无限维的

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。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

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。

Hence the distributed parameter neural networks can extensively been applied to the field problems in science and engineering.

分布参数神经网络的状态是时空连续变化的函数或者是无限维向量，分析它们的基本工具是泛函分析。。。。

The condition of squeezing is found, and the relation between antibunching effect and the dimensionality of the Hilbert space is shown by using numerical calculation.

理论计算表明该量子态存在压缩效应和反聚束效应，这与通常的无限维空间中的广义相干态是完全不同的。

And if H is an infinite dimensional Hilbert space, it is an inner derivation; Finally we get the same results when the nest is non-trivial.

首先证明了作用在Hilbert空间上的B上的r-Jordan可导映射是一个可加导子，并且当Hilbert空间是无限维时，它是一个内导子；最后在N≠{{0}，H}的情况下得到了相同的结论。

And then characterize the Jordan semi-triple derivable maps on the set of all linear bounded operators actingn on an infinite dimensional Hilbert space, then prove that it is additive and so is an inner derivation.

并且对作用在无限维Hilbert空间上的有界线性算子的全体上的拟三重Jordan可导映射进行了刻画，证明了它是一个内导子。

In order to study the stability of longitudinal following control system of vehicle in automated highway system,the following errors of vehicles were analyzed,a mathematic model of infinite-dimensional nonlinear interconnected large-scale system with delays was constructed,and the stability of the system was studied by applying vector Liapunov function .

为了提高自动化高速公路车辆纵向跟随控制系统的稳定性，建立了关于车辆跟随误差的具有时间滞后的无限维非线性关联大系统模型，应用向量李雅普诺夫函数对大系统的稳定性进行了分析。

Convex analysis part will study convex set, convex function and its subdifferential, Lipschitz function and its G-subdifferential in infinitive dimension.

第一，凸分析部分，包括无限维空间的凸集、凸函数和凸映射，凸函数的次微分，Lipschitz函数的G-次微分。

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橙海携手国内&中国第一手机富媒体广告商&星麦无线和维客网络，整合国内顶尖网络及无线技术旗下多款优势产品，致力于为企业提供全方位的无线、网络营销等多种新型媒体的专业性服务，包括企信通、手机DM、小区短信、彩信、手机地图、手机视频、手机报和WAP建站，WAP联盟、网络视频广告等到，借助新媒体力量为各类客户开辟&有限竞争创造无限商机&的崭新橙海。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。