Journal of the London Mathematical Society-Second Series最新文献_第2页

Decoding a mean field game by the Cauchy data around its unknown stationary states 解码平均场游戏的柯西数据围绕其未知的稳定状态

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-25 DOI: 10.1112/jlms.70173

Hongyu Liu, Catharine W. K. Lo, Shen Zhang

{"title":"Decoding a mean field game by the Cauchy data around its unknown stationary states","authors":"Hongyu Liu, Catharine W. K. Lo, Shen Zhang","doi":"10.1112/jlms.70173","DOIUrl":"https://doi.org/10.1112/jlms.70173","url":null,"abstract":"In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, social sciences, finance, and transportation. The inverse design and decoding of MFGs offer valuable means to extract information from observed data and gain insights into the intricate underlying dynamics and strategies of these complex physical systems. This paper presents a novel approach to the study of inverse problems in MFGs by analyzing the Cauchy data around their unknown stationary states. This study distinguishes itself from existing inverse problem investigations in three key significant aspects: First, we consider MFG problems in a highly general form. Second, we address the technical challenge of the probability measure constraint by utilizing Cauchy data in our inverse problem study. Third, we enhance existing high-order linearization methods by introducing a novel approach that involves conducting linearization around non-trivial stationary states of the MFG system, which are not a priori known. These contributions provide new insights and offer promising avenues for studying inverse problems for MFGs. By unraveling the hidden structure of MFGs, researchers and practitioners can make informed decisions, optimize system performance, and address real-world challenges more effectively.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70173","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The free boundary for semilinear problems with highly oscillating singular terms 具有高振荡奇异项的半线性问题的自由边界

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-23 DOI: 10.1112/jlms.70180

Mark Allen, Dennis Kriventsov, Henrik Shahgholian

{"title":"The free boundary for semilinear problems with highly oscillating singular terms","authors":"Mark Allen, Dennis Kriventsov, Henrik Shahgholian","doi":"10.1112/jlms.70180","DOIUrl":"https://doi.org/10.1112/jlms.70180","url":null,"abstract":"We investigate general semilinear (obstacle-like) problems of the form <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Delta u = f(u)$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(u)$</annotation>\u0000 </semantics></math> has a singularity/jump at <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$lbrace u=0rbrace$</annotation>\u0000 </semantics></math> giving rise to a free boundary. Unlike many works on such equations where <math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is approximately homogeneous near <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$lbrace u = 0rbrace$</annotation>\u0000 </semantics></math>, we work under assumptions allowing for highly oscillatory behavior. We establish the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$C^infty$</annotation>\u0000 </semantics></math> regularity of the free boundary <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mo>{</mo>\u0000 <mi>u</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$partial lbrace u>0rbrace$</annotation>\u0000 </semantics></math> at flat points. Our approach is to first establish that flat free boundaries are Lipschitz, using a comparison argument with the Kelvin transform. For higher regularity, we study the highly degenerate partial differential equations (PDE) satisfied by ratios of derivatives of <math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </se","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generic root counts and flatness in tropical geometry 热带几何中的一般根数和平整度

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-23 DOI: 10.1112/jlms.70171

Paul Alexander Helminck, Yue Ren

{"title":"Generic root counts and flatness in tropical geometry","authors":"Paul Alexander Helminck, Yue Ren","doi":"10.1112/jlms.70171","DOIUrl":"https://doi.org/10.1112/jlms.70171","url":null,"abstract":"We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space <math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math>. In particular, we are interested in the choices of parameters for which the generic root count is attained. Our families are given as subschemes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>⊆</mo>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <annotation>$Xsubseteq T$</annotation>\u0000 </semantics></math> where <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> is a relative torus over <math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$Y$</annotation>\u0000 </semantics></math>. We generalize Bernstein's theorem from an intersecting family of hypersurfaces <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>f</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∩</mo>\u0000 <mi>⋯</mi>\u0000 <mo>∩</mo>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>f</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X=V(f_1)cap dots cap V(f_n)$</annotation>\u0000 </semantics></math> to an intersecting family of higher-codimensional schemes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>∩</mo>\u0000 <mi>⋯</mi>\u0000 <mo>∩</mo>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$X=X_1cap dots cap X_k$</annotation>\u0000 </semantics></math>, replacing the mixed volume by a tropical intersection product. Central to our work is the notion of tropical flatness of <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70171","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Orbifold Kodaira–Spencer maps and closed-string mirror symmetry for punctured Riemann surfaces 穿孔黎曼曲面的轨道Kodaira-Spencer映射和闭弦镜像对称

