数学研究通讯Pub Date : 2018-07-28DOI: 10.4208/cmr.2020-0052
Yun Miao, L. Qi, Yimin Wei
{"title":"M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds","authors":"Yun Miao, L. Qi, Yimin Wei","doi":"10.4208/cmr.2020-0052","DOIUrl":"https://doi.org/10.4208/cmr.2020-0052","url":null,"abstract":"We generalized Xiang, Qi and Wei's results on the M-eigenvalues of Riemann curvature tensor to higher dimensional conformal flat manifolds. The expression of M-eigenvalues and M-eigenvectors are found in our paper. As a special case, M-eigenvalues of conformal flat Einstein manifold have also been discussed, and the conformal the invariance of M-eigentriple has been found. We also discussed the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold. We proved that the M-eigenvalue can determine the Riemann curvature tensor uniquely and generalize the real M-eigenvalue to complex cases. In the last part of our paper, we give an example to compute the M-eigentriple of de Sitter spacetime which is well-known in general relativity.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46618625","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 : 2017-10-29DOI: 10.4208/cmr.2020-0053
Wenhao Li, Bo Wang, Tianxiang Shen, Ronghua Zhu, Dehui Wang
{"title":"Research on Ruin Probability of RiskModel Based on AR(1) Time Series","authors":"Wenhao Li, Bo Wang, Tianxiang Shen, Ronghua Zhu, Dehui Wang","doi":"10.4208/cmr.2020-0053","DOIUrl":"https://doi.org/10.4208/cmr.2020-0053","url":null,"abstract":"In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton iteration method to figure out the adjustment coefficient and estimate the exponential upper bound of ruin probability. This is significant to refine the research of ruin theory. As a result, our theory will help develop insurance industry stably.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49057997","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 : 2017-02-10DOI: 10.4208/cmr.2021-0078
Li-Ping Wang, D. Wan, Weiqiong Wang, Haiyan Zhou
{"title":"On Jumped Wenger Graphs","authors":"Li-Ping Wang, D. Wan, Weiqiong Wang, Haiyan Zhou","doi":"10.4208/cmr.2021-0078","DOIUrl":"https://doi.org/10.4208/cmr.2021-0078","url":null,"abstract":"In this paper we introduce a new infinite class of bipartite graphs, called jumped Wenger graphs, which are closely related to Wenger graphs. An tight upper bound of the diameter and the exact girth of a jumped Wenger graph $J_m(q, i, j )$ for integers $i, j$, $1leq i <j leq m+2$, are determined. In particular, the exact diameter of the jumped Wenger graph $J_m(q, i, j)$ if $(i, j)=(m,m+2), (m+1,m+2)$ or $(m,m+1)$ is also obtained.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43751485","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 : 2015-10-07DOI: 10.4208/CMR.2020-0006
Yanzhao Cao, Jialin Hong, Zhihui Liu
{"title":"Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises","authors":"Yanzhao Cao, Jialin Hong, Zhihui Liu","doi":"10.4208/CMR.2020-0006","DOIUrl":"https://doi.org/10.4208/CMR.2020-0006","url":null,"abstract":"The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is approximated through the spectral projection of the covariance operator, which is not required to be commutative with the Laplacian operator. Through the convergence analysis of SPDEs with the noise terms replaced by the projected noises, the well-posedness of the SPDE is established under certain covariance operator-dependent conditions. These SPDEs with projected noises are then numerically approximated with the finite element method. A general error estimate framework is established for the finite element approximations. Based on this framework, optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are obtained. It is shown that with the proposed approach, convergence order of white noise driven SPDEs is improved by half for one-dimensional problems, and by an infinitesimal factor for higher-dimensional problems.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515662","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}
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