In section 4 , we first show that for two bicomodule algebra a # h and b # h , the cotensor product ( a # h ) h ( b # h ) is still a smash product ( a b ) # h . then we describe the structure on a b and give the corresponding equivalent conditions . in section 5 , we will complete the description of the bialgebra structures we have given , and give the equivalent conditions for such bialgebras to be hopf algebras 在第4部分中，我们得出结论：两个h -双余模代数a # h和b # h的余张量积( a # h ) _ h ( b # h )仍是smash积( ab ) # h ，并给出了ab应具有的结构及相应的等价条件。在第5部分中我们得出了a # h上双代数结构的完整描述，并刻划了这个双代数结构何时是一个hopf代数。
Wavelet transform has many properties which other analysis techniques ( for example , fourier analysis , gabor transform , etc ) do not have , the coefficients in each wavelet channel of a multiresolution decomposition of an image reflect some characteristics of the image . . especially , for texture image the texture energy in each channel represents the thickness and orientation of the texture . this dissertation introduce wavelet analysis to image segmentation . based on analysising deeply characteristics of wavelet transform , the author has made qualitative texture analysis using wavelet frames in this paper 小波分析具有其他许多分析手段(比如fourier变换、 gabor变换等)所不具备的一些优良特性。使用标准的张量积型二维小波对原始图象进行分解后，形成金字塔式小波变换的多通道(多子带) ，其各个通道的小波系数均反映了图象的某些特点，尤其对于纹理类图象，小波通道的纹理能量值描述了纹理的粗细度及其方向性。
Two methods are given . one is obtained by using degree reduction of interval rational bezier curves in two parameter directions according to the character of tensor product , which is called " single step method " . by comparison for degree reductions produced by the different order in two parameter directions , the relationships of the approximation results are discussed 然后讨论了矩形域上区间有理bezier曲面的降阶问题，给出两种降阶算法：一个是针对张量积的特点将问题转变为两参数方向的区间有理曲线的降阶逼近，即“单步法” ，并讨论单步法沿两参数方向不同次序降阶的关系。
The method takes advantage of bezier curve to work out a set of blade profiles of centrifugal pump , using thickening law to thicken the profiles . then the pressure and suction lines of the blade can be obtained . it takes advantage of bezier surface to create pressure and suction surface and makes use of mdt software to create the three - dimensional blade entity 首先采用速度系数法计算得到离心泵叶轮的基本参数，再由b zier曲线生成一组叶轮叶片型线，按照加厚原理对型线进行加厚，得到正背叶片线，再采用张量积b zier曲面生成叶片正背面，由mdt进行三维实体造型得到叶片，从而得到流场计算区域的模型。
The explicit formulas of control points of the reduced said - ball curves are obtained . in the last chapter , the above two methods are generalized to the tensor product of the said - ball surfaces , each of which reduces a given degree nxm tensor product said - ball surface to an n1 xm1 one . in the process of degree reduction for the tensor product said - ball surfaces , we not only discuss the case with constraints of corner interpolations , but also the case without that 在第四章作者将said - ball曲线一次降n - m阶的两种方法推广到张量积said - ball曲面，得到了n m阶张量积said - ball曲面一次降为n _ 1 m _ 1阶张量积said - ball曲面，在降阶过程中作者分别考虑了不带角点插值条件和具有角点插值条件的情形。
