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Operators with the Lipschitz bounded approximation property 具有Lipschitz有界逼近性质的算子
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-10-18 DOI: 10.1007/s11425-022-2000-y
R. Liu, Jie Shen, Bentuo Zheng
{"title":"Operators with the Lipschitz bounded approximation property","authors":"R. Liu, Jie Shen, Bentuo Zheng","doi":"10.1007/s11425-022-2000-y","DOIUrl":"https://doi.org/10.1007/s11425-022-2000-y","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84312893","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
Fast-slow stochastic dynamical system with singular coefficients 具有奇异系数的快慢随机动力系统
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-10-13 DOI: 10.1007/s11425-020-1971-1
Longjie Xie
{"title":"Fast-slow stochastic dynamical system with singular coefficients","authors":"Longjie Xie","doi":"10.1007/s11425-020-1971-1","DOIUrl":"https://doi.org/10.1007/s11425-020-1971-1","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80008743","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: 1
The Heisenberg double of the quantum Euclidean group and its representations 量子欧几里得群的海森堡双元及其表示
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-09-29 DOI: 10.1007/s11425-021-2043-7
Wenqing Tao
{"title":"The Heisenberg double of the quantum Euclidean group and its representations","authors":"Wenqing Tao","doi":"10.1007/s11425-021-2043-7","DOIUrl":"https://doi.org/10.1007/s11425-021-2043-7","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73465563","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: 1
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation 非局部Cahn-Hilliard方程二阶线性数值格式的双重稳定与收敛性分析
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-09-08 DOI: 10.48550/arXiv.2209.03647
Xiao Li, Zhonghua Qiao, Cheng Wang
{"title":"Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation","authors":"Xiao Li, Zhonghua Qiao, Cheng Wang","doi":"10.48550/arXiv.2209.03647","DOIUrl":"https://doi.org/10.48550/arXiv.2209.03647","url":null,"abstract":"In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization, and by applying the Fourier spectral collocation to the spatial discretization. In addition, two stabilization terms in different forms are added for the sake of the numerical stability. We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme, combined with the rough error estimate and the refined estimate. By regarding the numerical solution as a small perturbation of the exact solution, we are able to justify the discrete ℓ ∞ bound of the numerical solution, as a result of the rough error estimate. Subsequently, the refined error estimate is derived to obtain the optimal rate of convergence, following the established ℓ ∞ bound of the numerical solution. Moreover, the energy stability is also rigorously proved with respect to a modified energy. The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work, and the energy stability estimate has greatly improved the corresponding result therein.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80155954","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: 4
On unitary equivalence of compact operator tuples 紧算子元组的幺正等价
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-09-07 DOI: 10.1007/s11425-021-1976-8
Wei He, Rongwei Yang
{"title":"On unitary equivalence of compact operator tuples","authors":"Wei He, Rongwei Yang","doi":"10.1007/s11425-021-1976-8","DOIUrl":"https://doi.org/10.1007/s11425-021-1976-8","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82730613","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
Regularity for minimizing sequences of some variational integrals 一些变分积分的最小化序列的规则性
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-09-02 DOI: 10.1007/s11425-021-1975-5
Hongya Gao, Yanan Shan, Wei Ren
{"title":"Regularity for minimizing sequences of some variational integrals","authors":"Hongya Gao, Yanan Shan, Wei Ren","doi":"10.1007/s11425-021-1975-5","DOIUrl":"https://doi.org/10.1007/s11425-021-1975-5","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90984921","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: 1
On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group 具有不可约传递自同构群的有限经典极空间的m-仿形上
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-08-27 DOI: 10.1007/s11425-021-2060-3
Tao Feng, Weicong Li, Rao Tao
{"title":"On m-ovoids of finite classical polar spaces with an irreducible transitive automorphism group","authors":"Tao Feng, Weicong Li, Rao Tao","doi":"10.1007/s11425-021-2060-3","DOIUrl":"https://doi.org/10.1007/s11425-021-2060-3","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84709780","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
New existence of multi-spike solutions for the fractional Schrödinger equations 分数阶Schrödinger方程多尖峰解的新存在性
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-08-26 DOI: 10.1007/s11425-021-1991-3
Qing Guo, Yuxia Guo, Shuangjie Peng
{"title":"New existence of multi-spike solutions for the fractional Schrödinger equations","authors":"Qing Guo, Yuxia Guo, Shuangjie Peng","doi":"10.1007/s11425-021-1991-3","DOIUrl":"https://doi.org/10.1007/s11425-021-1991-3","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73078407","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
Bubbling solutions of fourth order mean field equations on $mathbb{S}^{4}$ $mathbb{S}^{4}$上四阶平均场方程的冒泡解
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-08-23 DOI: 10.1007/s11425-022-1993-x
C. Gui, Yeyao Hu, Weihong Xie
{"title":"Bubbling solutions of fourth order mean field equations on $mathbb{S}^{4}$","authors":"C. Gui, Yeyao Hu, Weihong Xie","doi":"10.1007/s11425-022-1993-x","DOIUrl":"https://doi.org/10.1007/s11425-022-1993-x","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77557129","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
The Morse index of minimal products of minimal submanifolds in spheres 球面上极小子流形极小积的莫尔斯指数
IF 1.4 2区 数学
Science China-Mathematics Pub Date : 2022-08-18 DOI: 10.1007/s11425-021-1963-3
C. Wang, Pengfu Wang
{"title":"The Morse index of minimal products of minimal submanifolds in spheres","authors":"C. Wang, Pengfu Wang","doi":"10.1007/s11425-021-1963-3","DOIUrl":"https://doi.org/10.1007/s11425-021-1963-3","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90568505","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: 1
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