. We prove L p bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Laba and M. Pramanik and in some cases are sharp up to the endpoint. A consequence of our main result is that there exist Ahlfors- regular Salem Cantor sets of any dimension > 1 / 2 such that the associated maximal operator is bounded on L 2 ( R ). We follow the overall scheme of Laba– Pramanik for the analytic part of the argument, while the probabilistic part is instead inspired by our earlier work on intersection properties of random measures.
{"title":"New bounds on Cantor maximal operators","authors":"Pablo Shmerkin, Ville Suomala","doi":"10.33044/revuma.3170","DOIUrl":"https://doi.org/10.33044/revuma.3170","url":null,"abstract":". We prove L p bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Laba and M. Pramanik and in some cases are sharp up to the endpoint. A consequence of our main result is that there exist Ahlfors- regular Salem Cantor sets of any dimension > 1 / 2 such that the associated maximal operator is bounded on L 2 ( R ). We follow the overall scheme of Laba– Pramanik for the analytic part of the argument, while the probabilistic part is instead inspired by our earlier work on intersection properties of random measures.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41481870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is injective, then its inverse is also continuous and shift-commuting.
{"title":"On the image set and reversibility of shift morphisms over discrete alphabets","authors":"J. Campos, N. Romero, R. Vivas","doi":"10.33044/revuma.1795","DOIUrl":"https://doi.org/10.33044/revuma.1795","url":null,"abstract":"In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is injective, then its inverse is also continuous and shift-commuting.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42512077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We study tilings of polygons R with arbitrary convex polygonal tiles. Such tilings come in continuous families obtained by moving tile edges parallel to themselves (keeping edge directions fixed). We study how the tile shapes and areas change in these families. In particular we show that if R is convex, the tile shapes can be arbitrarily prescribed (up to homothety). We also show that the tile areas and tile “orientations” determine the tiling. We associate to a tiling an underlying bipartite planar graph G and its corresponding Kasteleyn matrix K . If G has quadrilateral faces, we show that K is the differential of the map from edge intercepts to tile areas, and extract some geometric and probabilistic consequences.
{"title":"Families of convex tilings","authors":"R. Kenyon","doi":"10.33044/revuma.3127","DOIUrl":"https://doi.org/10.33044/revuma.3127","url":null,"abstract":". We study tilings of polygons R with arbitrary convex polygonal tiles. Such tilings come in continuous families obtained by moving tile edges parallel to themselves (keeping edge directions fixed). We study how the tile shapes and areas change in these families. In particular we show that if R is convex, the tile shapes can be arbitrarily prescribed (up to homothety). We also show that the tile areas and tile “orientations” determine the tiling. We associate to a tiling an underlying bipartite planar graph G and its corresponding Kasteleyn matrix K . If G has quadrilateral faces, we show that K is the differential of the map from edge intercepts to tile areas, and extract some geometric and probabilistic consequences.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44930407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let Z ( s ) be the Selberg zeta-function associated to a compact Riemann surface. We consider decompositions Z ( s ) = f ( h ( s )), where f and h are meromorphic functions, and show that such decompositions can only be trivial.
{"title":"Selberg zeta-function associated to compact Riemann surface is prime","authors":"R. Garunkštis","doi":"10.33044/REVUMA.1729","DOIUrl":"https://doi.org/10.33044/REVUMA.1729","url":null,"abstract":". Let Z ( s ) be the Selberg zeta-function associated to a compact Riemann surface. We consider decompositions Z ( s ) = f ( h ( s )), where f and h are meromorphic functions, and show that such decompositions can only be trivial.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42162572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Amp`ere equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games.
