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．     

A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices

In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.

     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

Corner view on the crown domain

In this paper we raise a question about the boundary of the crown domain of a Riemannian symmetric space X. In case X is of Hermitian type we give an affirmative answer.     

几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法

一类空间分数阶扩散方程经过有限差分离散后所得到的离散线性方程组的系数矩阵是两个对角矩阵与Toeplitz型矩阵的乘积之和.在本文中,对于几乎各向同性的二维或三维空间分数阶扩散方程的离散线性方程组,采用预处理Krylov子空间迭代方法,我们利用其系数矩阵的特殊结构和具体性质构造了一类分块快速正则Hermite分裂预处理子.通过理论分析,我们证明了所对应的预处理矩阵的特征值大部分都聚集于1的附近.数值实验也表明,这类分块快速正则Hermite分裂预处理子可以明显地加快广义极小残量(GMRES)方法和稳定化的双共轭梯度(BiCGSTAB)方法等Krylov子空间迭代方法的收敛速度.     

Two new bounds on the size of binary codes with a minimum distance of three

We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)76 andA(11, 3)152.     

On the classification of geometric codes by polynomial functions

It is shown how to represent algebraically all functions that have a zero sum on all -dimensional subspaces ofPG(n,q) or ofAG(n,q). In this way one can calculate the dimensions of related codes, or one can represent interesting sets of points by functions.     

QSPR Modeling of Gibbs Free Energy of Organic Compounds by Weighting of Nearest Neighboring Codes

We examine the encoding of chemical structure of organic compounds by Labeled Hydrogen-Filled Graphs (LHFGs). Quantitative Structure-Property Relationships (QSPR) for a representative set of 150 organic molecules have been derived by means of the optimization of correlation weights of local invariants of the LHFGs. We have tested as local invariants Morgan extended connectivity of zero- and first order, numbers of path of length 2 (P2) and valence shells of distance of 2 (S2) associated with each atom in the molecular structure, and the Nearest Neighboring Codes (NNC). The best statistical characteristics for the Gibbs free energy has been obtained for the NNC weighting. Statistical parameters corresponding to this model are the following n = 100, r² = 0.9974, s = 5.136 kJ/mol, F = 38319 (training set); n = 50, r² = 0.9990, s = 3.405 kJ/mol, F = 48717 (test set). Some possible further developments are pointed out.