范数

The least norm solutions of symmetric and skew antisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are also considered. 3. The least-squares solutions and the least norm solutions of the quaternion matrix equations AX = B and XD = E are studied by using

借助四元数的复表示方法，研究四元数矩阵方程组AX=B，XD=E的最小二乘问题和极小范数解的问题，并对主子阵约束下的方程组的解进行了讨论，得到了它们的显式表示。

The first part is the preparatory knowledge, introducing the contracting mapping principle which through the basis of vector and matrix norm, derivative and differential theorem of mean to thorough understanding the nature of soluble for nonlinear equations.

第一部分为预备知识，重点介绍压缩映象原理。通过引入向量与矩阵范数，导数与微分中值定理，以求深入理解非线性方程组可解性的基本理论。

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed spacer and obtains a fixed point theorem in metric linear spaces.

摘要证明了完备的一致局部半凸概率赋范空间上的概率压缩映象必有唯一不动点，得到了一类度量线性空间中关于伪范数族一致压缩映象的不动点定理。

Chapter 1 presents the concepts of normed linear spase, Banach spase, inner product spase and Hilbert space.

而为了讨论向量序列的极限，必须引入向量的范数。这样就有了赋范线性空间的概念。

By using matrix norm, matrix singular value, non-negative matrix theory, the regions of numaerical range and spectum of operator polynomial and the regularity of operator linear pencil are obtained.

8应用矩阵范数理论、矩阵的奇异值理论、非负矩阵的理论、友矩阵、算子的谱理论为工具，获得了算子多项式数值域具有的特性及其包含范围，算子多项式数值域与n-次数值域的关系，最后研究了算子线性束正则性的等价条件及谱分布情况。

This paper studies a fuzzy norm and its stratified properties. The completeness and separability of stratified space of fuzzy normed space are discussed.

摘要研究一类模糊范数及其层次结构性质，对模糊赋范空间的层次空间的完备性、分离性等性质进行了讨论。

In chapter5, the serial properties of numerical range of operator polynomial are put firstly. Secondly, the relation between numerical range of operator polynomial and n-numerical range are considered. Thirdly, in the light of matrix norm, matrix singular value, the regions and bounds of numerical range and spectrum of operator polynomial are dicussed carefully.

第五章研究了算子多项式数值域的性质、算子多项式数值域与n-次数值域的关系，特别地利用矩阵范数、矩阵的奇异值、非负矩阵的理论、友矩阵为工具，给出了算子多项式数值域及谱的范围全面刻画，并深刻地研究了算子线性束的正则性的等价条件及谱分布。

G■teaux differentiability of seminorm and completeness of seminorm space;2. It gives a new seminorm to solve the problem in motivating transient signals robust H∞control to persistent signals.

通过引入新的范数解决了瞬时信号鲁棒H∞控制理论向持续信号鲁棒H∞控制推广过程中A 半范定义的信号空间是非线性空间问题。

In the first pa.rt,we clolinc the TC inodnhis of convexity and TC modulus of smoothness of quasi-Baiiach space, and prove that the space which is characterized by uniform convexity is same as the space which is cliaracteri/,ed by uniform TC convcxity.Then we give several characterizations of q-uniformly TC convex quasi-Banach space.At the same time ,we prove the triionned-theorcm.In the second part, we give the relationships between some inequalities of martingales with values in quasi-Banach space and uniformly TC convex quasi-Banach space.

本文分四部分，第一部分在拟Banach空间上定义了TC凸性模和TC光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是一致的，即Banach空间X是一致TC凸的的充分必要条件是它是一致凸的，Banach空间X是一致TC光滑的充分必要条件是它是一致光滑的，还分别得出了判定一致TC凸和一致TC光滑的几个充分必要条件，同时还证明了在拟范数下的重赋范定理。

By using the Clifford matrix expression of n dimensional sense preserving M bius transformations, the trace s and norms of the Clifford matrix and chordal norms are discussed.

利用n维Mobius变换的Cliford矩阵表示，讨论了n维空间的Cliford矩阵的迹和范数以及弦范数，得到了它们在n维空间上一些不等式及它们间的相互关系。

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。