María Laura Barbagallo, Gabriela Jeronimo, J. Sabia
{"title":"On the zeros of univariate E-polynomials","authors":"María Laura Barbagallo, Gabriela Jeronimo, J. Sabia","doi":"10.33044/revuma.2305","DOIUrl":"https://doi.org/10.33044/revuma.2305","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43723791","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}
{"title":"Positivities in Hall–Littlewood expansions and related plethystic operators","authors":"Marino Romero","doi":"10.33044/revuma.2899","DOIUrl":"https://doi.org/10.33044/revuma.2899","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47159585","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}
Philippe Guyenne, Adilbek Kairzhan, Catherine Sulem
{"title":"Normal form transformations for modulated deep-water gravity waves","authors":"Philippe Guyenne, Adilbek Kairzhan, Catherine Sulem","doi":"10.33044/revuma.2918","DOIUrl":"https://doi.org/10.33044/revuma.2918","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"37 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135892663","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}
. Introducing the conformal vector fields on a statistical manifold, we present necessary and sufficient conditions for a vector field on a statistical manifold to be conformal. After presenting some examples, we classify the conformal vector fields on two famous statistical manifolds. Considering three statistical structures on the tangent bundle of a statistical manifold, we study the conditions under which the complete and horizontal lifts of a vector field can be conformal on these structures.
{"title":"Conformal vector fields on statistical manifolds","authors":"Leila Samereh, E. Peyghan","doi":"10.33044/revuma.2118","DOIUrl":"https://doi.org/10.33044/revuma.2118","url":null,"abstract":". Introducing the conformal vector fields on a statistical manifold, we present necessary and sufficient conditions for a vector field on a statistical manifold to be conformal. After presenting some examples, we classify the conformal vector fields on two famous statistical manifolds. Considering three statistical structures on the tangent bundle of a statistical manifold, we study the conditions under which the complete and horizontal lifts of a vector field can be conformal on these structures.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47417693","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 survey some of the recent developments in the study of the compactness and uniqueness problems for some classes of conformally compact Einstein manifolds.
.我们综述了最近在研究某些类共形紧致Einstein流形的紧致性和唯一性问题方面的一些进展。
{"title":"On conformally compact Einstein manifolds","authors":"S. Chang, Yuxin Ge","doi":"10.33044/revuma.3156","DOIUrl":"https://doi.org/10.33044/revuma.3156","url":null,"abstract":". We survey some of the recent developments in the study of the compactness and uniqueness problems for some classes of conformally compact Einstein manifolds.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42599343","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 consider a class of semilinear wave equations with both strongly and nonlinear weakly damped terms, u tt − ∆ u − ω ∆ u t + µ | u t | m − 2 u t = | u | p − 2 u, associated with initial and Dirichlet boundary conditions. Under certain con- ditions, we show that any solution with arbitrarily high positive initial energy blows up in finite time if m < p . Furthermore, we obtain a lower bound for the blow-up time.
． 考虑一类具有强阻尼项和非线性弱阻尼项的半线性波动方程，u tt−∆u−ω∆u t +µ| u t | m−2 u t = | u | p−2 u，具有初始边界条件和Dirichlet边界条件。在一定条件下，我们证明了当m < p时，具有任意高正初始能量的解在有限时间内爆炸。进一步，我们得到了爆破时间的下界。
{"title":"Blow-up of positive-initial-energy solutions for nonlinearly damped semilinear wave equations","authors":"M. Kerker","doi":"10.33044/revuma.2099","DOIUrl":"https://doi.org/10.33044/revuma.2099","url":null,"abstract":". We consider a class of semilinear wave equations with both strongly and nonlinear weakly damped terms, u tt − ∆ u − ω ∆ u t + µ | u t | m − 2 u t = | u | p − 2 u, associated with initial and Dirichlet boundary conditions. Under certain con- ditions, we show that any solution with arbitrarily high positive initial energy blows up in finite time if m < p . Furthermore, we obtain a lower bound for the blow-up time.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41958926","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 note we discuss some geometric analogs of the classical harmonic functions on Rn and their associated evolutions. Harmonic functions are ubiquitous in mathematics, with applications arising in complex analysis, potential theory, electrostatics, and heat conduction. A harmonic function u in R solves the Laplace equation ∆u = 0 in a domain Ω, where ∆ = ∑n j=1 ∂ 2 xj . The well-known Dirichlet principle says that harmonic functions are critical points of the Dirichlet energy 1 2 ∫ Ω |∇u| 2. The associated evolutions are the heat equation ∂tu − ∆u = 0 and the wave equation ∂2 t u − ∆u = 0. The geometric analogs we will be discussing (which also have applications in physics) are harmonic maps: functions u : R → M , where M is a Riemannian manifold. Introduced in the early 1960s by Eells and Sampson [15], they are also critical points of the Dirichlet energy. The resulting Euler–Lagrange equation is a nonlinear PDE, because of the nonlinear constraint that u(x) ∈M . When M = S2 with the round metric, the equation becomes ∆u = −|∇u|2u. The point of introducing harmonic maps was to use them as a tool to study the geometric and topological properties of the manifold M . For instance, Eells and Sampson showed, using the associated heat flow (the harmonic map heat flow), that smooth functions from R to M can be deformed (under certain geometric conditions on M) into harmonic maps. This work inspired Hamilton [20] to introduce his Ricci flow, which eventually led to the proof of the Poincaré conjecture by Perelman [28]. The study of the singularities of these flows led to the notion of bubbling in singularity formation. It turns out that the bubbling phenomenon is universal, and is analogous to the soliton resolution which we will be considering later. We now turn to wave maps, the wave flow associated with harmonic maps. The topic is vast, and I will concentrate only on aspects close to my interests. There are several ways to define wave maps u : R×R →M . A formal one is to consider the Lagrangian
