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Reverse Faber-Krahn inequality for a truncated Laplacian operator 截断拉普拉斯算子的反Faber-Krahn不等式
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-03-26 DOI: 10.5565/publmat6622201
E. Parini, J. Rossi, A. Salort
{"title":"Reverse Faber-Krahn inequality for a truncated Laplacian operator","authors":"E. Parini, J. Rossi, A. Salort","doi":"10.5565/publmat6622201","DOIUrl":"https://doi.org/10.5565/publmat6622201","url":null,"abstract":"In this paper we prove a reverse Faber-Krahn inequality for the principal eigenvalue $mu_1(Omega)$ of the fully nonlinear eigenvalue problem [ label{eq} left{begin{array}{r c l l} -lambda_N(D^2 u) & = & mu u & text{in }Omega, u & = & 0 & text{on }partial Omega. end{array}right. ] Here $ lambda_N(D^2 u)$ stands for the largest eigenvalue of the Hessian matrix of $u$. More precisely, we prove that, for an open, bounded, convex domain $Omega subset mathbb{R}^N$, the inequality [ mu_1(Omega) leq frac{pi^2}{[text{diam}(Omega)]^2} = mu_1(B_{text{diam}(Omega)/2}),] where $text{diam}(Omega)$ is the diameter of $Omega$, holds true. The inequality actually implies a stronger result, namely, the maximality of the ball under a diameter constraint. \u0000Furthermore, we discuss the minimization of $mu_1(Omega)$ under different kinds of constraints.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44748448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Curvature of the completion of the space of Sasaki potentials 佐佐木势空间的曲率补全
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-03-19 DOI: 10.5565/publmat6712309
Thomas Franzinetti
{"title":"Curvature of the completion of the space of Sasaki potentials","authors":"Thomas Franzinetti","doi":"10.5565/publmat6712309","DOIUrl":"https://doi.org/10.5565/publmat6712309","url":null,"abstract":"Given a compact Sasaki manifold, we endow the space of the Sasaki potentials with an analogue of Mabuchi metric. We show that its metric completion is negatively curved in the sense of Alexandrov.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44419160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks 具有汇的超图移位空间的KMS态和连续轨道等价
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-03-12 DOI: 10.5565/publmat6622208
F. A. Tasca, D. Gonçalves
{"title":"KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks","authors":"F. A. Tasca, D. Gonçalves","doi":"10.5565/publmat6622208","DOIUrl":"https://doi.org/10.5565/publmat6622208","url":null,"abstract":"We extend ultragraph shift spaces and the realization of ultragraph C*-algebras as partial crossed products to include ultragraphs with sinks (under a mild condition, called (RFUM2), which allow us to dismiss the use of filters) and we describe the associated transformation groupoid. Using these characterizations we study continuous orbit equivalence of ultragraph shift spaces (via groupoids) and KMS and ground states (via partial crossed products).","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46209030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A simple proof of the optimal power in Liouville theorems 刘维尔定理中最优幂的一个简单证明
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-03-09 DOI: 10.5565/publmat6622212
S. Villegas
{"title":"A simple proof of the optimal power in Liouville theorems","authors":"S. Villegas","doi":"10.5565/publmat6622212","DOIUrl":"https://doi.org/10.5565/publmat6622212","url":null,"abstract":"Consider the equation div$(varphi^2 nabla sigma)=0$ in $mathbb{R}^N,$ where $varphi>0$. It is well-known that if there exists $C>0$ such that $int_{B_R}(varphi sigma)^2 dxleq CR^2$ for every $Rgeq 1$ then $sigma$ is necessarily constant. In this paper we prove that this result is not true if we replace $R^2$ by $R^k$ for $k>2$ in any dimension $N$. This question is related to a conjecture by De Giorgi.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45356679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals 关于多重常积分对多重Stratonovich积分的强收敛性
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-02-14 DOI: 10.5565/PUBLMAT6522114
X. Bardina, C. Rovira
{"title":"On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals","authors":"X. Bardina, C. Rovira","doi":"10.5565/PUBLMAT6522114","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522114","url":null,"abstract":"Given ${W^{(m)}(t), t in [0,T]}_{m ge 1}$ a sequence of approximations to a standard Brownian motion $W$ in $[0,T]$ such that $W^{(m)}(t)$ converges almost surely to $W(t)$ we show that, under regular conditions on the approximations, the multiple ordinary integrals with respect to $dW^{(m)}$ converge to the multiple Stratonovich integral. We are integrating functions of the type $$f(x_1,ldots,x_n)=f_1(x_1)ldots f_n(x_n) I_{{x_1le ldots le x_n}},$$ where for each $i in {1,ldots,n}$, $f_i$ has continuous derivatives in $[0,T].$ We apply this result to approximations obtained from uniform transport processes.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43348082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Groups with no proper contranormal subgroups 没有适当逆正规子群的群
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-01-01 DOI: 10.5565/publmat6412008
B. Wehrfritz
{"title":"Groups with no proper contranormal subgroups","authors":"B. Wehrfritz","doi":"10.5565/publmat6412008","DOIUrl":"https://doi.org/10.5565/publmat6412008","url":null,"abstract":"We consider which groups G are nilpotent if they have a nilpotent normal subgroup N with G/N a restricted soluble group and if G is the only contranormal subgroup of G. This supplements Kurdachenko, Otal, and Subbotin work of 2009, where they consider the corresponding question but with G/N nilpotent and N a restricted soluble normal subgroup.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42355437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Ergodic properties of Markov semigroups in von Neumann algebras von Neumann代数中Markov半群的遍历性质
