查询词典 infinite dimensional

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

Therefore,the complicated problem is simplified into asolving procedure of a group of infinite dimensional algebra equations.In thefact,not only is a general solution of the problem obtained,but also a method tocompute the dynamic thermal stress distribution at the surface of the cavity afterthe definition of the coefficient of the dynamic thermal stress distribution isgiven.

事实上，不但得到了单连通区域或复连通区域型二维孔洞表面的动态热应力分布问题的一个一般的解析解，而且，在定义了非耦合和耦合无量纲化动态热应力分布系数后，推导出计算单连通区域或复连通区域型二维孔洞表面的动态热应力分布的方法。

In infinite dimensional RDS, different to finite case, the cocycle can be usually considered only in the positive half-time line.

无穷维的随机动力系(来源：ABd454C论文网www.abclunwen.com)统和有限维的相比，其中的cocycle往往只能定义在正半时间轴上，为此我们首先对无穷维半动力系统进行了负向延拓，使得在负半时间轴上也有定义。

Since bounded closed sets in infinite dimensional space are notcompact generally,in order to employ Horn's fixed point theorem the compactness of operator Pis initially proved in section 3 in this chapter.

由于无限维空间的有界闭集一般不具备紧性，为了应用Horn不动点定理，我们先证明了Poincare算子P的紧性。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

The convex differential analysis in infinite-dimensional spaces has been studied almost seventy years.

无穷维空间的凸微分分析的研究已有近七十年的历史。

In this paper,we mainly make a deep and systematic study of sample path prop-erties for high and infinite dimensional Gaussian processes,especially for high andinfinite dimensional Wiener process in stronger norm-Holder norm than ever(everbefore,there used to be uniform norm and the process was limited to one dimen-sion).We not only deal with all kinds of functional moduli of continuity,but alsoconcern with different forms of functional limit theorems of C-R increments.

本文主要对高维的以至无穷维的Gauss过程、特别是Wiener过程的样本轨道性质在较以往更强的范数—〓范数下作了系统深入的研究（以往通常采用一致范数，过程限于一维），研究的内容不仅包括各种形式的泛函连续模，而且还包括各种形式的C-R增量的泛函极限定理。

At present time thesemaps have become important objectors and tools in studying operator algebras. Nestalgebras is a class of most importaut non-semisimple, non-prime and non-self adjointoperator algebras. Their finite dimensional models are upper triangular matrix algebras,but the infinite dimensional models are more complex.

本文在已有成果的基础上，研究了一些类型的算子代数上的Jordan可乘映射，Jordan-triple可乘映射，Lie-skew可乘映射，初等映射，Jordan-triple初等映射，Lie导子，Jordan导子，局部导子和局部同构及其刻画问题。

The sufficient and neccessary con-dition is given for finite-dimensional or infinite-dimensional dissipativity of the methods,respectively.

在上述两章，我们还给出了某些一般性的结果。

Since symplectic algorithms were brought forward by Kang Feng, two overflying developments took on: one is the generalization from finite dimensional Hamiltonian system to the infinite dimensional, the other is the generalization to multisymplectic algorithms.

自从冯康院士提出辛算法以后，这一算法有了两次大的飞跃和发展，一次是从有限维向无限维的推广，一次是向多辛算法的深入发展。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。