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Several sufficient conditions for judgement of the invariant set and the attraction for the equations are obtained by using the properties of nonnegative matrices and some analytical methods.

对一类大型非线性偏泛函微分方程的渐近行为进行研究，利用非负矩阵性质和适当的分析技巧，建立了判断其不变集和吸引性的充分条件。

Based on the invariability of the sought for chemical subspace to the linear transformation, a novel approach, called chemical subspace invariant to linear transformation method, is developed for estimation of chemical rank of two way data matrices.

提出了一个新的化学计量学方法，即线性变换下稳定的化学子空间法，用于二维数据的化学秩估计。

In the new method, the dynamic equilibrium equation of non-proportionally damped structure is expressed in the iteration form, based on which the inverse operation of the matrices is avoided.

此外，文中还对比了相关失效模式和基于独立重复试验的结构体系可靠度，分析了基于独立重复试验假定的串联可靠度计算方法的误差。

This paper is focused on the inverse problem of doubly center matrices .

本文研究双中心矩阵反问题。

Inverse M-matrices often occur in relation to systems of linear or non-linear equations or eigenvalues problems in a wide variety of areas including finite difference methods for partial differential equations, input-output production and growth model in economics, iterative methods in numerical analysis, and Markov processes in probability and statistics.

其中包括偏微分方程的有限差分法、经济中的投入产出和增长模型、数值分析中的迭代法以及概率论和数理统计中的马尔可夫过程。

Optimizing and Realization of the Finite Field Inversion Algorithm Based on FPGA;2. The stability and operation of the inversion formula for Toeplitz matrices are also considered.

利用两个线性方程组是否有解给出了Toeplitz矩阵可逆的条件，表明Toeplitz矩阵之逆阵可以表示为φ-循环矩阵与上三角Toeplitz矩阵的乘积之和，给出了其逆矩阵列的递推公式，得到了求Toeplitz矩阵之逆矩阵的快速算法。

Every invertible matrix is a product of elementary matrices.

每一可逆矩阵系基本矩阵之乘积而得。

Eliminating the restriction of the characteristic of field ,the forms of invertible linear operator preserving inverses of matrices over full matrix space with at least four elements are described.

去掉了域的特征限制，刻画了至少包含4个元素的任意域 F上的全矩阵空间Mn的保逆的可逆线性算子形式。利用保幂等的结论证明了f为Mn上保持逆矩阵的可逆线性算子当且仅当存在P∈GLn，使得f=εPAP-1，A∈Mn，ε=±1∈F；或者存在P∈GLn，使得f=εPATP-1，A∈Mn，ε=±1∈F

Zhan has determined the maximum and minimum numbers of positive entries of imprimitive irreducible nonnegative matrices with a given imprimitivity index. In this paper, we prove that if a positive integer is between the maximum and minimum numbers, then there exists an irreducible nonnegative matrix A with the given imprimitivity index and with the given number of positive entries.

非负矩阵是矩阵论中研究比较活跃的领域，不可约非负矩阵是比较重要的非负矩阵，本文分两部分，一部分主要在詹兴致教授的研究基础上研究了给定非本原性指标的不可约非负矩阵中非零元个数的连续性，肯定地回答了詹兴致提出的一个自然的问题。

The completely diagonalized Hamiltonian matrices of 3d2/3d8 ion configuration in the trigonal symmetry have been established by irreducible representation method. Taken into account the influence of the spin-spin coupling interactions omitted in previous publications, the spectra and the constants of crystal structure and zero-field splitting parameters of CsNiCl3 crystal and CsNiCl3: Mg2+ crystal are calculated and the influence of the doping to the spectra, the constants of crystal structure, zero-field splitting parameters and Jahn-Teller effect are studied. The results show that doping can change the structure of crystal which brings about the changes in the spectra and zero-field splitting parameters as well as Jahn-Teller effect.

应用不可约张量理论构造了三角对称晶场中3d2/3d8态离子的45阶可完全对角化的微扰哈密顿矩阵，在考虑了以前工作中被忽略的自旋-自旋耦合作用的基础上计算了CsNiCl3晶体和CsNiCl3：Mg2+晶体的基态能级、晶体结构、零场分裂参量和Jahn-Teller效应，研究了掺入Mg2+对CsNiCl3晶体的光谱、零场分裂参量及Jahn-Teller效应的影响和自旋单重态对基态能级的贡献，发现掺杂使得晶体结构产生畸变，从而改变晶体光谱的精细结构和零场分裂参量，不改变Jahn-Teller效应的分裂规律但改变分裂的大小。

I was up all night because I was in pain, she said.

我整夜，因为我在疼痛，她说。

A crow caws /craoks.

乌鸦叫。 51-论文网