Advances in Mathematics最新文献_第10页

Totally integrable symplectic billiards are ellipses 完全可积分的交点台球是椭圆

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-02 DOI: 10.1016/j.aim.2024.109873

Luca Baracco, Olga Bernardi

引用次数: 0

On the cohomology of SLn(Z) 论 SLn(Z) 的同调性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-02 DOI: 10.1016/j.aim.2024.109868

Avner Ash

引用次数: 0

Orbital stability of smooth solitons for the modified Camassa-Holm equation 修正卡马萨-霍尔姆方程的光滑孤子轨道稳定性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-02 DOI: 10.1016/j.aim.2024.109870

Ji Li , Yue Liu , Guangming Zhu

引用次数: 0

Old meets new: Connecting two infinite families of congruences modulo powers of 5 for generalized Frobenius partition functions 新旧交替：连接广义弗罗贝尼乌斯分区函数 5 次幂模的两个无限全等族

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-02 DOI: 10.1016/j.aim.2024.109866

Frank G. Garvan , James A. Sellers , Nicolas Allen Smoot

{"title":"Old meets new: Connecting two infinite families of congruences modulo powers of 5 for generalized Frobenius partition functions","authors":"Frank G. Garvan , James A. Sellers , Nicolas Allen Smoot","doi":"10.1016/j.aim.2024.109866","DOIUrl":"10.1016/j.aim.2024.109866","url":null,"abstract":"<div>In 2012 Paule and Radu proved a difficult family of congruences modulo powers of 5 for Andrews' 2-colored generalized Frobenius partition function. The family is associated with the classical modular curve of level 20. We demonstrate the existence of a congruence family for a related generalized Frobenius partition function associated with the same curve. We construct an isomorphism between this new family and the original family of congruences via a mapping on the associated rings of modular functions. The pairing of the congruence families provides a new strategy for future work on congruences associated with modular curves of composite level. We show how a similar approach can be made to multiple other recent examples in the literature. We also give some important insights into the behavior of these congruence families with respect to the Atkin–Lehner involution which proved very important in Paule and Radu's original proof.</div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824003815/pdfft?md5=2166b82a4f610852822f986028088e68&pid=1-s2.0-S0001870824003815-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141960891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra 汤普森群和昆兹代数的不可还原毕达哥拉斯表征

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-02 DOI: 10.1016/j.aim.2024.109871

Arnaud Brothier , Dilshan Wijesena

{"title":"Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra","authors":"Arnaud Brothier , Dilshan Wijesena","doi":"10.1016/j.aim.2024.109871","DOIUrl":"10.1016/j.aim.2024.109871","url":null,"abstract":"<div>We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson groups called Pythagorean. For each finite Pythagorean dimension d we completely classify (in a functorial manner) all such representations using finite dimensional linear algebra. Their irreducible classes form a nice moduli space: a real manifold of dimension <math><mn>2</mn><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn></math>. Apart from a finite disjoint union of circles, each point of the manifold corresponds to an irreducible unitary representation of Thompson's group F (which extends to the other Thompson groups and the Cuntz algebra) that is not monomial. The remaining circles provide monomial representations which we previously fully described and classified. We translate in our language a large number of previous results in the literature. We explain how our techniques extend them.</div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824003864/pdfft?md5=f7ff86adb8bd83e5426f196f622bf16f&pid=1-s2.0-S0001870824003864-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141960892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 regularity of the solutions to the Muskat equation: The degenerate regularity near the turnover points 穆斯卡特方程解的正则性：周转点附近的退化正则性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-08-01 DOI: 10.1016/j.aim.2024.109850

Jia Shi

引用次数: 0

The discrete horospherical p-Minkowski problem in hyperbolic space 双曲空间中的离散角球 p-Minkowski 问题

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-07-31 DOI: 10.1016/j.aim.2024.109851

Haizhong Li , Yao Wan , Botong Xu

引用次数: 0

(Looking for) the heart of abelian Polish groups (寻找）波兰无性群的核心

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-07-30 DOI: 10.1016/j.aim.2024.109865

Martino Lupini

{"title":"(Looking for) the heart of abelian Polish groups","authors":"Martino Lupini","doi":"10.1016/j.aim.2024.109865","DOIUrl":"10.1016/j.aim.2024.109865","url":null,"abstract":"<div>We prove that the category <math><mi>M</mi></math> of abelian groups with a Polish cover introduced in collaboration with Bergfalk and Panagiotopoulos is the left heart of (the derived category of) the quasi-abelian category <math><mi>A</mi></math> of abelian Polish groups in the sense of Beilinson–Bernstein–Deligne and Schneiders. Thus, <math><mi>M</mi></math> is an abelian category containing <math><mi>A</mi></math> as a full subcategory such that the inclusion functor <math><mi>A</mi><mo>→</mo><mi>M</mi></math> is exact and finitely continuous. Furthermore, <math><mi>M</mi></math> is uniquely characterized up to equivalence by the following universal property: for every abelian category <math><mi>B</mi></math>, a functor <math><mi>A</mi><mo>→</mo><mi>B</mi></math> is exact and finitely continuous if and only if it extends to an exact and finitely continuous functor <math><mi>M</mi><mo>→</mo><mi>B</mi></math>. In particular, this provides a description of the left heart of <math><mi>A</mi></math> as a concrete category.We provide similar descriptions of the left heart of a number of categories of algebraic structures endowed with a topology, including: non-Archimedean abelian Polish groups; locally compact abelian Polish groups; totally disconnected locally compact abelian Polish groups; Polish R-modules, for a given Polish group or Polish ring R; and separable Banach spaces and separable Fréchet spaces over a separable complete non-Archimedean valued field.</div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824003803/pdfft?md5=02d0807b27142f50d4a5680236c5cd39&pid=1-s2.0-S0001870824003803-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

On Shimura curves generated by families of Galois G-covers of curves 论由曲线的伽罗瓦 G 盖族生成的志村曲线

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-07-30 DOI: 10.1016/j.aim.2024.109855

Abolfazl Mohajer

引用次数: 0

On extremizing sequences for adjoint Fourier restriction to the sphere 关于对球面的邻接傅立叶限制的极化序列

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2024-07-29 DOI: 10.1016/j.aim.2024.109854

Taryn C. Flock , Betsy Stovall

引用次数: 0