Pub Date : 2023-06-13DOI: 10.1007/s11425-022-2056-6
C. Gopalakrishna, Murugan Veerapazham, Suyun Wang, Weinian Zhang
{"title":"Existence, construction and extension of continuous solutions of an iterative equation with multiplication","authors":"C. Gopalakrishna, Murugan Veerapazham, Suyun Wang, Weinian Zhang","doi":"10.1007/s11425-022-2056-6","DOIUrl":"https://doi.org/10.1007/s11425-022-2056-6","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"5 1","pages":"2261 - 2276"},"PeriodicalIF":1.4,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75182751","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}
Pub Date : 2023-06-07DOI: 10.1007/s11425-021-2062-6
Tao Wang, Yanping Chen
{"title":"Nitsche-XFEM for a time fractional diffusion interface problem","authors":"Tao Wang, Yanping Chen","doi":"10.1007/s11425-021-2062-6","DOIUrl":"https://doi.org/10.1007/s11425-021-2062-6","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81653326","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}
Pub Date : 2023-05-25DOI: 10.1007/s11425-023-2144-6
Huitao Feng, Ming Li
{"title":"Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds","authors":"Huitao Feng, Ming Li","doi":"10.1007/s11425-023-2144-6","DOIUrl":"https://doi.org/10.1007/s11425-023-2144-6","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"1 1","pages":"1903 - 1932"},"PeriodicalIF":1.4,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85559646","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}
Pub Date : 2023-05-15DOI: 10.1007/s11425-022-2149-2
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensional unit sphere. Compared with the saddle dynamics without constraints, the constrained high-index saddle dynamics has more complex dynamical forms, and additional operations such as the retraction and vector transport are required due to the constraint, which significantly complicate the numerical scheme and the corresponding numerical analysis. Furthermore, as the existing numerical analysis results usually depend on the index of the saddle points implicitly, the proved numerical accuracy may be reduced if the index is high in many applications, which indicates the lack of robustness with respect to the index. To address these issues, we derive the error estimates for numerical discretization of the constrained high-index saddle dynamics on the high-dimensional sphere, and then improve it by providing an index-robust error analysis in an averaged norm by adjusting the relaxation parameters. The developed results provide mathematical supports for the accuracy of numerical computations.
{"title":"Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere","authors":"Lei Zhang, Pingwen Zhang, Xiangcheng Zheng","doi":"10.1007/s11425-022-2149-2","DOIUrl":"https://doi.org/10.1007/s11425-022-2149-2","url":null,"abstract":"We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensional unit sphere. Compared with the saddle dynamics without constraints, the constrained high-index saddle dynamics has more complex dynamical forms, and additional operations such as the retraction and vector transport are required due to the constraint, which significantly complicate the numerical scheme and the corresponding numerical analysis. Furthermore, as the existing numerical analysis results usually depend on the index of the saddle points implicitly, the proved numerical accuracy may be reduced if the index is high in many applications, which indicates the lack of robustness with respect to the index. To address these issues, we derive the error estimates for numerical discretization of the constrained high-index saddle dynamics on the high-dimensional sphere, and then improve it by providing an index-robust error analysis in an averaged norm by adjusting the relaxation parameters. The developed results provide mathematical supports for the accuracy of numerical computations.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136215922","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}
Pub Date : 2023-05-15DOI: 10.1007/s11425-022-2042-6
Kaijie Xue
{"title":"Distribution/correlation-free test for two-sample means in high-dimensional functional data with eigenvalue decay relaxed","authors":"Kaijie Xue","doi":"10.1007/s11425-022-2042-6","DOIUrl":"https://doi.org/10.1007/s11425-022-2042-6","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"20 1","pages":"2337 - 2346"},"PeriodicalIF":1.4,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75227196","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}
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