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On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets 二步卡诺群凸集的内锥性质，并在单调集上的应用
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-08-20 DOI: 10.5565/publmat6422002
Daniele Morbidelli
{"title":"On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets","authors":"Daniele Morbidelli","doi":"10.5565/publmat6422002","DOIUrl":"https://doi.org/10.5565/publmat6422002","url":null,"abstract":"In the setting of step two Carnot groups, we show a \"cone property\" for horizontally convex sets. Namely we prove that, given a horizontally convex set $C$, a pair of points $Pin partial C$ and $Qin $ int $C$, both belonging to a horizontal line $ell$, then an open truncated subRiemannian cone around $ell$ and with vertex at $P$ is contained in $C$. We apply our result to the problem of classification of horizontally monotone sets in Carnot groups. We are able to show that monotone sets in the direct product $mathbb{H} timesmathbb{R}$ of the Heisenberg group with the real line have hyperplanes as boundaries.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43933740","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 combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation Yang-Baxter方程非对合集论解的组合方法
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-08-12 DOI: 10.5565/PUBLMAT6522111
T. Gateva-Ivanova
{"title":"A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation","authors":"T. Gateva-Ivanova","doi":"10.5565/PUBLMAT6522111","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522111","url":null,"abstract":"We study noninvolutive set-theoretic solutions $(X,r)$ of the Yang-Baxter equations on a set $X$ in terms of the induced left and right actions of $X$ on itself and in terms of the combinatorial properties of the canonically associated algebraic objects-the braided monoid $S(X,r)$ and the graded quadratic $textbf{k}$-algebra $A= A(textbf{k}, X, r)$ over a field $textbf{k}$. We investigate the class of (noninvolutive) square-free solutions $(X,r)$. It contains the particular class of self distributive solutions (i.e. quandles). We show that, similarly to the involutive case, every square-free braided set (possibly infinite, and not involutive) satisfies the cyclicity condions. We make a detailed characterization in terms of various algebraic and combinatorial properties each of which shows the contrast between involutive and noninvolutive square-free solutions. We study an interesting class of finite square-free braided sets $(X,r)$ of order $ngeq 3$ which satisfy emph{the minimality condition} M, that is $dim_{textbf{k}} A_2 =2n-1$ (equivalently, $A$ can be defined via exactly $(n-1)^2$ reduced binomial relations with special properties). In particular, every such solution is indecomposable. Examples are dihedral racks of prime order $p$. \u0000Finally, for general nondegenerate braided sets $(X,r)$ we discuss extensions of solutions with a special emphasis on emph{strong twisted unions on braided sets}. We prove that if $(Z,r)$ is a nondegenerate 2-cancellative braided set which split as a strong twisted union $Z = Xnatural Y$ of its $r$-invariant subsets $X$ and $Y$ then its braided monoid $S_Z$ is a strong twisted union $S_Z= S_Xnatural S_Y$ of the braided monoids $S_X$ and $S_Y$. Moreover, if $(Z,r)$ is injective then its braided group $G_Z=G(Z,r)$ is also a strong twisted union $G_Z= G_Xnatural G_Y$ of the associated braided groups of $X$ and $Y$.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46745124","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: 18
Multiple vector-valued, mixed norm estimates for Littlewood-Paley square functions Littlewood-Paley平方函数的多向量值混合范数估计
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-08-09 DOI: 10.5565/publmat6622205
C. Benea, Camil Muscalu
{"title":"Multiple vector-valued, mixed norm estimates for Littlewood-Paley square functions","authors":"C. Benea, Camil Muscalu","doi":"10.5565/publmat6622205","DOIUrl":"https://doi.org/10.5565/publmat6622205","url":null,"abstract":"We prove that for any $L^Q$-valued Schwartz function $f$ defined on $mathbb{R}^d$, one has the multiple vector-valued, mixed norm estimate $$ | f |_{L^P(L^Q)} lesssim | S f |_{L^P(L^Q)} $$ valid for every $d$-tuple $P$ and every $n$-tuple $Q$ satisfying $0 < P, Q < infty$ componentwise. Here $S:= S_{d_1}otimes ... otimes S_{d_N}$ is a tensor product of several Littlewood-Paley square functions $S_{d_j}$ defined on arbitrary Euclidean spaces $mathbb{R}^{d_j}$ for $1leq jleq N$, with the property that $d_1 + ... + d_N = d$. This answers a question that came up implicitly in our recent works and completes in a natural way classical results of the Littlewood-Paley theory. The proof is based on the emph{helicoidal method} introduced by the authors.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49445706","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: 5
Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture Hijikata-Pizer-Shemanske曲线上的Heegner点以及Birch和Swinnerton-Dyer猜想
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-07-01 DOI: 10.5565/PUBLMAT6221803
M. Longo, V. Rotger, Carlos de Vera-Piquero
{"title":"Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture","authors":"M. Longo, V. Rotger, Carlos de Vera-Piquero","doi":"10.5565/PUBLMAT6221803","DOIUrl":"https://doi.org/10.5565/PUBLMAT6221803","url":null,"abstract":"We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rathergeneral type of quaternionic orders. We address several questions arising from the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In particular, under mild technical conditions, we show the existence of non-torsion Heegner points on elliptic curves in all situations in which the BSD conjecture predicts their existence.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48952251","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: 3
