数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/cmr.2021-0013
Jianlong Chen
{"title":"The Pseudo Drazin inverses in Banach Algebras","authors":"Jianlong Chen","doi":"10.4208/cmr.2021-0013","DOIUrl":"https://doi.org/10.4208/cmr.2021-0013","url":null,"abstract":"Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if and only if a+ J is Drazin invertible in A /J. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in A . We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order. AMS subject classifications: 15A09, 16U90, 46H05","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48556321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/cmr.2021-0052
Yuhang Liu & HaifengMa
{"title":"Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product","authors":"Yuhang Liu & HaifengMa","doi":"10.4208/cmr.2021-0052","DOIUrl":"https://doi.org/10.4208/cmr.2021-0052","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43829295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/cmr.2021-0015
Ting Zhang
{"title":"Global Solutions of Modified One-Dimensional Schrödinger Equation","authors":"Ting Zhang","doi":"10.4208/cmr.2021-0015","DOIUrl":"https://doi.org/10.4208/cmr.2021-0015","url":null,"abstract":"In this paper, we consider the modified one-dimensional Schrödinger equation: ( Dt−F(D) ) u=λ|u|u, where F(ξ) is a second order constant coefficients classical elliptic symbol, and with smooth initial datum of size ε≪1. We prove that the solution is global-intime, combining the vector fields method and a semiclassical analysis method introduced by Delort. Moreover, we get a one term asymptotic expansion for u when t→+∞. AMS subject classifications: Primary: 35Q55; Secondary: 35A01, 35B40, 35S50","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41443360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/CMR.2020-0040
P. Ducomet
{"title":"Spectral Properties of an Energy-Dependent Hamiltonian","authors":"P. Ducomet","doi":"10.4208/CMR.2020-0040","DOIUrl":"https://doi.org/10.4208/CMR.2020-0040","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44497390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/cmr.2021-0014
Chunmeng Liu
{"title":"Further Results on the Drazin Inverse of Tensors via Einstein Product","authors":"Chunmeng Liu","doi":"10.4208/cmr.2021-0014","DOIUrl":"https://doi.org/10.4208/cmr.2021-0014","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42402039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-06-01DOI: 10.4208/cmr.2021-0008
X. Junji
{"title":"A Finite Method for Computing the Drazin and Core-EP Inverses of Matrices Based on Partial Full-Rank Factorization","authors":"X. Junji","doi":"10.4208/cmr.2021-0008","DOIUrl":"https://doi.org/10.4208/cmr.2021-0008","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48880783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-03-30DOI: 10.4208/cmr.2021-0039
Hai-liang Li, Ling-Yun Shou
{"title":"Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System","authors":"Hai-liang Li, Ling-Yun Shou","doi":"10.4208/cmr.2021-0039","DOIUrl":"https://doi.org/10.4208/cmr.2021-0039","url":null,"abstract":"The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, the long time behavior of the weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48734036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
数学研究通讯Pub Date : 2021-03-01DOI: 10.4208/cmr.2021-0029
Alexander Bors, Qiang Wang
{"title":"Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form","authors":"Alexander Bors, Qiang Wang","doi":"10.4208/cmr.2021-0029","DOIUrl":"https://doi.org/10.4208/cmr.2021-0029","url":null,"abstract":"This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field Fq, which are functions Fq → Fq that agree with a suitable monomial function x 7→ axr on each coset of the index d subgroup of Fq. We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index d generalized cyclotomic permutations of Fq and pertain to cycle structures, the classification of (q − 1)-cycles and involutions, as well as inversion.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}