We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton--Jacobi equations can be approximated by iterated twisted Lax--Oleinik like operators. We establish convergence to the solution of the iterated scheme and discuss further properties of the approximate solutions.
{"title":"Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations","authors":"M. Zavidovique","doi":"10.5802/AFST.1598","DOIUrl":"https://doi.org/10.5802/AFST.1598","url":null,"abstract":"We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton--Jacobi equations can be approximated by iterated twisted Lax--Oleinik like operators. We establish convergence to the solution of the iterated scheme and discuss further properties of the approximate solutions.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131476518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose an approach of Mellin type for the approximation of integration currents or the effective realization of normalized Green currents associated with a cycle $ bigwedge_1^m[{rm div} (s_j)] $, where $s_j $ is a meromorphic section of a line bundle $ mathscr{L}_j rightarrow U$ over an open $U$ in a good Berkovich space when each $ mathscr{L}_j$ has a smooth metric and $ {rm codim}_{U}big (bigcap_{j in J} {rm Supp} [{rm div (s_j)}] big)geq # J$ for every set $ J subset {1, ..., p } $. We also study the transposition to the non archimedean context of Crofton and King formulas, particularly the approximate realization of Vogel and Segre currents.
我们提出了一种Mellin类型的方法来逼近积分电流或与循环$ bigwedge_1^m[{rm div} (s_j)] $相关的归一化Green电流的有效实现，其中$s_j $是在良好Berkovich空间中开放$U$上的线束$ mathscr{L}_j rightarrow U$的亚纯截面，当每个$ mathscr{L}_j$和$ {rm codim}_{U}big (bigcap_{j in J} {rm Supp} [{rm div (s_j)}] big)geq # J$对于每个集$ J subset {1, ..., p } $都有一个光滑度规。我们还研究了Crofton和King公式在非阿基米德背景下的转换，特别是Vogel和Segre电流的近似实现。
{"title":"Approches courantielles à la Mellin dans un cadre non archimédien","authors":"Ibrahima Hamidine","doi":"10.5802/afst.1602","DOIUrl":"https://doi.org/10.5802/afst.1602","url":null,"abstract":"We propose an approach of Mellin type for the approximation of integration currents or the effective realization of normalized Green currents associated with a cycle $ bigwedge_1^m[{rm div} (s_j)] $, where $s_j $ is a meromorphic section of a line bundle $ mathscr{L}_j rightarrow U$ over an open $U$ in a good Berkovich space when each $ mathscr{L}_j$ has a smooth metric and $ {rm codim}_{U}big (bigcap_{j in J} {rm Supp} [{rm div (s_j)}] big)geq # J$ for every set $ J subset {1, ..., p } $. We also study the transposition to the non archimedean context of Crofton and King formulas, particularly the approximate realization of Vogel and Segre currents.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121304029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was available in the Artin case.
{"title":"Shifted cotangent stacks are shifted symplectic","authors":"D. Calaque","doi":"10.5802/afst.1593","DOIUrl":"https://doi.org/10.5802/afst.1593","url":null,"abstract":"We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was available in the Artin case.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122173884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the theory to the broadest class of problems. We deal with two main issues. We first derive transparent numerical boundary conditions, that is, we exhibit the relations satisfied by the solution to the pure Cauchy problem when the initial condition vanishes outside of some domain. Our derivation encompasses discretized transport, diffusion and dispersive equations with arbitrarily wide stencils. The second issue is to prove sharp stability estimates for the initial boundary value problem obtained by enforcing the boundary conditions derived in the first step. We focus here on discretized transport equations. Under the assumption that the numerical boundary is non-characteristic, our main result characterizes the class of numerical schemes for which the corresponding transparent boundary conditions satisfy the so-called Uniform Kreiss-Lopatinskii Condition introduced in [GKS72]. Adapting some previous works to the non-local boundary conditions considered here, our analysis culminates in the derivation of trace and semigroup estimates for such transparent numerical boundary conditions. Several examples and possible extensions are given.
