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Positive neighborhoods of curves 曲线的正邻域
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-03-19 DOI: 10.5565/publmat6412013
M. F. Luza, P. Sad
{"title":"Positive neighborhoods of curves","authors":"M. F. Luza, P. Sad","doi":"10.5565/publmat6412013","DOIUrl":"https://doi.org/10.5565/publmat6412013","url":null,"abstract":"In this work we study neighborhoods of curves in surfaces with positive self-intersection that can be embeeded as a germ of neighborhood of a curve on the projective plane.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43557629","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
Summability in a monomial for some classes of singularly perturbed partial differential equations 一类奇摄动偏微分方程的单项可和性
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-03-18 DOI: 10.5565/publmat6512103
S. A. Carrillo
{"title":"Summability in a monomial for some classes of singularly perturbed partial differential equations","authors":"S. A. Carrillo","doi":"10.5565/publmat6512103","DOIUrl":"https://doi.org/10.5565/publmat6512103","url":null,"abstract":"The aim of this paper is to complete the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in terms of bounded derivatives and we develop tauberian theorems for the summability processes involved. Furthermore, we develop and apply the Borel-Laplace analysis in this framework to prove the monomial summability of solutions of a specific class of singularly perturbed PDEs.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48062870","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: 4
Computation of Hopf Galois structures on low degree separable extensions and classification of those for degrees $p^2$ and $2p$ 低次可分扩展上Hopf伽罗瓦结构的计算及p^2$和p^2$的分类
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-02-26 DOI: 10.5565/publmat6412005
T. Crespo, Marta Salguero
{"title":"Computation of Hopf Galois structures on low degree separable extensions and classification of those for degrees $p^2$ and $2p$","authors":"T. Crespo, Marta Salguero","doi":"10.5565/publmat6412005","DOIUrl":"https://doi.org/10.5565/publmat6412005","url":null,"abstract":"A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $mu$ a Hopf action. In this paper we present a program written in the computational algebra system Magma which gives all Hopf Galois structures on separable field extensions of degree up to eleven and several properties of those. Besides, we exhibit several results on Hopf Galois structures inspired by the program output. We prove that if $(H,mu)$ is an almost classically Hopf Galois structure, then it is the unique Hopf Galois structure with underlying Hopf algebra $H$, up to isomorphism. For $p$ an odd prime, we prove that a separable extension of degree $p^2$ may have only one type of Hopf Galois structure and determine those of cyclic type; we determine as well the Hopf Galois structures on separable extensions of degree $2p$. We highlight the richness of the results obtained for extensions of degree 8 by computing an explicit example and presenting some tables which summarizes these results.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43015736","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
Sums, products, and ratios along the edges of a graph 沿图边的和、积和比
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-02-18 DOI: 10.5565/publmat6412006
N. Alon, I. Ruzsa, J. Solymosi
{"title":"Sums, products, and ratios along the edges of a graph","authors":"N. Alon, I. Ruzsa, J. Solymosi","doi":"10.5565/publmat6412006","DOIUrl":"https://doi.org/10.5565/publmat6412006","url":null,"abstract":"In their seminal paper ErdH{o}s and Szemer'edi formulated conjectures on the size of sumset and product set of integers. The strongest form of their conjecture is about sums and products along the edges of a graph. In this paper we show that this strong form of the ErdH{o}s-Szemer'edi conjecture does not hold. We give upper and lower bounds on the cardinalities of sumsets, product sets and ratio sets along the edges of graphs.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48524079","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: 10
Some extensions of the modular method and Fermat equations of signature $(13,13,n)$ 符号$(13,13,n)$的模方法和费马方程的一些推广
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-02-12 DOI: 10.5565/publmat6722309
Nicolas Billerey, I. Chen, Lassina Dembélé, L. Dieulefait, Nuno Freitas
{"title":"Some extensions of the modular method and Fermat equations of signature $(13,13,n)$","authors":"Nicolas Billerey, I. Chen, Lassina Dembélé, L. Dieulefait, Nuno Freitas","doi":"10.5565/publmat6722309","DOIUrl":"https://doi.org/10.5565/publmat6722309","url":null,"abstract":"We provide several extensions of the modular method which were motivated by the problem of completing previous work to prove that, for any integer $n geq 2$, the equation [ x^{13} + y^{13} = 3 z^n ] has no non-trivial solutions. In particular, we present four elimination techniques which are based on: (1) establishing reducibility of certain residual Galois representations over a totally real field; (2) generalizing image of inertia arguments to the setting of abelian surfaces; (3) establishing congruences of Hilbert modular forms without the use of often impractical Sturm bounds; and (4) a unit sieve argument which combines information from classical descent and the modular method. \u0000The extensions are of broader applicability and provide further evidence that it is possible to obtain a complete resolution of a family of generalized Fermat equations by remaining within the framework of the modular method. As a further illustration of this, we complete a theorem of Anni-Siksek to show that, for $ell, mge 5$, the only solutions to the equation $x^{2ell} + y^{2m} = z^{13}$ are the trivial ones.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48955188","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: 9
