Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics

Cauchy problems for a second order linear differential operator equation

Blended kernel approximation in the ℋ︁‐matrix techniques

Several types of ??‐matrices were shown to provide a data‐sparse approximation of non‐local (integral) operators in FEM and BEM applications. The general construction is applied to the operators with asymptotically smooth kernel function provided that the Galerkin ansatz space has a hierarchical structure. The new class of ??‐matrices is based on the so‐called blended FE and polynomial approximations of the kernel function and leads to matrix blocks with a tensor‐product of block‐Toeplitz (block‐circulant) and rank‐k matrices. This requires the translation (rotation) invariance of the kernel combined with the corresponding tensor‐product grids. The approach allows for the fast evaluation of volume/boundary integral operators with possibly non‐smooth kernels defined on canonical domains/manifolds in the FEM/BEM applications. (Here and in the following, we call domains canonical if they are obtained by translation or rotation of one of their parts, e.g. parallelepiped, cylinder, sphere, etc.) In particular, we provide the error and complexity analysis for blended expansions to the Helmholtz kernel. Copyright © 2002 John Wiley & Sons, Ltd.     

整环上几类矩阵空间的保持伴随矩阵线性算子

本文刻画了整环上的全矩阵空间、对称矩阵空间和上三角矩阵空间上保持伴随矩阵的线性算子的结构。     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

Some New Results on Circulant Weighing Matrices

We obtain a few structural theorems for circulant weighing matrices whose weight is the square of a prime number. Our results provide new schemes to search for these objects. We also establish the existence status of several previously open cases of circulant weighing matrices. More specifically we show their nonexistence for the parameter pairs (n, k) (here n is the order of the matrix and k its weight) = (147, 49), (125, 25), (200, 25), (55, 25), (95, 25), (133, 49), (195, 25), (11 w, 121) for w < 62.     

一类(0,1)-矩阵的最大积和式的积分表达式

给出了线和n-2的n阶（0，1）－矩阵的最大积和式的积分表达式，并证明了该积分表达式与[1]得到的组合表达式等价。     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Sufficient conditions are given for the Q-superlinear convergence of the iterates produced by primal-dual interior-point methods for linear complementarity problems. It is shown that those conditions are satisfied by several well known interior-point methods. In particular it is shown that the iteration sequences produced by the simplified predictor–corrector method of Gonzaga and Tapia, the simplified largest step method of Gonzaga and Bonnans, the LPF+ algorithm of Wright, the higher order methods of Wright and Zhang, Potra and Sheng, and Stoer, Wechs and Mizuno are Q-superlinearly convergent. Received: February 9, 2000 / Accepted: February 20, 2001?Published online May 3, 2001