A DIRECT METHOD FOR THE UNIT CIRCLE PROBLEM

The unit circle problem is the problem of finding the number of eigenvalues of a non-Hermitian matrix inside and outside the unit circle . To reduce the cost of computing eigenvalues for the problem, a direct method, which is analogous to that given in [5], is proposed in this paper.     

Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.     

THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE SOLVABILITY OF A CLASS OF THE MATRIX INVERSE PROBLEM

Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.     

Hermitian阵的 Hadamard积的Schur补的一些不等式（英文）

本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式，进而，给出了他们的一些应用，这些改进了近期的一些结束．     

ON THE CONVERGENCE OF THE RELAXATION METHODS FOR POSITIVE DEFINITE LINEAR SYSTEMS

1.IntroductionTheclassicaliterativemethods,suchastheJacobimethod,theGauss-SeidelmethodandtheSORmethod,aswellastheirsymmetrizedvariants,playanimportantroleforsolvingthelargesparsesystemoflinearequationsInaccordancewiththebasicextrapolationprincipleofthelineariterativemethod,Hadjidimos[1]furtherproposedaclassofacceleratedoverrelaxation(AOR)methodforsolyingthelinearsystem(1.1)in1978.Thismethodincludestwoarbitraryparameters,andtheirsuitablechoicesnotonlycannaturallyrecovertheJacobi,theGauss-S…     

Infinite classes of anti‐mitre and 5‐sparse Steiner triple systems

In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class modulo 36. The third construction generates many infinite classes of anti‐mitre STSs in the remaining possible orders. As a consequence of these three constructions we can construct anti‐mitre systems for at least 13/14 of the admissible orders. For 5‐sparse STS(υ), we give a construction for υ ≡ 1, 19 (mod 54) and υ ≠ 109. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 237–250, 2006     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

置换环上的稳定矩阵

本文证明了置换环上的正则稳定矩阵是幂等矩阵和可逆矩阵的积,进一步证明了置换环上的正则稳定矩阵可以对角化。     

ICP-AES中Ca、Al之间相互干扰的研究

本文在不同条件下比较详细地研究了Ca与Al在ICP-AES中的相互干扰,结果表明:这种干扰的垂直空间分布与其它元素的基体效应不同,特别在低观察区域Ca、Al之间呈现较为明显的相互抑制效应,说明Ca和Al之间产生了溶质挥发干扰。对分析条件特别是入射功率、载气流量及观察高度进行最优化可以使这种干扰减至最小。     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)