BMO from dyadic BMO for nonhomogeneous measures 非齐次测度的并矢BMO的BMO
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-06-27 DOI: 10.5565/publmat6412014
José M. Conde-Alonso
{"title":"BMO from dyadic BMO for nonhomogeneous measures","authors":"José M. Conde-Alonso","doi":"10.5565/publmat6412014","DOIUrl":"https://doi.org/10.5565/publmat6412014","url":null,"abstract":"The usual one third trick allows to reduce problems involving general cubes to a countable family. Moreover, this covering lemma uses only dyadic cubes, which allows to use nice martingale properties in harmonic analysis problems. We consider alternatives to this technique in spaces equipped with nonhomogeneous measures. This entails additional difficulties which forces us to consider martingale filtrations that are not regular. The dyadic covering that we find can be used to clarify the relationship between martingale BMO spaces and the most natural BMO space in this setting, which is the space RBMO introduced by Tolsa.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41898795","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: 3
The fibering method approach for a non-linear Schrödinger equation coupled with the electromagnetic field 非线性电磁场耦合Schrödinger方程的纤维化方法
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-06-13 DOI: 10.5565/publmat6422001
G. Siciliano, K. Silva
{"title":"The fibering method approach for a non-linear Schrödinger equation coupled with the electromagnetic field","authors":"G. Siciliano, K. Silva","doi":"10.5565/publmat6422001","DOIUrl":"https://doi.org/10.5565/publmat6422001","url":null,"abstract":"We study, with respect to the parameter $qneq0$, the following Schrodinger-Bopp-Podolsky system in $mathbb R^{3}$ begin{equation*} left{ begin{aligned} -&Delta u+omega u+q^2phi u=|u|^{p-2}u, &-Delta phi+a^2Delta^2 phi = 4pi u^2, end{aligned} right. \u0000end{equation*} where $pin(2,3], omega>0, ageq0$ are fixed. We prove, by means of the fibering approach, that the system has no solutions at all for large values of $q's$, and has two radial solutions for small $q's$. We give also qualitative properties about the energy level of the solutions and a variational characterization of these extremals values of $q$. Our results recover and improve some results in the literature.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42550602","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: 28
An irrational-slope Thompson’s group 一个非理性斜率汤普森组
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-05-31 DOI: 10.5565/PUBLMAT6522112
J. Burillo, Brita Nucinkis, Lawrence Reeves
{"title":"An irrational-slope Thompson’s group","authors":"J. Burillo, Brita Nucinkis, Lawrence Reeves","doi":"10.5565/PUBLMAT6522112","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522112","url":null,"abstract":"The purpose of this paper is to study the properties of the irrational-slope Thompson's group $F_tau$ introduced by Cleary in 1995. We construct presentations, both finite and infinite and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of $F$ in $F_tau$ are undistorted.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45136683","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: 14
Global existence for vector valued fractional reaction-diffusion equations 向量值分数阶反应扩散方程的整体存在性
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-05-25 DOI: 10.5565/PUBLMAT6522108
A. Besteiro, D. Rial
{"title":"Global existence for vector valued fractional reaction-diffusion equations","authors":"A. Besteiro, D. Rial","doi":"10.5565/PUBLMAT6522108","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522108","url":null,"abstract":"In this paper, we study the initial value problem for infinite dimensional fractional non-autonomous reaction-diffusion equations. Applying general time-splitting methods, we prove the existence of solutions globally defined in time using convex sets as invariant regions. We expose examples, where biological and pattern formation systems, under suitable assumptions, achieve global existence. We also analyze the asymptotic behavior of solutions.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48271956","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
On the jumping lines of bundles of logarithmic vector fields along plane curves 沿平面曲线的对数向量场束的跳线
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-04-17 DOI: 10.5565/publmat6422006
A. Dimca, Gabriel Sticlaru
{"title":"On the jumping lines of bundles of logarithmic vector fields along plane curves","authors":"A. Dimca, Gabriel Sticlaru","doi":"10.5565/publmat6422006","DOIUrl":"https://doi.org/10.5565/publmat6422006","url":null,"abstract":"For a reduced curve $C:f=0$ in the complex projective plane $mathbb{P}^2$, we study the set of jumping lines for the rank two vector bundle $Tlangle C rangle $ on $mathbb{P}^2$, whose sections are the logarithmic vector fields along $C$. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of $f$ and with the Bourbaki ideal of the module of Jacobian syzygies of $f$. In particular, when the vector bundle $Tlangle C rangle $ is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne and Hulek resurface in the study of this special class of rank two vector bundles.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41723250","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: 8
Key polynomials over valued fields 值域上的关键多项式
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-03-22 DOI: 10.5565/publmat6412009
E. Nart
{"title":"Key polynomials over valued fields","authors":"E. Nart","doi":"10.5565/publmat6412009","DOIUrl":"https://doi.org/10.5565/publmat6412009","url":null,"abstract":"Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting key polynomials.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41642964","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: 23
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