查询词典 completely continuous linear operator

Simultaneously, we identify that the perturbation of these operators by a small norm operator is still nonwandering; further, we can obtain the theory that every bounded linear operator can be decompositioned into nonwandering operators.

同时，证明了这些算子经一小扰动后，可保持它们的非游荡性不变；进而可获得有界线性算子关于非游荡算子的分解理论。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

Firstly,we introduce its definition,then construct two groups of operator functions by an elementary method,and extend the function f= t(t+2)log(t+2)/(t+1)~2 to linear situation,at last we discuss some results about operator monotone function under the complex order and conjugate complex order.

首先介绍了Furuta不等式的几何结构，将普通的算子序推广到更弱的算子序A~4≥(A~2B~2A~2)~2/3，讨论在此序下的函数的算子单调性，并且推广到更一般的序A~(2m)≥(A~mB~2A~m)~m/m+1，得到了一些新的研究方法与结果。

If F is a space of functions defined on a domain Ω and ψ is a function taking Ωinto itself, then the composition operator C〓 induced by ψ is defined by C〓: f〓fοψ,〓f∈F. It is obvious that C〓 is a linear operator.

设F是定义在区域Ω上的一个函数空间，φ：Ω→Ω是Ω到自身的一个映射，则可通过函数的复合定义一个线性算子C〓：f→foφ，〓f∈F，称为由φ诱导的复合算子。

The circular convolution operator is compared with the linear convolution operator in the calculation of local statistics.

比较了循环卷积算予和线性卷积算子在计算局部统计量上的异同点。

In order to discuss the structure of operator algebras, in recent years, a lot of schol-ars both here and abroad have focused on linear mappings of operator algebras andhave introduced more and more new methods.

为了进一步探讨算子代数的结构，近年来，国内外许多学者对算子代数上的线性映射进行了深入研究，并不断提出新的思路。

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。

In order to determine the Poincare normal form of linear operator in the operator differetial equation, we need to reduce the vector-value function to the two dimensional case on center manifold.

要证明以上的结论，我们所采用的方法是[24]中的Hopf分支定理所给出的判断Hopf分支存在性及分支周期解稳定性方法。

Linear edge detection operator can implement the one to one mapping of edge detection operator to edge type, that is, one kind of edge detector can only detect one kind of edge.

线性边缘检测算子，只能实现边缘检测算子到边缘类型的一一映射，即一种边缘检测算子只能检测一种边缘类型。

With the development of linear operator hypercyclic theory, We get some equivalent conditions about weighted sequence, on which weighted shift operator in l~2 and l~2 become hypercyclic.

随着线性算子超循环性理论的发展，对于空间l~2和l~2中的加权移位超循环算子已经得到了许多利用加权序列所作的等价刻画。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。