范数

Irreducible matrix. A probabilistic proof is proposed, together with

对不可约的非负方阵，其谱半径和诱导的无穷-范数之间满足

In chapter 3 we further analyze the Moore-Penrose inverse of Kronecker product of A and B and the linear least squares problems involving Kronecker product, then obtain normwise mixed and componentwise condition numbers and the upper bounds similarly.

在第三章中我们进一步在列满秩情形下，对A与的Kronecker积的Moore-Penrose逆和带Kronecker积的线性最小二乘问题做了分析，同样得出了范数型，混合型和分量型这三种条件数及其上界。

In addition, the corresponding analog transconductance neural optimizer based on modified augmented Lagrange multiplier approach is developed.

对单测试激励下线性约束L〓范数估计问题的求解，提出了基于改进的罚函数法和Lagrange乘子法两种跨导神经优化求解器。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

Based on the explicit formulation of matrices on the given linear manifold, the general expression of the solutions to this least squares problem is obtained by using the method of the singular value decomposition and the unitarily invariant of the Frobenius norm.

在推导出所给线性流形中任意矩阵的显式表达的基础上，利用奇异值分解和Frobenius范数的酉不变性得到了该最小二乘问题通解的一般表达式。

The largest radius of the region is given by the condition of critical D-stability and character of linear operator.

利用系统临界D-稳定时的特性和线性算子范数的特性，得到了这个范围半径的解析表达式。

In the forth part, we mainly discuss the properties of cosine operators, such as the normcontinuity, locally Lipschitz continuity, which are preserved under the multiplicative perturbation with the-condition.

第四部分讨论了余弦算子在条件下的乘积扰动和扰动下的不变性。如条件下的乘积扰动仍保持范数连续、局部Lipschitz连续不变。

Let X be a real linear space,P a family of separated seminorms on X and TP the locally convex separated topology on X generated by P.

设X是实线性空间，P是X上的一族分离半范数且Tp是X上由P生成的局部凸分离拓扑。

To the discrete-time systems, we introduce a new discrete-time norm, the algorithm given is not depend upon the initial data. For a class of uncertain discrete-time systems, we also adopt the method of iterative learning control, we convert the problem of learning control into a global stability of trivial solution for lower triangular matrix dynamic systems, and obtain the result of tracking to desired state of the system.

对于一般非线性离散系统，引进了离散的范数，所给的算法不依赖于学习控制算法中的初始数据，对于一类不确定离散系统的状态跟踪问题，我们也采用迭代学习控制的方法，将相应的学习控制问题转化为一个下三角动力系统的平凡解全局稳定性问题，获得了对系统理想状态的跟踪结果，并对所给的算法的收敛性进行了分析。

Then, the robust admissibility of uncertain discrete-time fuzzy descriptor systems is analyzed in terms of matrix norm.

然后，由矩阵范数给出系统鲁棒容许性的充分条件。

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。