广义特征空间

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the βperturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the fi-perturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

We investigate the eigen-subspace approximation space-time adaptive processing method of clutter suppression based on the generalized sidelobe canceler .

基于广义旁瓣相消结构，我们研究一种特征子空间近似空时自适应处理杂波抑制方法。

On the basis of the definition of the extraordinary Radon transform, the theory of rebuilding image from extraordinary Radon transform result is proposed, and some category such as image structure notation, topology of image structure notation and topological space, homeomorphism in topological space, equivalence of homeomorphism relation, topological constant of image structure notation.

与现有的基于区域内部或外形变换的形状分析方法相比，在理论方法上本质不同的是，本文提出的广义Radon变换，直接将原始的图象数据影射到特征空间，给出图象构图特征的描述，给出了可以用来进行图象检索或图象识别的结构特征谱。

Thus, we propose a new depth function to deal with such concave shape data sets using the principal of smallest hypersphere in the Gaussian kernel feature space.

本文从样本深度的角度，利用高斯核特征空间最小球原理，提出了一种广义的数据深度。

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。

Firstly, we discuss the characterization of eigenprojections at zero of thegeneralized Drazin invertible operator on Banach space. By using the techniqueof block operator matrices, we extend the results that the characterization of eigen-projections at zero of matrices to operators in B.

中文摘要我们首先讨论了广义Drazin可逆算子在0点的特征投影的刻画，利用算子矩阵分快的技巧将关于矩阵在0点特征投影的刻画的一些结果推广到了Banach空间上。

In the third chapter,We study some geometric properties and spectral propertiesof the Jacobi operator on a solvable extension G of Heisenberg groups H.In the firstsection,we give the definition of G and some fundamental geometric properties on G.Inthe second section,we discuss the Integrability of certain subbundles and the geometricstructure of the induced foliations in case of integrability.In the third section,we studythe spectral properties of the Jacobi operator of G.

可解李群与类对称空间亦密切相关，Damcek-Ricci空间即是广义Heisenberg的一可解扩张李群，在第三章中，我们构造且研究了Heisenberg群的一可解扩张李群G的几何性质，第一节讨论了G的曲率，李指数映射，整体坐标等基本几何性质；第二章研究了TG的某些子丛的可积性及可积时诱导叶片的几何结构；第三节给出了G的Jacobi算子的特征值和相应的特征子空间。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。