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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dirichlet is not just singular and bad
狄利克雷 单数 坏的
2023/4/27
The subject of Diophantine approximation studies how a real vector is approximated by rational vectors. Diophantine sets are subsets of real vectors defined by certain approximate functions. Among the...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Singular value thresholding Stein’s unbiased risk estimate (SURE) differentiability of eigenvalues and eigenvectors magnetic resonance cardiac imaging
2015/6/17
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian...
Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups
Singular integrals self-similar sets removability Heisenberg group
2011/1/20
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean space...
A frequency function and singular set bounds for branched minimal immersions
frequency function singular branched minimal immersions
2011/2/25
In [Wic08], the second author established a local C1,α partial regularity theory for stable
branched minimal hypersurfaces of multiplicity < 3. The main regularity theorem of [Wic08] in particular im...
Eigenfunctions and Very Singular Similarity Solutions of Odd-Order Nonlinear Dispersion PDEs
Eigenfunctions Very Singular Similarity Solutions Odd-Order Nonlinear Dispersion PDEs
2010/11/11
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed....
Existence of positive solutions to semipositone singular Dirichlet boundary value problems
existence positive solution semipositone singular problem Dirichlet boundary conditions $\phi$-Laplacian
2007/12/13
The paper presents the conditions which guarantee that for some positive value of $\mu$ there are positive solutions of the differential equation $(\phi(x'))'+\mu Q(t,x,x')=0$ satisfying the Dirichlet...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...