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New low-rank optimization model and algorithms for spectral compressed sensing
《Science China Mathematics》2024年第10期2409-2432,共24页Zai Yang Xunmeng Wu Zongben Xu 
supported by National Natural Science Foundation of China (Grant Nos. 61977053 and 11922116)。
In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resol...
关键词：low-rank double Hankel model doubly enhanced matrix completion line spectral estimation spectral compressed sensing Kronecker's theorem 
Concentration breaking on two optimization problems
《Science China Mathematics》2024年第7期1555-1570,共16页Yong Huang Qinfeng Li Qiuqi Li 
supported by National Natural Science Foundation of China (Grant Nos. 11625103 and 12171144);Hunan Science and Technology Planning Project (Grant No. 2019RS3016);supported by the National Natural Science Fund for Youth Scholars (Grant No. 12101215);Scientific Research Start-Up Funds by Hunan University;supported by the National Natural Science Fund for Youth Scholars (Grant No. 12101216 );the Natural Science Fund of Hunan Province (Grant No. 2022JJ40030)。
In the present paper, we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined result, the perturbation argument, and ...
关键词：spectral inequalities symmetry breaking Laplacian eigenvalue 
Spectral decimation for a graph-directed fractal pair
《Science China Mathematics》2022年第12期2503-2520,共18页Shiping Cao Hua Qiu Haoran Tian Lijian Yang 
supported by National Natural Science Foundation of China(Grant No.12071213);the Natural Science Foundation of Jiangsu Province in China(Grant No.BK20211142);。
We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s celebrated criterion, we point out that one admits the spectral decimatio...
关键词：fractal Laplacian spectral decimation Dirichlet spectrum Neumann spectrum 
A local discontinuous Galerkin method for the pattern formation dynamical model in polymerizing action flocks
《Science China Mathematics》2022年第4期849-868,共20页Lulu Tian Xiuhui Guo Hui Guo Maosheng Jiang Yang Yang Jiansong Zhang 
supported by National Natural Science Foundation of China(Grant Nos.11801569 and 11571367);Natural Science Foundation of Shandong Province(CN)(Grant Nos.ZR2018BA011 and ZR2019MA015);the Fundamental Research Funds for the Central Universities(Grant Nos.18CX02021A and 18CX05003A);National Science Foundation of USA(Grant No.DMS-1818467).
In this paper,we apply local discontinuous Galerkin methods to the pattern formation dynamical model in polymerizing action flocks.Optimal error estimates for the density and filament polarization in different norms a...
关键词：local discontinuous Galerkin method error estimate pattern formation spectral deferred correction time method 
Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients
《Science China Mathematics》2020年第11期2343-2362,共20页Renming Song Longjie Xie Yingchao Xie 
supported by the Simons Foundation(Grant No.#429343);supported by the Alexander-von-Humboldt Foundation;National Natural Science Foundation of China(Grant No.11701233);National Science Foundation of Jiangsu(Grant No.BK20170226);supported by National Natural Science Foundation of China(Grant No.11771187);The Priority Academic Program Development of Jiangsu Higher Education Institutions。
Using Duhamel’s formula,we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains.In addition,we obtain a gradient esti...
关键词：spectral fractional Laplacian Dirichlet heat kernel Kato class gradient estimate 
A spectral projection method for transmission eigenvalues被引量：2
《Science China Mathematics》2016年第8期1613-1622,共10页ZENG Fang SUN JiGuang XU LiWei 
supported by National Natural Science Foundation of China (Grant Nos. 11501063 and 11371385);National Science Foundation of USA (Grant No. DMS-1521555);the US Army Research Laboratory and the US Army Research Office (Grant No. W911NF-11-2-0046);the Start-up Fund of Youth 1000 Plan of China;that of Youth 100 plan of Chongqing University
We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization...
关键词：spectral projection boundary element method transmission eigenvalues 
A Marcinkiewicz criterion for L^(p)-multipliers related to Schrodinger operators with constant magnetic fields被引量：4
《Science China Mathematics》2015年第2期389-404,共16页DENG Liu Rui MA Bo Lin LIU Shao Yue 
supported by National Natural Science Foundation of China(Grant Nos.10771054 and 71201051);Natural Science Foundation of Zhejiang Province(Grant No.Y6100810);the State Scholarship Fund(Grant No.2014BQ11);Young Talents Training Plan of Hunan Normal University(GrantNo.2014YX04)
In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absol...
关键词：magnetic Schrodinger operator spectral multiplier Riesz means 
Spectral self-affine measures on the planar Sierpinski family被引量：4
《Science China Mathematics》2013年第8期1619-1628,共10页LI JianLin 
supported by National Natural Science Foundation of China (Grant No.11171201)
The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The...
关键词：self-affine measure Sierpinski family orthogonal exponentials spectrality 
Analysis of a class of spectral pair conditions被引量：2
《Science China Mathematics》2011年第10期2099-2110,共12页LI JianLin 
supported by the Key Project of Chinese Ministry of Education (Grant No. 108117);National Natural Science Foundation of China (Grant No. 10871123, 11171201)
For an expanding integer matrix M ∈ Mn（Z） and two finite digit sets D, S C Z^n with O∈ D ∩ S, we shall investigate and study the possible conditions on the spectral pair （μM,D,A（M, S）） associated with the it...
关键词：iterated function system self-affine measure spectral pair compatible pair digit set 
A new method of spectral decomposition of covariance matrix in mixed effects models and its applications被引量：4
《Science China Mathematics》2005年第11期1451-1464,共14页WU Mixia WANG Songgui 
supported by the National Nature Science Foundation of China(Grant No.10271010);the Natural Science Foundation of Bejng(Grant No.1032001)
For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare wit...
关键词：mixed effects model spectral decomposition analysis of variance estimate maximum LIKELIHOOD ESTIMATE 
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