空间同构

The proof is given that the category of linear fuzzy neighborhood spaces in the sense of Katsaras is isomorphic to that of co-towers of topological vector spaces and the intersection of the category of linear fuzzy neighborhood spaces with the category of type fuzzy topological vector spaces is the extract category of induced fuzzy topological vector spaces.

证明了Katsaras的线性fuzzy邻域空间范畴与分明线性拓扑空间的余塔空间范畴同构，而Katsaras的线性fuzzy邻域空间范畴与型fuzzy拓扑线性空间范畴的交集恰为诱导的fuzzy拓扑线性空间范畴。

It is pointed out that the category of L-fuzzy topological vector spaces is isomorphic to the full subcategory of the category of I -fuzzy topological vector spaces, whose elements are induced I -fuzzy topological spaces.

指出了格值模糊拓扑线性空间范畴同构于I型fuzzy线性拓扑空间范畴中诱导空间构成的满子范畴。

E〓 is endowed with a new metric D, such that becomes a complete metric space. After that a locally convex complete pseudonormed space is constructed. Finally, E〓 is embedded into isometrically, and isomorphically.

在n维非紧模糊数空间E〓上引入一个新的度量D，使得成为一个完备的度量空间，然后我们构造了一个局部凸的完备赋准范空间，并将n维非紧模糊数空间等距同构地嵌入到空间之中。

In this paper, granularity in rough set theory is used to describe rules based on the concept of rough degree. A tool for knowledge dependent relation diagram is put forward. Then dimensional knowledge granularity decision space and the same construction mapping decision space based on multi-decision sorts is established, and decision algorithm based on KDRD and decision space is introduced. Finally, through combining with the technique of fault diagnosis, it is proved that the approach is very appropriate to the intelligent decision system.

本文利用粗糙集理论中的粗度概念，在对获取规则进行扩展性的粒度描述的基础上，提出了一种工具―知识依赖关系图，构造了n维知识粒度决策空间以及基于多决策类的同构映射决策空间，建立了基于KDRD和决策空间的决策算法，并结合机械故障诊断说明了本方法非常适于故障诊断等通过结论获取原因的智能决策系统。

Lastly,Using the extension theory of〓-algebras founded and developed by Brown-Douglas-Fillmore in 70s,inparticular,using the homotopy invariance of the extensions and the indexformule of Toeplitz operator matrices,the paper characterized the automorphismgroup of the continuous function symbol Toeplitz 〓-algebra in terms of thetopological degrees of the continuous mappings on the n-dimensional sphere.

最后，本文利用Brown-Douglas-Fillmore在七十年代建立并发展起来的C*-代数扩张理论，尤其是扩张的同伦不变性，以及Toeplitz算子矩阵的指标公式，通过球面上连续映射的拓扑度，刻划了高维球面Hardy空间上连续符号Toeplitz 〓代数的自同构群。

We establish an asymptotic Lipschitz homotopy invariance theorem for these K-homology groups and K-theory groups. We show that the asymptotic index maps are isomorphisms for the asymptotically scaleable spaces, which include Euclidean cones, simply connected complete Riemannian manifolds with nonpositive curvature.

我们证明了这些K-同调群和K-理论群具有渐近Lipschitz同伦不变性；对于渐近可标度的几何空间（包括欧氏锥、单连通非正曲率完备黎曼流形等），证明了渐近指标映射为同构。

In section four, we consider a normal π-subgroup in π-separable group, a normal set and a complex value class function space defined on G, using the B_π-character theory and character-triple isomorphism, and find a classical basis of this space such that it behaves as the set of irreducible Brauer characters, and satisfies the Fong-Swan property.

在第四节中我们考虑了π-可分群G中的一个正规π-子群，以及定义在G上的一个正规集和它上面的一个复值类函数空间，利用B_π-特征标理论和特征三元组同构，我们找到了这个空间的一个经典基，使得这个基具有类似于不可约Brauer特征标的集合的性质，并且满足Fong-Swan性质。

Based on the theory of isomorphic mapping and singular value decomposition theorem, the maximum of the kernel Fisher discrimination criterion can be skillfully acquired by solving the minimum of its reciprocal in a small space, and the final solution is acquired without taking account of the null space and non-null space of the kernel within-class scatter matrices separately.

基于同构映射原理和奇异值分解定理，在一个更小的空间内将核Fisher描述准则函数的极大值问题转化为其倒数的极小值问题，使最终的解不需要分开考虑核类内散度矩阵的零空间和非零空间。

Pisier\'s results,under tree martingale valued space X is isomorphic toan a-uniformly convex space (2≤a＜∞),some quasi-normal or normal inequalitiesof a-variation maximal operator and a-conditional variation maximal operator of X-valued predictable tree martingales are identified.

同时，用G.Pisier's结果在树鞅取值空间X同构于a一致凸Banach空间条件下，证明了几个X-值树鞅α-方极大算子和a-条件方极大算子的拟范数不等式与范数不等式。

Firstly, some basic properties of the limit shadowing are given; Secondly, we give the characterization of both lin-ear automorphisms and linear flows on R~ with the limit shadowing property; Thirdly, as applications we prove that the hyperbolic endomorphisms on T~ have the limit shadowing properties, Smale "horseshoes" have the same prop-...

首先，给出了极限跟踪性的一些基本性质；其次，得到了n维欧氏空间上线性自同构及线性流具有极限跟踪性的特征；最后，作为应用证明了双曲环面自同态以及Smale&马蹄&在其不变集上具有极限跟踪性。

By using competitive adsorption of activated carbom to remove unfavorable influence of carbon in carbonaceous gold concentrate on leaching process, the leaching rate of gold concentrate can be improved to 88% as compared with 10%by direct cyanidation.

本文论述了利用活性炭竞争吸附作用，消除含炭金精矿中炭在浸出过程中的影响，使金精矿的浸出率可由直接氰化的10％提高到88％。

The only thing you're ever gonna be king of is King of the Stupids!

你只配做傻瓜的国王！