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-23 DOI: 10.1112/jlms.70179

Hansol Hong, Hyeongjun Jin, Sangwook Lee

引用次数: 0

On Diophantine graphs 在丢番图上

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-22 DOI: 10.1112/jlms.70163

Gergő Batta, Lajos Hajdu, András Pongrácz

引用次数: 0

Realization of spaces of commutative rings 交换环空间的实现

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-20 DOI: 10.1112/jlms.70175

Laura Cossu, Bruce Olberding

{"title":"Realization of spaces of commutative rings","authors":"Laura Cossu, Bruce Olberding","doi":"10.1112/jlms.70175","DOIUrl":"https://doi.org/10.1112/jlms.70175","url":null,"abstract":"Motivated by recent work on the use of topological methods to study collections of rings between an integral domain and its quotient field, we examine spaces of subrings of a commutative ring, endowed with the Zariski or patch topologies. We introduce three notions to study such a space <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>: patch bundles, patch presheaves and patch algebras. When <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is compact and Hausdorff, patch bundles give a way to approximate <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> with topologically more tractable spaces, namely Stone spaces. Patch presheaves encode the space <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> into stalks of a presheaf of rings over a Boolean algebra, thus giving a more geometrical setting for studying <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. To both objects, a patch bundle and a patch presheaf, we associate what we call a patch algebra, a commutative ring that efficiently realizes the rings in <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> as factor rings, or even localizations, and whose structure reflects various properties of the rings in <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70175","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis 通过渐近分析获得流形上高阶Sobolev不等式的最优常数

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-09 DOI: 10.1112/jlms.70170

Lorenzo Carletti

{"title":"Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis","authors":"Lorenzo Carletti","doi":"10.1112/jlms.70170","DOIUrl":"https://doi.org/10.1112/jlms.70170","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M,g)$</annotation>\u0000 </semantics></math> be a closed Riemannian manifold of dimension <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$kgeqslant 1$</annotation>\u0000 </semantics></math> an integer such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>></mo>\u0000 <mn>2</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$n>2k$</annotation>\u0000 </semantics></math>. We show that there exists <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$B_0>0$</annotation>\u0000 </semantics></math> such that for all <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>k</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$u in H^{k}(M)$</annotation>\u0000 </semantics></math>,\u0000\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Outer Lipschitz classification of normal pairs of Hölder triangles Hölder三角形法线对的外Lipschitz分类

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-08 DOI: 10.1112/jlms.70168

Lev Birbrair, Andrei Gabrielov

{"title":"Outer Lipschitz classification of normal pairs of Hölder triangles","authors":"Lev Birbrair, Andrei Gabrielov","doi":"10.1112/jlms.70168","DOIUrl":"https://doi.org/10.1112/jlms.70168","url":null,"abstract":"A normal pair of Hölder triangles is the union of two normally embedded Hölder triangles satisfying some natural conditions on the tangency orders of their boundary arcs. It is a special case of a surface germ, a germ at the origin of a two-dimensional closed semialgebraic (or, more general, definable in a polynomially bounded o-minimal structure) subset of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math>. Classification of normal pairs considered in this paper is a step toward outer Lipschitz classification of definable surface germs. In the paper of Birbrair and Gabrielov, we introduced a combinatorial invariant of the outer Lipschitz equivalence class of normal pairs, called <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$sigma tau$</annotation>\u0000 </semantics></math>-pizza, and conjectured that it is complete: two normal pairs of Hölder triangles with the same <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$sigma tau$</annotation>\u0000 </semantics></math>-pizzas are outer Lipschitz equivalent. In this paper, we prove that conjecture and define realizability conditions for the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$sigma tau$</annotation>\u0000 </semantics></math>-pizza invariant. Moreover, only one of the two pizzas in the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>σ</mi>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$sigma tau$</annotation>\u0000 </semantics></math>-pizza invariant, together with some admissible permutations related to <math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>, is sufficient for the existence and uniqueness, up to outer Lipschitz equivalence, of a normal pair of Hölder triangles.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70168","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fixed-point ratios, Sylow numbers, and coverings of p $p$ -elements in finite groups 有限群中p$ p$ -元素的不动点比、慢数和覆盖

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-05 DOI: 10.1112/jlms.70167

Robert M. Guralnick, Attila Maróti, Juan Martínez Madrid, Alexander Moretó, Noelia Rizo

{"title":"Fixed-point ratios, Sylow numbers, and coverings of \u0000 \u0000 p\u0000 $p$\u0000 -elements in finite groups","authors":"Robert M. Guralnick, Attila Maróti, Juan Martínez Madrid, Alexander Moretó, Noelia Rizo","doi":"10.1112/jlms.70167","DOIUrl":"https://doi.org/10.1112/jlms.70167","url":null,"abstract":"Fixed-point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> and a finite group <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, we use fixed-point ratios to study the number of Sylow <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-subgroups of <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> and the minimal size of a covering by proper subgroups of the set of <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-elements of <math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Moving vectors I: Representation type of blocks of Ariki–Koike algebras 移动向量I: Ariki-Koike代数块的表示类型

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-05 DOI: 10.1112/jlms.70169

Yanbo Li, Xiangyu Qi

引用次数: 0