嵌入算子

Corresponding chaotic evolution operators and chaotic population embedding operator are designed, and the species conservation strategy based on chaotic basin of attraction is proposed to treat with asymmetric distribution of extremum and to find all or near all minima.

设计了相应的混沌进化算子以及混沌群体嵌入算子，提出了基于混沌吸引域概念的种群保护策略，适应了极值点分布不均匀的情况，达到求解全部／大部分极小点的目的。

We discussed the coupled generalized BBM equations with pseudodifferential operator in Chapter three.In this chapter we get the global existence for the Cauchy problem by Banach-fixed point theorem ,a priori estimates and Sobolev embedding theorem.

第三章讨论了具拟微分算子的广义BBM方程组，通过Banach不动点定理、解的先验估计和Sobolev嵌入定理得到了解的整体存在性。

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。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

First, the proposed scheme uses contourlet transform to extract multidirectional and multiscale texture information, and then obtains the feature points invariant to the affine transformation from the low and middle directional subbands by Harris-Affine detector. Second, the feature regions are adaptively computed by the feature scale of the local structure and normalized by U transform. The watermarking is embedded adaptively in those characteristic regions which are normalized. Finally, by vector quantization, several copies of the watermark are embedded into the no overlapped local feature regions in different directional subbands.

首先，用Contourlet变换提取出多尺度、多方向的纹理信息；再用Harris-Affine检测算子从变换域的中、低频方向子带中提取出仿射不变特征点，结合自适应局部结构的特征尺度确定特征区域，并用U变换对其归一化处理，水印就自适应地嵌入到归一化后的区域中；水印嵌入采纳矢量量化的策略，将水印信息重复嵌入到不同方向子带、多个不相交的局部仿射不变特征区域。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。