张量形式

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

The space-like hypersurfaces with constant scalar curvature in a de Sitter space were studied and a pinching theorem on the square of the norm of the second fundamental form was obtained.

研究de Sitter空间中具有常数量曲率的类空超曲面，将Cheng-Yau的自共轨运算元口作用在对称张量T上，得到了这类超曲面关於第二基本形式模长平方的一个拼挤定理，加强了已有的相应结果。

With the help of Stokes theorem, the restriction condition of elastic-response functional is obtained.

进一步讨论了由于使用上述背应力张量的定义对屈服函数形式的限制。

It is emphasized that the key problem in tensor analysis is to establish the mathematical equations of physical laws which are invariable when the coordinate system is changed.

在数学上将客观定律用量的分量形式表达为对坐标系具有不变性的方程，是张量分析所要解决的核心问题。

They conclude their paper by showing how some partial differential equations and physical law can be expressed in tensor form.

他们在文章的末尾指出了如何把某些偏微分方程及物理规律表示成张量的形式。

The main purpose of the present paper is to obtain the relation between the abstract presentation of Euclidean objectivity and its component representation with respect to the general curvilinear coordinate systems with a relative rigid motion under a fixed frame of reference, so that the tensor representation of Euclidean objective quantity has its component form.

建立了欧几里德标架无关性的一般表述与某一参考标架\phi 下作相对刚体运动的一般曲线坐标、分量表述之间的关系，从而使欧几里德标架无关性的张量表述有相应的分量表述形式。

Diffusion tensor imaging is actually a specialized form of magnetic resonance imaging.

弥散张量成像其实是核磁共振成像的特殊形式。

Next, the Bandelet transform is taken on each directional subband. The proposed multidirectional and multiscale transform with critical sampling can represent the geometrical features such as edges and texture more sparsely, which is of great benefit to image compression.

原始的Contourlet变换有大于1的冗余度而不适于图像压缩的要求，采用传统的张量积小波变换取代其中的拉普拉斯金字塔式变换可获得非冗余的变换形式[8]，Bandelet变换是一种基于图像边缘的变换方法，它能自适应地跟踪图像的几何正则方向。

Daubechies'wavelet frame theorem is extended from one dimension to n dimensions. According to this framework, an example of n-dimensional radial wavelet is given. Differing from tensor product multidimensional wavelet, the radial wavelet is inseparable, locally supported and infinitely differentiable. The family, obtained by dilations and translations from this radial wavelet, constitutes a special type of radial wavelet frame in L〓.

Daubechies的框架定理推广到了n维情形，同时，也按照这一理论框架，给出了高维二进径向小波的具体例子，具有下列性质：ψ是无穷次连续可微的；ψ是局部支撑的，支集为‖x‖≤1；ψ含有分式因子，因此对&奇异点&更为敏感；ψ是不可分的，不同于张量积形式的高维小波；ψ是各向同性的。

In this paper, we consider the n-dimensional hypersurfaces (n≥3) with vanishing Mbius form Φ.

本文考虑了S(上标 n+1)(n≥3)中具有消失Mbius形式Φ的超曲面：对具有调和曲率张量的超曲面进行分类，进而，在Mbius度量的意义下，对Einstein超曲面和具有常截面曲率的超曲面也进行了分类。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。