{"title":"Transparent numerical boundary conditions for evolution equations: Derivation and stability analysis","authors":"J. Coulombel","doi":"10.5802/AFST.1600","DOIUrl":"https://doi.org/10.5802/AFST.1600","url":null,"abstract":"The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the theory to the broadest class of problems. We deal with two main issues. We first derive transparent numerical boundary conditions, that is, we exhibit the relations satisfied by the solution to the pure Cauchy problem when the initial condition vanishes outside of some domain. Our derivation encompasses discretized transport, diffusion and dispersive equations with arbitrarily wide stencils. The second issue is to prove sharp stability estimates for the initial boundary value problem obtained by enforcing the boundary conditions derived in the first step. We focus here on discretized transport equations. Under the assumption that the numerical boundary is non-characteristic, our main result characterizes the class of numerical schemes for which the corresponding transparent boundary conditions satisfy the so-called Uniform Kreiss-Lopatinskii Condition introduced in [GKS72]. Adapting some previous works to the non-local boundary conditions considered here, our analysis culminates in the derivation of trace and semigroup estimates for such transparent numerical boundary conditions. Several examples and possible extensions are given.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123491542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Ampere equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge-Ampere equations and optimal transport.
{"title":"Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations","authors":"Jakob Hultgren","doi":"10.5802/afst.1592","DOIUrl":"https://doi.org/10.5802/afst.1592","url":null,"abstract":"Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Ampere equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge-Ampere equations and optimal transport.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126419090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.
{"title":"The Curie-Weiss Model of SOC in Higher Dimension","authors":"M. Gorny","doi":"10.5802/AFST.1594","DOIUrl":"https://doi.org/10.5802/AFST.1594","url":null,"abstract":"We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115176546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the group Tame($mathbf A^3$) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simplified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame($mathbf A^3$). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame($mathbf A^3$) acts by isometries.
我们研究了特征为零的域上三维仿射空间的驯服自同构群驯服($mathbf A^3$)。我们以一种统一的(希望)简化的方式恢复了Kuroda, Shestakov, Umirbaev和Wright先前关于约简理论和Tame($mathbf a ^3$)中的关系的结果。在我们的演示中，新颖之处在于强调了一个单连通的二维简单复合体，其中Tame($mathbf a ^3$)通过等距作用。
{"title":"Combinatorics of the tame automorphism group","authors":"St'ephane Lamy","doi":"10.5802/afst.1597","DOIUrl":"https://doi.org/10.5802/afst.1597","url":null,"abstract":"We study the group Tame($mathbf A^3$) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified and (hopefully) simplified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame($mathbf A^3$). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame($mathbf A^3$) acts by isometries.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121031483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
— We study dynamical degree > 1 real automorphisms of compact complex surfaces with a real structure. We show that a surface with such an automorphism is necessarily projective. We classify real abelian surfaces into eight types, according to the number of connected components of the real part and the simplicity of the underlying complex abelian surface. For each type, we determine the set of values of dynamical degrees which can be realized by real automorphisms. We also prove that the minimum dynamical degree on a complex K3 surface can not be realized on a real K3 surface.
{"title":"Automorphismes loxodromiques de surfaces abéliennes réelles","authors":"Shen Zhao","doi":"10.5802/AFST.1595","DOIUrl":"https://doi.org/10.5802/AFST.1595","url":null,"abstract":"— We study dynamical degree > 1 real automorphisms of compact complex surfaces with a real structure. We show that a surface with such an automorphism is necessarily projective. We classify real abelian surfaces into eight types, according to the number of connected components of the real part and the simplicity of the underlying complex abelian surface. For each type, we determine the set of values of dynamical degrees which can be realized by real automorphisms. We also prove that the minimum dynamical degree on a complex K3 surface can not be realized on a real K3 surface.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128132136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"L^2-theory for the protect overline{partial }-operator on complex spaces with isolated singularities","authors":"J. Ruppenthal","doi":"10.5802/afst.1599","DOIUrl":"https://doi.org/10.5802/afst.1599","url":null,"abstract":"","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"55 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113936565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the restriction of the Kontsevich formality to the subalgebra of the linear polyvectors in the algebra of polyvector fields on Rd. We prove that this formality is an analytic map.
{"title":"Formalité linéaire analytique","authors":"D. Arnal, M. Chaabouni, Mabrouka Hfaiedh","doi":"10.5802/AFST.1596","DOIUrl":"https://doi.org/10.5802/AFST.1596","url":null,"abstract":"In this paper, we study the restriction of the Kontsevich formality to the subalgebra of the linear polyvectors in the algebra of polyvector fields on Rd. \u0000We prove that this formality is an analytic map.","PeriodicalId":122059,"journal":{"name":"Annales de la faculté des sciences de Toulouse Mathématiques","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132592726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：