查询词典 invariant subspace

Thin film equations; nonlinear cross-diffusion systems; two-dimensional nonlinear reaction-diffusion equations; invariant subspace method; invariant sets

基础科学，数学，数学分析薄膜方程；非线性交错扩散方程组；二维非线性反应扩散方程；不变子空间方法；不变集

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

Compared with the invariant features of single parameter group, entirely global affine invariant features are more applicable, and chapter 4 introduces a new global affine invariant feature extraction method called EC-ARC, which is based on the invariance in affine geometry.

然后，提出了扩展质心(Extended Centroid， EC)和仿射区域划分(Affine Region Cutting， ARC)的新概念，并在EC和ARC的基础上，结合仿射几何性质，提出了构造具有完全仿射不变性的特征提取方法EC-ARC。

Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.

第三章 算子级数乘数收敛的不变性：利用算子级数乘数收敛、AK—空间的定义，得到了算子级数乘数收敛的不变性定理，从而将以往的普通级数乘数收敛的不变性定理作为特殊情况。

We give the reconstruction of series expansion in lattice-invariant spaces and prove that the improved A-P iterative algorithm is valid in the common shift-invariant spaces. Under adding proper conditions, the improved algorithm holds in the lattice-invariant spaces too.

我们给出了在格不变空间中的级数展开重构，并证明了在一般的平移不变空间中的改进A-P迭代算法也是可行的，说明了在适当增加条件时此改进A-P迭代算法在格不变空间中也是成立的。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The spectral curve vs invariant mass is becoming wider and the peak is shifted towards the high invariant mass region with the increase of temperature. However, in ultra high temperature or density envi- ronment, the peak is shifted towards lower region and the curve is changed narrower with the increase of temperature. In the invariant mass region M 憕.-?0.4 GeV?.6 Ge1~, the spectral function is enhanced very much. which contributes to the interpretation of dilepton enhancement results in relevant experi

结果显示高温高密强子物质环境对其有非常重要的影响：ρ谱函数在温度或密度不太高时谱函数曲线变宽，并且峰朝不变质量高的方向移动；在极端高温或高密情况下谱函数却变窄，并且峰朝不变质量低的方向移动，在不变质量M～0.4-0.6 GeV区间谱函数有比较明显的增强，这有助于解释双轻子产生的相关实验现象。

The new problems and challenges appearing in the nonlinear applicationes are solved, which makes subspace identification more applicable to the modeling and control of industrial process. With regards to bilinear system, a major drawback is that the subspace identification methods induce enormous dimension of the data matrices, which grows exponentially with the increase of the model order.

针对两类特殊的非线性系统，双线性系统和分段线性系统，从子空间辨识的设计与实现出发，提出新的辨识算法，解决子空间方法应用于非线性系统辨识遇到的新问题，使得子空间方法在工业过程的辨识与建模中具有更强的实用性。

Based on random subspace,a complementary subspace linear discriminant analysis approach is presented for face recognition.

基于随机子空间，提出了一种用于人脸识别的互补子空间线性判别分析方法。

Ringrose began to study nest algebras in the 1960s, many people have devoted themselves to the study of non-selfadjoint and reflexive operator algebras including nest algebras, commutative subspace lattice algebras, completely distributive subspace lattice algebras and so on, and obtain a lot of beautiful achievements.

自从60年代J.Ringrose开始研究套代数以来，人们对套代数、交换子空间格代数和完全分配子空间格代数等非自伴自反算子代数进行了深入研究，并且取得了大量出色的研究成果。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。