范数

Inverse eigenvalue problem; Constrained matrix equation problem; Procrustes problem; Matrix norm; Optimal approximation solution

矩阵逆特征值问题；约束矩阵方程问题； Procrustes问题；矩阵范数；最佳逼近解

The relationship between selecting range of controlled weighted factor and state matrix norm of discrete state equation is proposed when multi-step predictive selftuning control algorithm is adopted.

4提出了多步预测的自校正控制GPC算法控制加权因子的选择范围与离散状态方程状态矩阵范数之间的关系，给出了其它参数的选择方法，通过不同采样周期条件下仿真和实验研究与理论计算结果是一致。

Keywords constrained matrix equation problem;sub matrix constraint problem; matrix norm; optimal approximation solution;least-squares solution

约束矩阵方程问题；子矩阵约束问题；矩阵范数；最佳逼近解；最小二乘解

The new updating method is to minimize the error matrix norm under the condition of a quadratic constraint under which the mode orthogonality should be satisfied and the mass and stiffness matrices should be fitted into the eigen equation.

该方法是在质量矩阵和刚度矩阵满足正交性条件和特征方程的约束下，使修正矩阵的范数最小，将模型修正问题转化为一个带二次约束的最小二乘问题。

Some methods for dealing with the stability problem has presented and these methods include: Lyapunov function, differential inequality, matrix norm and measure, Razumikhin theorem method etc. The results of stability for these systems are derived by using these methods. This paper may be summarized as follows.

本文考察了区间Lurie型控制系统与不确定时滞系统的稳定性问题，给出了判定系统稳定的一些处理方法，这些方法包括：Lyapunov函数法、微分不等式法、矩阵范数与测度法、Razumikhin定理等方法，并且应用这些方法得到了系统稳定的判别条件。

In Chapter 5, some knowledge about large-scale system and methods for investigating them are introduced, Lyapunov function, differential inequality, Razumikhin theorem, matrix norm and measure methods have been used to discuss the stability of uncertain large-scale system with delays and decay estimates for uncertain time-varying large-scale system with delays, the criteria of stability and decay estimates for uncertain large-scale system with delays are given.

第五章首先介绍了大系统的有关知识以及时滞大系统研究的方法，然后利用Lyapunov函数法、微分不等式法、Razumikhin定理法、矩阵范数与测度法研究了不确定定常时滞大系统的稳定性以及不确定时变时滞大系统的稳定性与系统衰减率的估计问题，得到了系统稳定的判别条件以及系统衰减率的估计。

Finally,the inequality of maximal operators of tree martingale transformsis applied for obtaining the UMD space valued Vilenkin system and the sum ofVilenkin-Fourier series of UMD space valued Vilenkin system is convergent a.e.or convergent in LP-norm.

最后，应用UMD空间值树鞅鞅变换的极大算子不等式，我们获得了UMD空间值Vilenkin系统以范数收敛和几乎处处收敛定理，即Carleson定理的扩展。

With regard to the estimation of the variance components, many statisticians proposed a number of approaches, such as the Analysis of Variance Estimator, Maximum Likelihood Estimator, Restricted MLE, and the Minimum Norm Quadratic Unbiased Estimator, etc.

关于方差分量的估计统计学家们提出了许多方法，如方差分析估计，极大似然估计，限制极大似然估计，最小范数二次无偏估计等。

In this thesis, we study stable and complete submanifolds with constant mean curvature and some L~p-norm curvature in Euclidean spaces and hyperbolic spaces.

在本文中，我们较系统的研究了欧氏空间和双曲空间中具有常平均曲率和某一有限L~p范数曲率的稳定完备子流形。

Firstly, we apply block AOR method to find the least square solution of minimal norm to the rank deficient linear systems where A is a complex m*n matrix with rank k.

首先，我们把求解线性方程组的块加速超松弛迭代法应用于求解亏秩线性方程组的最小范数最小二乘解，其中线性方程组的系数矩阵A是秩为k的m*n复矩阵。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。