{"title":"Asymptotic mean value formulas for parabolic nonlinear equations","authors":"P. Blanc, Fernando Charro, J. Manfredi, J. Rossi","doi":"10.33044/revuma.3169","DOIUrl":"https://doi.org/10.33044/revuma.3169","url":null,"abstract":". In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Amp`ere equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43170259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let n be a non-negative integer, R a commutative Noetherian ring with dim( R ) ≤ n + 2, a an ideal of R , and X an arbitrary R -module. In this paper, we first prove that X is an (FD
． 设n为非负整数，R为dim(R)≤n + 2的交换诺瑟环，a为R的理想，X为任意R -模。本文首先证明了如果X是a -扭转R -模，使得hm R (cid:0) R a,X (cid:1)和Ext 1 R (cid:0) R a,X (cid:1)是FD
{"title":"Cofiniteness of local cohomology modules in the class of modules in dimension less than a fixed integer","authors":"A. Vahidi, Mahdieh Papari-Zarei","doi":"10.33044/REVUMA.1786","DOIUrl":"https://doi.org/10.33044/REVUMA.1786","url":null,"abstract":". Let n be a non-negative integer, R a commutative Noetherian ring with dim( R ) ≤ n + 2, a an ideal of R , and X an arbitrary R -module. In this paper, we first prove that X is an (FD <n , a )-cofinite R -module if X is an a -torsion R -module such that Hom R (cid:0) R a ,X (cid:1) and Ext 1 R (cid:0) R a ,X (cid:1) are FD <n R -modules. Then, we show that H i a ( X ) is an (FD <n , a )-cofinite R -module and { p ∈ Ass R (H i a ( X )) : dim (cid:0) R p (cid:1) ≥ n } is a finite set for all i when Ext iR (cid:0) R a ,X (cid:1) is an FD <n R -module for all i ≤ n + 2. As a consequence, it follows that Ass R (H i a ( X )) is a finite set for all i whenever R is a semi-local ring with dim( R ) ≤ 3 and X is an FD < 1 R -module. Finally, we observe that the category of (FD <n , a )-cofinite R -modules forms an Abelian subcategory of the category of R -modules.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"10 1","pages":"191-198"},"PeriodicalIF":0.5,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79930808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this work is to study the existence and multiplicity of positive solutions for a class of singular elliptic systems involving the p(x)Laplace operator and nonlinear boundary conditions.
{"title":"The fibering map approach for a singular elliptic system involving the $p(x)$-Laplacian and nonlinear boundary conditions","authors":"M. Kratou, K. Saoudi","doi":"10.33044/REVUMA.1221","DOIUrl":"https://doi.org/10.33044/REVUMA.1221","url":null,"abstract":"The purpose of this work is to study the existence and multiplicity of positive solutions for a class of singular elliptic systems involving the p(x)Laplace operator and nonlinear boundary conditions.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.
{"title":"Canal surfaces with generalized 1-type Gauss map","authors":"J. Qian, Mengfei Su, Young Ho Kim","doi":"10.33044/REVUMA.1685","DOIUrl":"https://doi.org/10.33044/REVUMA.1685","url":null,"abstract":"This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"17 1","pages":"199-211"},"PeriodicalIF":0.5,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88423079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the structure of simple multiplicative Hom-Jordan algebras. We discuss equivalent conditions for multiplicative Hom-Jordan algebras to be solvable, simple, and semi-simple. Moreover, we give a theorem on the classification of simple multiplicative Hom-Jordan algebras and obtain some propositions about bimodules of multiplicative Hom-Jordan algebras.
{"title":"Structure of simple multiplicative Hom-Jordan algebras","authors":"Chenrui Yao, Yao Ma, Liangyun Chen","doi":"10.33044/REVUMA.1727","DOIUrl":"https://doi.org/10.33044/REVUMA.1727","url":null,"abstract":"We study the structure of simple multiplicative Hom-Jordan algebras. We discuss equivalent conditions for multiplicative Hom-Jordan algebras to be solvable, simple, and semi-simple. Moreover, we give a theorem on the classification of simple multiplicative Hom-Jordan algebras and obtain some propositions about bimodules of multiplicative Hom-Jordan algebras.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"24 1","pages":"143-170"},"PeriodicalIF":0.5,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75286451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Liouville closed H-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order 1 has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed H-field K with small derivation we show: K has the Intermediate Value Property for differential polynomials iff K is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.
{"title":"On a differential intermediate value property","authors":"Matthias Aschenbrenner, L. Dries, J. Hoeven","doi":"10.33044/revuma.2892","DOIUrl":"https://doi.org/10.33044/revuma.2892","url":null,"abstract":"Liouville closed H-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order 1 has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed H-field K with small derivation we show: K has the Intermediate Value Property for differential polynomials iff K is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47668127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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