特征值

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论，研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性，其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

Firstly, The sufficient con-ditions of the existence and uniquity of the positive equlibria by applying functional derivative isobtained; Secondly, the global attractability of the positive equlibria is investigated by charateristicroots theory and oscillation theory; Thirdly, regarding the delay as a parameter, conditions of theexistence of Hopf bifurcation and the peridic solution, furthermore, the form of the approximateperidic solution are obtained; Finally, Some specific examples are given and the solution diagrameappears by Matlab.

首先利用导数性质，得到了该模型正平衡态存在惟一性的充分条件；其次，利用特征值和振动性理论得到了该模型正平衡态全局渐近稳定性充分条件；然后，应用Hopf分支理论证明了该模型Hopf分支及近似分支周期解的存在性，并给出了周期解的近似表达式；最后，借助于MATLAB数学软件，举例并绘出了模型数值解的拟合图象，验证了文中定理条件的可行性。

The operations for extracting the smallest eigenvalue and the corresponding eigenvectors of the augmented data co rrelation matrix is O and less than the ones of Davila′s RTLS algorithm per time step.

在追踪与增广协方差矩阵的最小特征值相关联的特征矢量过程中，这个算法每步须O乘法运算，比Davila的RTLS算法的运算量少。

Abnormal distribution is not rare in practical measurement. Beta distribution contains not only central distribution but also non-central distribution. It is a good method to simplify the research of practical measurement distribution.

为了解决实际测量中的非正态分布的表示问题，本文采用含有两个参数的Beta分布来统示表示多种类型分布，并且解决了该分布的参数、特征值的计算。

By local bifurcation theory and perturbation theory,the existence of local bifurcating solution and its stability are obtained.

研究了一类带简化的Mound-Haldane反应项的捕食-食铒模型的局部共存解存在性及其稳定性，运用局部分歧理论及特征值扰动理论，得到了该模型的局部分歧解存在的充分条件及其解的稳定性。

The red and black ordering method about the coefficient matrix of a class of linear equations and the condition number of schur complement matrix deduced from red and black matrix are studied.

利用矩阵相似变换推导出红黑排序矩阵中的舒尔补的特征值和条件数表达式。

In the paper, we study the existence and eigenvalue problem of p-Laplacian equation with No flux boundary condition in a bounded domainΩ?

中文摘要：本文主要研究了R~N中有界域上p-Laplacian方程在无流边界条件下问题解的存在性及特征值问题。

And it can be sorted into eigenvalue buckling analysis and nonlinear buckling analysis.

结构的屈曲分析可分为特征值屈曲分析和非线性屈曲分析。

Generalized ridge estimation ; kantorovich inequality ; eigenvalue ; trace of matrix ; canonical correlation coefficient ; generalized correlation coefficient

广义岭估计； Kantorovich不等式；特征值；矩阵的迹；典型相关系数；广义相关系数

The pupose of the research is to develops public key encryption and digital signature shemes based on matrix canonical decomposition problem, or matrix diagonalization problem over Z/n, the ring of integers with modulo-n addition and multiplication in particular, where n is an RSA modulus.

本课题研究基于矩阵经典分解问题，特别是Z/n上矩阵对角化问题的公钥密码与数字签名算法，其中n是一个RSA模数。新算法采用由一个矩阵多项式构成的多维单向陷门函数，其单向性由矩阵对角分解问题(即通过相似变换将矩阵化为对角型的问题)的复杂性来保障，对该函数求逆的陷门由矩阵的特征值或特征向量提供。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。