convexity and geometric means for convex bodies","authors":"Liran Rotem","doi":"10.3934/ERA.2016.23.005","DOIUrl":"https://doi.org/10.3934/ERA.2016.23.005","url":null,"abstract":"In this note we construct Banach limits on the class of sequences \u0000of convex bodies. Surprisingly, the construction uses the recently \u0000introduced geometric mean of convex bodies. In the opposite direction, \u0000we explain how Banach limits can be used to construct a new variant \u0000of the geometric mean that has some desirable properties.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"23 1","pages":"41-51"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233679","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: 6
NONEXISTENCE RESULTS FOR A FULLY NONLINEAR EVOLUTION INEQUALITY 一类完全非线性演化不等式的不存在性
Electronic Research Announcements in Mathematical Sciences Pub Date : 2016-06-01 DOI: 10.3934/ERA.2016.23.003
Qianzhong Ou
{"title":"NONEXISTENCE RESULTS FOR A FULLY NONLINEAR EVOLUTION INEQUALITY","authors":"Qianzhong Ou","doi":"10.3934/ERA.2016.23.003","DOIUrl":"https://doi.org/10.3934/ERA.2016.23.003","url":null,"abstract":"In this paper, a Liouville type theorem is proved for some global fully nonlinear evolution inequality via suitable choices of test functions and the argument of integration by parts.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"27 1","pages":"19-24"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233645","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
Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity 具有密度依赖粘度的Navier-Stokes-Korteweg系统的渐近极限
Electronic Research Announcements in Mathematical Sciences Pub Date : 2015-07-01 DOI: 10.3934/ERA.2015.22.20
Jianwei Yang, Peng Cheng, Yudong Wang
{"title":"Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity","authors":"Jianwei Yang, Peng Cheng, Yudong Wang","doi":"10.3934/ERA.2015.22.20","DOIUrl":"https://doi.org/10.3934/ERA.2015.22.20","url":null,"abstract":"In this paper, we study a combined incompressible and vanishing \u0000capillarity limit in the barotropic compressible \u0000Navier-Stokes-Korteweg equations for weak solutions. For well \u0000prepared initial data, the convergence of solutions of the \u0000compressible Navier-Stokes-Korteweg equations to the \u0000solutions of the incompressible Navier-Stokes equation are justified \u0000rigorously by adapting the modulated energy method. Furthermore, the \u0000corresponding convergence rates are also obtained.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"22 1","pages":"20-31"},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70233967","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: 1
The $boldsymbol{q}$-deformed Campbell-Baker-Hausdorff-Dynkin theorem $boldsymbol{q}$-变形的Campbell-Baker-Hausdorff-Dynkin定理
Electronic Research Announcements in Mathematical Sciences Pub Date : 2015-07-01 DOI: 10.3934/ERA.2015.22.32
Rüdiger Achilles, A. Bonfiglioli, J. Katriel
{"title":"The $boldsymbol{q}$-deformed Campbell-Baker-Hausdorff-Dynkin theorem","authors":"Rüdiger Achilles, A. Bonfiglioli, J. Katriel","doi":"10.3934/ERA.2015.22.32","DOIUrl":"https://doi.org/10.3934/ERA.2015.22.32","url":null,"abstract":"We announce an analogue of the celebrated theorem by Campbell, Baker, Hausdorff, and Dynkin for the $q$-exponential $exp_q(x)=sum_{n=0}^{infty} frac{x^n}{[n]_q!}$, with the usual notation for $q$-factorials: $[n]_q!:=[n-1]_q!cdot(q^n-1)/(q-1)$ and $[0]_q!:=1$. Our result states that if $x$ and $y$ are non-commuting indeterminates and $[y,x]_q$ is the $q$-commutator $yx-q,xy$, then there exist linear combinations $Q_{i,j}(x,y)$ of iterated $q$-commutators with exactly $i$ $x$'s, $j$ $y$'s and $[y,x]_q$ in their central position, such that $exp_q(x)exp_q(y)=exp_q!big(x+y+sum_{i,jgeq 1}Q_{i,j}(x,y)big)$. Our expansion is consistent with the well-known result by Schutzenberger ensuring that one has $exp_q(x)exp_q(y)=exp_q(x+y)$ if and only if $[y,x]_q=0$, and it improves former partial results on $q$-deformed exponentiation. Furthermore, we give an algorithm which produces conjecturally a minimal generating set for the relations between $[y,x]_q$-centered $q$-commutators of any bidegree $(i,j)$, and it allows us to compute all possible $Q_{i,j}$.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"22 1","pages":"32-45"},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70234032","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: 2
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