Acta Mathematica Sinica-English Series最新文献_第7页

On the Geometry of the Anti-canonical Bundle of the Bott-Samelson-Demazure-Hansen Varieties 论博特-萨梅尔森-德马祖尔-汉森变项反规范束的几何图形

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-05-09 DOI: 10.1007/s10114-024-2739-4

Indranil Biswas, S. Senthamarai Kannan, Pinakinath Saha

{"title":"On the Geometry of the Anti-canonical Bundle of the Bott-Samelson-Demazure-Hansen Varieties","authors":"Indranil Biswas, S. Senthamarai Kannan, Pinakinath Saha","doi":"10.1007/s10114-024-2739-4","DOIUrl":"10.1007/s10114-024-2739-4","url":null,"abstract":"<div>Let G be a semi-simple simply connected algebraic group over the field ℂ of complex numbers. Let T be a maximal torus of G, and let W be the Weyl group of G with respect to T. Let Z(w, i) be the Bott-Samelson-Demazure-Hansen variety corresponding to a tuple i associated to a reduced expression of an element w ∈ W. We prove that for the tuple i associated to any reduced expression of a minuscule Weyl group element w, the anti-canonical line bundle on Z(w, i) is globally generated. As consequence, we prove that Z(w, i) is weak Fano.Assume that G is a simple algebraic group whose type is different from A2. Let S = {α1, …, αn} be the set of simple roots. Let w be such that support of w is equal to S. We prove that Z(w, i) is Fano for the tuple i associated to any reduced expression of w if and only if w is a Coxeter element and ({w^{ - 1}}(sumnolimits_{t = 1}^n {{alpha _t}) in - S} ).</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1920 - 1940"},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Boundary Points, Minimal L2 Integrals and Concavity Property III—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces 边界点、最小 L2 积分和凹性特性 III-黎曼曲面上的线性和开黎曼曲面上的纤度

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-05-09 DOI: 10.1007/s10114-024-2344-6

Qi An Guan, Zhi Tong Mi, Zheng Yuan

引用次数: 0

Bi-Frobenius Algebra Structures on Quantum Complete Intersections 量子完全交叉上的双弗罗贝纽斯代数结构

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-05-09 DOI: 10.1007/s10114-024-2370-4

Hai Jin, Pu Zhang

{"title":"Bi-Frobenius Algebra Structures on Quantum Complete Intersections","authors":"Hai Jin, Pu Zhang","doi":"10.1007/s10114-024-2370-4","DOIUrl":"10.1007/s10114-024-2370-4","url":null,"abstract":"<div>This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k. We find a class of comultiplications, such that if (sqrt{-1}in k), then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters qij = ±1. Also, it is proved that if (sqrt{-1}in k) then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q = ±1. While if (sqrt{-1}notin k), then the exterior algebra with two variables admits no bi-Frobenius algebra structures. We prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure, if and only if it is commutative, the characteristic of k is a prime p, and every ai a power of p. This also provides a large class of examples of bi-Frobenius algebras which are not bialgebras (and hence not Hopf algebras). In commutative case, other two comultiplications on complete intersection rings are given, such that they admit non-isomorphic bi-Frobenius algebra structures.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 6","pages":"1481 - 1504"},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140996768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Boundary Regularity of Isometries Between Infinitely Flat Complex Domains 无限平复域间等距的边界正则性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-05-09 DOI: 10.1007/s10114-024-1251-1

Jin Song Liu, Fei Tao, Hong Yu Wang

引用次数: 0

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements 巴拿赫空间有值随机元素规范化双和最大值的一些均值收敛定理

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-20 DOI: 10.1007/s10114-024-2669-1

Andrew Rosalsky, Lê Vǎn Thành, Nguyen Thi Thuy

引用次数: 0

Compressed Data Separation via ℓq-Split Analysis with ℓ∞-Constraint 通过带 ℓ∞ 约束条件的 ℓq 分裂分析进行压缩数据分离

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-20 DOI: 10.1007/s10114-024-2083-8

Ming Yang Gu, Song Li, Jun Hong Lin

{"title":"Compressed Data Separation via ℓq-Split Analysis with ℓ∞-Constraint","authors":"Ming Yang Gu, Song Li, Jun Hong Lin","doi":"10.1007/s10114-024-2083-8","DOIUrl":"10.1007/s10114-024-2083-8","url":null,"abstract":"<div>In this paper, we study compressed data separation (CDS) problem, i.e., sparse data separation from a few linear random measurements. We propose the nonconvex ℓq-split analysis with ℓ∞-constraint and 0 < q ≤ 1. We call the algorithm ℓq-split-analysis Dantzig selector (ℓq-split-analysis DS). We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓq-split-analysis DS, provided that the measurement matrix satisfies either a classical D-RIP (Restricted Isometry Property with respect to Dictionaries and ℓ2 norm) or a relatively new (D, q)-RIP (RIP with respect to Dictionaries and ℓq-quasi norm) condition and the two different dictionaries satisfy a mutual coherence condition between them. For the Gaussian random measurements, the measurement number needed for the (D, q)-RIP condition is far less than those needed for the D-RIP condition and the (D, 1)-RIP condition when q is small enough.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 7","pages":"1655 - 1673"},"PeriodicalIF":0.8,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Operator Equations Inducing Some Generalizations of Slant Hankel Operators 诱导斜向汉克尔算子某些广义化的算子方程

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-3084-3

Gopal Datt, Bhawna Bansal Gupta

引用次数: 0

Variable Selection for Generalized Linear Model with Highly Correlated Covariates 具有高度相关变量的广义线性模型的变量选择

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2198-y

Li Li Yue, Wei Tao Wang, Gao Rong Li

引用次数: 0

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity 用松弛惯性法求解多输出集的分裂单调变分包容问题（无共卷性和立普茨连续性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2594-3

Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo

引用次数: 0

Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System 可压缩纳维-斯托克斯/阿伦-卡恩耦合系统的全局球对称解

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-3399-0

Chang Ming Song, Jian Lin Zhang, Yuan Yuan Wang

引用次数: 0