不等式

The frame is a special Besselsequence, which extends the Parseval equality of orthonormal basis in Hilbert space tothe two-sided inequality in general sequence.

框架是一类特殊的Bessel序列，框架是把Hilbert空间中的规范正交基满足的Parseval等式推广到比较一般的序列所满足的双边不等式的结果。

In Chapter 6, we study a kind of system of nonlinear variational inequalities and its related auxiliary problems in real Hilbert space.

针对一类非线性变分不等式系统，我们研究了其相关辅助问题，建立了辅助问题解的存在性定理。

The sufficient condition of stochastic delay population system with diffusion is obtained in Hilbert space.

利用Ito公式和Burkholder-Davis-Gandy定理及Gronwall-Bellman不等式，通过构造一个有界的柯西列，给出了Hilbert空间中随机时滞种群扩散系统解的存在性和唯一性的充分条件，文章所得到的结论是目前现有结果的推广。

In the chapter 7, by virtue of Ky Fan's results in operator spectral theory, we convert several meaningful conclustions in the theory of Holomorphic fucntions into the corresponding results of operator functions in Hilbert space.

在第7章中，我们应用算子谱集理论中的Ky Fan关于Von Neauman不等式的一个结果，把解析函数论中一些有意义的结论转化到Hilbert空间的算子函数上来建立相应的结果。

By using homeomorphism method and the extended inverse function theorem,the existence and uniqueness of the solution for the semi-linear pseudoparabolic equations is obtained.

首先在Hilbert空间中建立了强制不等式，利用同胚方法和抽象的反函数定理，得到了半线性伪抛物方程初边值问题解的存在性和惟一性定理。

And the generalized Schwarz inequality for complex Riesz homomorphism is obtained as well as some useful corollaries.

证明了复Riesz同态满足推广的Schwarz不等式，并得到相关的有用推论。

By using new inequality techniques, homotopic mapping and constructing a new type Lyapunov func tional method, we obtain some new criteria guaranteeing global asymptoticstability.

研究多时滞Cohen-Grossberg神经网络的全局渐近稳定性，利用新的不等式技术，同伦映射及李雅普诺夫泛函方法，我们获得了几个新的准则。

We obtained a kind of sufficient condition for 2-harmonic submanifolds becoming minimal submanifolds in hyperbolic space and an integral inequality like Simons integral inequality.

得到了双曲空间中2-调和子流形成为极小子流形的一个充分条件，以及一个Simons型积分不等式。

These strategies include: an improved adaptive movement penalty method which prevent ill condition matrix based numerical instability, a network topology based identification method which prevent too much tuning and a limited times skipping method of trial iteration.

在上篇中，本文给出了以下内容：第二章详细描述了最优潮流牛顿算法的实现，着重分析了牛顿法实际应用中存在着的两个主要问题：数值不稳定性和如何快速正确地识别起作用的不等式约束集，并提出了相应的处理对策。

In chapter 3,we analyze the global attractor of static reaction-diffusion neural networks with time-varying delays using the semigroup theory of operators, the inequality skills and the imbedding method in Soblev space. A very useful and convenient criterion on the existence of the location of this global attractor is given. Furthermore, we can estimate the location of this global attractor in the space.

在第三章中，我们用算子的半群理论，不等式技巧和Soblev空间的嵌入方法分析了变时滞静态反应扩散神经网络的全局吸引子，给出了一个简洁实用的判定全局吸引子存在的准则，进而，估计了全局吸引子在空间中的位置。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