Weighted square function inequalities 加权平方函数不等式
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-01-01 DOI: 10.5565/PUBLMAT6211804
A. Osȩkowski
{"title":"Weighted square function inequalities","authors":"A. Osȩkowski","doi":"10.5565/PUBLMAT6211804","DOIUrl":"https://doi.org/10.5565/PUBLMAT6211804","url":null,"abstract":"For an integrable function f on [0, 1)d, let S(f) and M f denote the corresponding dyadic square function and the dyadic maximal function of f, respectively. The paper contains the proofs of the following statements. (i) If w is a dyadic A1 weight on [0, 1)d, then ||S(f)||L1(w) ≤√ 5[w] 1/2 A1 ||M f||L1(w). The exponent 1/2 is shown to be the best possible. (ii) For any p > 1, there are no constants cp, αp  epending only on p such that for all dyadic Ap weights w on [0, 1)d, ||S(f)||L1(w) ≤ cp[w] αp Ap ||M f||L1(w).","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73095665","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
On the exponent of convergence of negatively curved manifolds without Green's function 无格林函数负弯曲流形的收敛指数
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-01-01 DOI: 10.5565/PUBLMAT6211809
M. Melian, José M. Rodríguez, E. Tourís
{"title":"On the exponent of convergence of negatively curved manifolds without Green's function","authors":"M. Melian, José M. Rodríguez, E. Tourís","doi":"10.5565/PUBLMAT6211809","DOIUrl":"https://doi.org/10.5565/PUBLMAT6211809","url":null,"abstract":"In this paper we prove that for every complete n-dimensional Riemannian manifold without Green’s function and with its sectional curvatures satisfying K ≤−1, the exponent of convergence is greater than or equal to n − 1. Furthermore, we show that this inequality is sharp. This result is well known for manifolds with constant sectional curvatures K = −1.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89550794","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
Infinite series identities involving quadratic and cubic harmonic numbers 涉及二次和三次调和数的无穷级数恒等式
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-01-01 DOI: 10.5565/PUBLMAT6211813
Xiaoyuan Wang, W. Chu
{"title":"Infinite series identities involving quadratic and cubic harmonic numbers","authors":"Xiaoyuan Wang, W. Chu","doi":"10.5565/PUBLMAT6211813","DOIUrl":"https://doi.org/10.5565/PUBLMAT6211813","url":null,"abstract":"By means of the modified Abel lemma on summation by parts, we investigate infinite series involving quadratic and cubic harmonic numbers. Several infinite series identities are established for π 2 and ζ(3) as consequences.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73458082","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: 4
Stability of generalized linear Weingarten hypersurfaces immersed in the Euclidean space 广义线性Weingarten超曲面在欧氏空间中的稳定性
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-01-01 DOI: 10.5565/PUBLMAT6211805
J. F. Silva, H. F. Lima, M. Velásquez
{"title":"Stability of generalized linear Weingarten hypersurfaces immersed in the Euclidean space","authors":"J. F. Silva, H. F. Lima, M. Velásquez","doi":"10.5565/PUBLMAT6211805","DOIUrl":"https://doi.org/10.5565/PUBLMAT6211805","url":null,"abstract":"Given a positive function F defined on the unit Euclidean sphere and satisfying a suitable convexity condition, we consider, for hypersurfaces Mn immersed in the Euclidean space Rn+1, the so-called k-th anisotropic mean curvatures HF k, 0 ≤ k ≤ n. For fixed 0 ≤ r ≤ s ≤ n, a hypersurface Mn of Rn+1 is said to be (r, s, F)-linear Weingarten when its k-th anisotropic mean curvatures HF k, r ≤ k ≤ s, are linearly related. In this setting, we establish the concept of stability concerning closed (r, s, F)-linear Weingarten hypersurfaces  immersed in Rn+1 and, afterwards, we prove that such a hypersurface is stable if, and only if, up to translations and homotheties, it is the Wulff shape of F. For r = s and F ≡ 1, our results amount to the standard stability studied, for instance, by Alencar–do Carmo–Rosenberg.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82912713","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
Entire solutions for critical $p$-fractional Hardy Schrödinger Kirchhoff equations 临界$p$分数阶Hardy Schrödinger Kirchhoff方程的全解
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2018-01-01 DOI: 10.5565/PUBLMAT6211801
Paolo Piersanti, P. Pucci
{"title":"Entire solutions for critical $p$-fractional Hardy Schrödinger Kirchhoff equations","authors":"Paolo Piersanti, P. Pucci","doi":"10.5565/PUBLMAT6211801","DOIUrl":"https://doi.org/10.5565/PUBLMAT6211801","url":null,"abstract":"Existence theorems of nonnegative entire solutions of stationary critical p-fractional Hardy Schr¨odinger Kirchhoff equations are presented in this paper. The equations we treat deal with Hardy terms and critical nonlinearities and the main theorems extend several recent results on the topic. The paper contains also some open problems.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87835055","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: 27
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