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QoS multicast routing problem is a nonlinear combinatorial optimization problem,which has been proved that the problem is NP-complete problems.

QoS组播路由问题是一个非线性的组合优化问题，已证明了该问题是NP完全问题。

This proved that Fairchild is as adept at comedy as she is at drama.

这证明费尔切尔德像擅长喜剧一样擅长戏剧。

It has been proved that a good lawyer has to be commercially sensitive.

实践证明，一个好的律师要有很强的商业敏感性。

Based on the experimental methods, our paper proved that common –measure bias also existed in china.

本文通过实验研究的方法，证明了在我国通用指标偏见的存在。

In chapter 2, a new concept- property T〓 is introduced, it is proved that nest subalgebras of von Neumann algebras, finite width CSL and atomic CSL subalgebras of von Neumann algebras have property T〓. Some tensor product formulae of nest subalgebras and CSL subalgebras in von Neumann algebras are obtained. Tensor products of W〓-dynamical systems are studied. Finally, the essential commutant of tensor product of operator algebras is discussed.

第二章我们引入了性质T〓这一新概念，并证明了任一vonNeumann中的任何套子代数，有限宽度的可交换格子代数和原子可交换格子代数都具有性质T〓；得到了von Neumann代数中套子代数和可交换格子代数的张量积公式；研究了W*-动力系统的张量积问题；最后讨论了张量积代数的本性换位。

Based on analyzing the d-δ commutation relation for the linear stationay differential constrained systems and affine differential constrained systems, the relationship between noncommutator of differentiation and variation and nonholonomicity of the differential constraints is briefly proved by means of Frobenius integrability theory.

文中以微分约束的Frobenius可积性理论为依据，在分析线性稳定微分约束系统和仿射微分约束系统的d-δ对易关系基础上，简要论证了微分与变分的非对易子与微分约束的非完整性之间的关系。

Xu Jinzhong proved that a simple module over commutative ring is injective if and only if it is flat.

徐金中证明了交换环上单模是内射的当且仅当它为平坦的。

It is proved that this algorithm can be used to build a B|spline neural network with minimum hidden units to approximate any continuous function defined on compact set to a prescribed accuracy.

对于3层神经网络而言，输入至输出的映射实际上是通过基函数的加权组合来实现的，当基函数取不同时，网络有不同的性质

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。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。