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-01-01 DOI: 10.5565/publmat6412012
K. Kielanowicz, A. Luczak
{"title":"Ergodic properties of Markov semigroups in von Neumann algebras","authors":"K. Kielanowicz, A. Luczak","doi":"10.5565/publmat6412012","DOIUrl":"https://doi.org/10.5565/publmat6412012","url":null,"abstract":"We investigate ergodic properties of Markov semigroups in von Neumann algebras with the help of the notion of constrictor, which expresses the idea of closeness of the orbits of the semigroup to some set, as well as the notion of \"generalised averages\", which generalises to arbitrary abelian semigroups the classical notions of Ces`aro, Borel, or Abel means. In particular, mean ergodicity, asymptotic stability, and structure properties of the fixed-point space are analysed in some detail.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74589231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The generic dimension of spaces of $mathbf{A}$-harmonic polynomials $mathbf{A}$-调和多项式空间的一般维数
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2020-01-01 DOI: 10.5565/publmat6412007
P. Rabier
{"title":"The generic dimension of spaces of $mathbf{A}$-harmonic polynomials","authors":"P. Rabier","doi":"10.5565/publmat6412007","DOIUrl":"https://doi.org/10.5565/publmat6412007","url":null,"abstract":"Let A1,...,Ar be linear partial differential operators in N variables, with constant coefficients in a field K of characteristic 0. With A := (A1,...,Ar), a polynomial u is A-harmonic if Au = 0, that is, A1u = ··· = Aru = 0. Denote by mi the order of the first nonzero homogeneous part of Ai (initial part). The main result of this paper is that if r ≤ N, the dimension over K of the space of A-harmonic polynomials of degree at most d is given by an explicit formula depending only upon r, N, d, and m1,...,mr (but not K) provided that the initial parts of A1,...,Ar satisfy a simple generic condition. If r > N and A1,...,Ar are homogeneous, the existence of a generic formula is closely related to a conjecture of Froberg on Hilbert functions. The main result holds even if A1,...,Ar have infinite order, which is unambiguous since they act only on polynomials. This is used to prove, as a corollary, the same formula when A1,...,Ar are replaced with finite difference operators. Another application, when K = C and A1,...,Ar have finite order, yields dimension formulas for spaces of A-harmonic polynomial-exponentials.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83245708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structure monoids of set-theoretic solutions of the Yang-Baxter equation Yang-Baxter方程集论解的结构单群
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-12-20 DOI: 10.5565/PUBLMAT6522104
F. Cedó, E. Jespers, C. Verwimp
{"title":"Structure monoids of set-theoretic solutions of the Yang-Baxter equation","authors":"F. Cedó, E. Jespers, C. Verwimp","doi":"10.5565/PUBLMAT6522104","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522104","url":null,"abstract":"Given a set-theoretic solution $(X,r)$ of the Yang--Baxter equation, we denote by $M=M(X,r)$ the structure monoid and by $A=A(X,r)$, respectively $A'=A'(X,r)$, the left, respectively right, derived structure monoid of $(X,r)$. It is shown that there exist a left action of $M$ on $A$ and a right action of $M$ on $A'$ and 1-cocycles $pi$ and $pi'$ of $M$ with coefficients in $A$ and in $A'$ with respect to these actions respectively. We investigate when the 1-cocycles are injective, surjective or bijective. In case $X$ is finite, it turns out that $pi$ is bijective if and only if $(X,r)$ is left non-degenerate, and $pi'$ is bijective if and only if $(X,r)$ is right non-degenerate. In case $(X,r) $ is left non-degenerate, in particular $pi$ is bijective, we define a semi-truss structure on $M(X,r)$ and then we show that this naturally induces a set-theoretic solution $(bar M, bar r)$ on the least cancellative image $bar M= M(X,r)/eta$ of $M(X,r)$. In case $X$ is naturally embedded in $M(X,r)/eta$, for example when $(X,r)$ is irretractable, then $bar r$ is an extension of $r$. It also is shown that non-degenerate irretractable solutions necessarily are bijective.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47832605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
The monodromy conjecture for a space monomial curve with a plane semigroup 具有平面半群的空间单项式曲线的单项式猜想
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-12-12 DOI: 10.5565/PUBLMAT6522105
J. Mart'in-Morales, W. Veys, L. Vos
{"title":"The monodromy conjecture for a space monomial curve with a plane semigroup","authors":"J. Mart'in-Morales, W. Veys, L. Vos","doi":"10.5565/PUBLMAT6522105","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522105","url":null,"abstract":"This article investigates the monodromy conjecture for a space monomial curve that appears as the special fiber of an equisingular family of curves with a plane branch as generic fiber. Roughly speaking, the monodromy conjecture states that every pole of the motivic, or related, Igusa zeta function induces an eigenvalue of monodromy. As the poles of the motivic zeta function associated with such a space monomial curve have been determined in earlier work, it remains to study the eigenvalues of monodromy. After reducing the problem to the curve seen as a Cartier divisor on a generic embedding surface, we construct an embedded $mathbb Q$-resolution of this pair and use an A'Campo formula in terms of this resolution to compute the zeta function of monodromy. Combining all results, we prove the monodromy conjecture for this class of monomial curves.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45432241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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