{"title":"Wave maps into the sphere","authors":"C. Kenig","doi":"10.33044/revuma.3159","DOIUrl":"https://doi.org/10.33044/revuma.3159","url":null,"abstract":"In this note we discuss some geometric analogs of the classical harmonic functions on Rn and their associated evolutions. Harmonic functions are ubiquitous in mathematics, with applications arising in complex analysis, potential theory, electrostatics, and heat conduction. A harmonic function u in R solves the Laplace equation ∆u = 0 in a domain Ω, where ∆ = ∑n j=1 ∂ 2 xj . The well-known Dirichlet principle says that harmonic functions are critical points of the Dirichlet energy 1 2 ∫ Ω |∇u| 2. The associated evolutions are the heat equation ∂tu − ∆u = 0 and the wave equation ∂2 t u − ∆u = 0. The geometric analogs we will be discussing (which also have applications in physics) are harmonic maps: functions u : R → M , where M is a Riemannian manifold. Introduced in the early 1960s by Eells and Sampson [15], they are also critical points of the Dirichlet energy. The resulting Euler–Lagrange equation is a nonlinear PDE, because of the nonlinear constraint that u(x) ∈M . When M = S2 with the round metric, the equation becomes ∆u = −|∇u|2u. The point of introducing harmonic maps was to use them as a tool to study the geometric and topological properties of the manifold M . For instance, Eells and Sampson showed, using the associated heat flow (the harmonic map heat flow), that smooth functions from R to M can be deformed (under certain geometric conditions on M) into harmonic maps. This work inspired Hamilton [20] to introduce his Ricci flow, which eventually led to the proof of the Poincaré conjecture by Perelman [28]. The study of the singularities of these flows led to the notion of bubbling in singularity formation. It turns out that the bubbling phenomenon is universal, and is analogous to the soliton resolution which we will be considering later. We now turn to wave maps, the wave flow associated with harmonic maps. The topic is vast, and I will concentrate only on aspects close to my interests. There are several ways to define wave maps u : R×R →M . A formal one is to consider the Lagrangian","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47116582","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 k be a finite field of characteristic p and let X → Spec k [[ t ]] be a semistable family of varieties over k . We prove that there exists a Clemens– Schmid type exact sequence for this family. We do this by constructing a larger family defined over a smooth curve and using a Clemens–Schmid exact sequence in characteristic p for this new family.
{"title":"A Clemens–Schmid type exact sequence over a local basis","authors":"Genaro Hernandez-Mada","doi":"10.33044/revuma.2163","DOIUrl":"https://doi.org/10.33044/revuma.2163","url":null,"abstract":". Let k be a finite field of characteristic p and let X → Spec k [[ t ]] be a semistable family of varieties over k . We prove that there exists a Clemens– Schmid type exact sequence for this family. We do this by constructing a larger family defined over a smooth curve and using a Clemens–Schmid exact sequence in characteristic p for this new family.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184404","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 present the basic ( k,a )-generalized wavelet theory and prove several Heisenberg-type inequalities for this transform. After reviewing Pitt’s and Beckner’s inequalities for the ( k,a )-generalized Fourier transform, we connect both inequalities to show a generalization of uncertainty principles for the ( k,a )-generalized wavelet transform. We also present two concentration uncertainty principles, namely the Benedicks–Amrein–Berthier’s uncertainty principle and local uncertainty principles. Finally, we connect these inequalities to show a generalization of the uncertainty principle of Heisenberg type and we prove the Faris–Price uncertainty principle for the ( k,a )-generalized wavelet transform.
{"title":"New uncertainty principles for the $(k,a)$-generalized wavelet transform","authors":"H. Mejjaoli","doi":"10.33044/revuma.2051","DOIUrl":"https://doi.org/10.33044/revuma.2051","url":null,"abstract":". We present the basic ( k,a )-generalized wavelet theory and prove several Heisenberg-type inequalities for this transform. After reviewing Pitt’s and Beckner’s inequalities for the ( k,a )-generalized Fourier transform, we connect both inequalities to show a generalization of uncertainty principles for the ( k,a )-generalized wavelet transform. We also present two concentration uncertainty principles, namely the Benedicks–Amrein–Berthier’s uncertainty principle and local uncertainty principles. Finally, we connect these inequalities to show a generalization of the uncertainty principle of Heisenberg type and we prove the Faris–Price uncertainty principle for the ( k,a )-generalized wavelet transform.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45108437","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}
Trees with a unique maximum independent set encode the maximum matching structure in every tree. In this work we study some of their linear properties and give two graph operations, stellare and S-coalescence, which allow building all trees with a unique maximum independent set. The null space structure of any tree can be understood in terms of these graph operations.
{"title":"Trees with a unique maximum independent set and their linear properties","authors":"D. Jaume, Gonzalo Molina, Rodrigo Sota","doi":"10.33044/revuma.1145","DOIUrl":"https://doi.org/10.33044/revuma.1145","url":null,"abstract":"Trees with a unique maximum independent set encode the maximum matching structure in every tree. In this work we study some of their linear properties and give two graph operations, stellare and S-coalescence, which allow building all trees with a unique maximum independent set. The null space structure of any tree can be understood in terms of these graph operations.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46546140","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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