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The chain covering number of a poset with no infinite antichains 无无限反链的偏序集的链覆盖数
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.511
Uri Abraham, Maurice Pouzet
{"title":"The chain covering number of a poset with no infinite antichains","authors":"Uri Abraham, Maurice Pouzet","doi":"10.5802/crmath.511","DOIUrl":"https://doi.org/10.5802/crmath.511","url":null,"abstract":"The chain covering number Cov(P) of a poset P is the least number of chains needed to cover P. For an uncountable cardinal ν, we give a list of posets of cardinality and covering number ν such that for every poset P with no infinite antichain, Cov(P)≥ν if and only if P embeds a member of the list. This list has two elements if ν is a successor cardinal, namely [ν] 2 and its dual, and four elements if ν is a limit cardinal with cf(ν) weakly compact. For ν=ℵ 1 , a list was given by the first author; his construction was extended by F. Dorais to every infinite successor cardinal ν.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869711","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}
引用次数: 0
A simple construction of the Rumin algebra 鲁米代数的一个简单构造
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.510
Jeffrey S. Case
{"title":"A simple construction of the Rumin algebra","authors":"Jeffrey S. Case","doi":"10.5802/crmath.510","DOIUrl":"https://doi.org/10.5802/crmath.510","url":null,"abstract":"","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135872826","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}
引用次数: 0
Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci 非退化多项式的几何:接触轨迹的动力邻近环与上同调
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.492
Quy Thuong Lê, Tat Thang Nguyen
{"title":"Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci","authors":"Quy Thuong Lê, Tat Thang Nguyen","doi":"10.5802/crmath.492","DOIUrl":"https://doi.org/10.5802/crmath.492","url":null,"abstract":"We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit description of these quantities we can answer in part to questions concerning the motivic nearby cycles of restriction functions and the integral identity conjecture in the context of Newton nondegenerate polynomials. Furthermore, in the nondegeneracy in the sense of Kouchnirenko, we give calculations on cohomology groups of the contact loci.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765675","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}
引用次数: 0
Analysis of non scalar control problems for parabolic systems by the block moment method 用块矩法分析抛物系统的非标量控制问题
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.487
Franck Boyer, Morgan Morancey
{"title":"Analysis of non scalar control problems for parabolic systems by the block moment method","authors":"Franck Boyer, Morgan Morancey","doi":"10.5802/crmath.487","DOIUrl":"https://doi.org/10.5802/crmath.487","url":null,"abstract":"This article deals with abstract linear time invariant controlled systems of parabolic type. In [9], with A. Benabdallah, we introduced the block moment method for scalar control operators. The principal aim of this method is to compute the minimal time needed to drive an initial condition (or a space of initial conditions) to zero, in particular in the case when spectral condensation occurs. The purpose of the present article is to push forward the analysis to deal with any admissible control operator. The considered setting leads to applications to one dimensional parabolic-type equations or coupled systems of such equations.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765828","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}
引用次数: 2
Derivations with values in noncommutative symmetric spaces 非交换对称空间中带值的导数
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-31 DOI: 10.5802/crmath.508
Jinghao Huang, Fedor Sukochev
{"title":"Derivations with values in noncommutative symmetric spaces","authors":"Jinghao Huang, Fedor Sukochev","doi":"10.5802/crmath.508","DOIUrl":"https://doi.org/10.5802/crmath.508","url":null,"abstract":"","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871740","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}
引用次数: 0
On the Birman–Krein Theorem 关于Birman-Krein定理
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI: 10.5802/crmath.473
Vanderléa R. Bazao, César R. de Oliveira, Pablo A. Diaz
{"title":"On the Birman–Krein Theorem","authors":"Vanderléa R. Bazao, César R. de Oliveira, Pablo A. Diaz","doi":"10.5802/crmath.473","DOIUrl":"https://doi.org/10.5802/crmath.473","url":null,"abstract":"It is shown that if X is a unitary operator so that a singular subspace of U is unitarily equivalent to a singular subspace of UX (or XU), for each unitary operator U, then X is the identity operator. In other words, there is no nontrivial generalization of Birman–Krein Theorem that includes the preservation of a singular spectral subspace in this context.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220099","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}
引用次数: 0
Optimal weak estimates for Riesz potentials Riesz势的最优弱估计
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI: 10.5802/crmath.479
Liang Huang, Hanli Tang
{"title":"Optimal weak estimates for Riesz potentials","authors":"Liang Huang, Hanli Tang","doi":"10.5802/crmath.479","DOIUrl":"https://doi.org/10.5802/crmath.479","url":null,"abstract":"where γ s =2 -s π -n 2 Γ(n-s 2) Γ(s 2). We also consider the behavior of the best constant 𝒞 n,s of weak type estimate for Riesz potentials, and we prove 𝒞 n,s =O(γ s s) as s→0.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135268166","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}
引用次数: 0
Compactly supported cohomology of a tower of graphs and generic representations of PGL n over a local field 图塔的紧支持上同调和局部域上PGL n的一般表示
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI: 10.5802/crmath.485
Anis Rajhi
{"title":"Compactly supported cohomology of a tower of graphs and generic representations of PGL n over a local field","authors":"Anis Rajhi","doi":"10.5802/crmath.485","DOIUrl":"https://doi.org/10.5802/crmath.485","url":null,"abstract":"Let F be a non-archimedean locally compact field and let G n be the group PGL n (F). In this paper we construct a tower (X ˜ k ) k⩾0 of graphs fibred over the one-skeleton of the Bruhat–Tits building of G n . We prove that a non-spherical and irreducible generic complex representation of G n can be realized as a quotient of the compactly supported cohomology of the graph X ˜ k for k large enough. Moreover, when the representation is cuspidal then it has a unique realization in a such model.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267542","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}
引用次数: 0
Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients Littlewood-Richardson系数和plethystic系数正的必要条件
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI: 10.5802/crmath.468
Álvaro Gutiérrez, Mercedes H. Rosas
{"title":"Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients","authors":"Álvaro Gutiérrez, Mercedes H. Rosas","doi":"10.5802/crmath.468","DOIUrl":"https://doi.org/10.5802/crmath.468","url":null,"abstract":"We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if S λ (V) appears as a summand in the decomposition into irreducibles of S μ (S ν (V)), then ν’s diagram is contained in λ’s diagram.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220359","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}
引用次数: 1
The variance-gamma ratio distribution 方差-比值分布
4区 数学
Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI: 10.5802/crmath.495
Robert E. Gaunt, Siqi Li
{"title":"The variance-gamma ratio distribution","authors":"Robert E. Gaunt, Siqi Li","doi":"10.5802/crmath.495","DOIUrl":"https://doi.org/10.5802/crmath.495","url":null,"abstract":"Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including identification of parameter regimes under which the density is bounded, asymptotic approximations of tail probabilities, and fractional moments; in particular, we see that the mean is undefined. In the case that $X$ and $Y$ are independent symmetric variance-gamma random variables, an exact formula is also given for the cumulative distribution function of the ratio $X/Y$.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267545","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}
引用次数: 1
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