分解的

This paper focuses on the construction of true bidimensional wavelets by lifting scheme and the relevant image coding. We research the nonseparable bidimensional interpolator designed by different standards, carry out the true bidimensional wavelet decomposition and improve the SPIHT coding in order to adapt to the characteristic of true bidimensional wavelet decomposition. It is proved by experiments that the subjective and objective quality of binary tree SPIHT on true bidimensional wavelet decomposition is better than famous 9/7 wavelet under the condition of low bits compression.

本文以基于提升格式的纯二维小波滤波器组的构造为中心，研究了不同类型的二维不可分离内插滤波器，实现了图像的纯二维小波分解，并改进了SPIHT编码算法，使其适合纯二维小波的分解特点，实验证明在低比特压缩下，纯二维小波分解的二叉树SPIHT在主观和客观质量上要好于著名的9/7小波。

The study indicates that the optimum windows width decides the layering precision, interface partition with sym6 wavelet is better than with db4, canonical wavelet decomposition of conventional logging curves can well meet the demand of coenocorrelation.

研究表明，选择恰当窗宽小波决定测井曲线小波分层精度、测井数据sym6小波分解的小层界面划分效果要稍好于db4小波、常规测井曲线正则性小波分解可以很好地满足高分辨率层序地层划分要求。

The activation energy of cellular decomposition calculated by DSC date was 88.24kJ/mol, which showed that the decomposition was controlled by Zn atom diffusion.

DSC数据计算得出，胞状分解的相变激活能为88.24kJ/mol，表明其分解主要受锌原子扩散控制。

In this paper, experimental work of the decomposition of methane gas hydrate by depressurization in porous media was carried out with the 1D experimental apparatus.

在天然气水合物一维分解模拟系统上进行模拟多孔介质中水合物降压分解的实验。

The CPM signal can be expressed as a sum of finite number of time limited amplitude modulation pulses by Laurent Decomposition. The optimum receiver of CPM is simplified by Laurent Decomposition.

引入了Laurent分解技术将非线性的CPM分解为一系列的PAM波形叠加的形式，利用Laurent分解的特性在保持性能的条件下给出了CPM的最佳接收机的简化模型。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

In this paper, three methods for color image retrieval have been presented: hypercomplex SVD image retrieval, combination of hypercomplex convolution filter and hypercomplex SVD image retrieval and hypercomplex matrix correlation image retrieval. We made comparison among these hypercomplex-methods, and compared them with the traditional image retrieval methods. Experiment results showed that the hypercomplex-methods we presented in this paper could well conquer the problems existed in traditional image retrieval methods, and their retrieval results are much better. Meanwhile, this paper presented a new color image quality assessment based on hypercomplex SVD. It is a novel color image quality assessment that can be used as a graphical or a scalar measure to predict the distortion introduced by a wide range of noise sources. It reliably measures the distortion not only within a distortion type at different distortion levels, but also across different distortion types.

提出了超复数奇异值分解检索法，超复数卷积滤波与超复数奇异值分解相结合的检索法以及超复数矩阵相关检索法等三种超复数彩色图像检索方法，在对提出的三种算法进行比较的同时也将其与传统图像检索方法进行了比较，结果证明，超复数彩色图像检索法能较好地克服传统图像检索方法存在的问题，且检索结果更优；同时，本文提出了基于超复数奇异值分解的彩色图像质量客观评估法，这种全新的图形化与数值化相结合的方法不仅能够准确评估出彩色图像的不同失真等级，还能够区分不同的失真类型，从真正意义上实现了彩色图像的质量评估。

In chapter 4, Based on the orthogonality relations and duality of C-algebras, we study the decompositions of C-algebras, and give a Fourier inversion formula on C-algebras, which generalizes the Fourier inversion formula on the center of a finite group algebra over complex. As an application, we characterize the integral closure of C-algebras over the ring of integers, and show a necessary and sufficitient condition for elements of C-algbras being algbraic integral over integers.

第四章 我们应用C-代数的正交性及对偶性刻画了C-代数的一个分解，给出了C-代数上这个完全分解的Fourier反演公式，从而推广了Z分解的Fourier反演公式；作为Fourier反演公式的一个应用，我们刻画了Z在整数环Z上的整闭包，进一步我们研究了C-代数在整数环Z上的整闭包，给出了C-代数在整数环Z上为整元的一个充要条件。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The closed-cell aluminum foam was fabricated by direct foaming in melt. Through sampling aluminum foam in different stages the cross-section of them were observed and analyzed. It was explained how TiH_2 was decomposed after entered into the melt, how initial bubbles were formed and what was the state that generated bubbles and undecomposed TiH_2 lay in.

以熔体直接发泡法制备闭孔泡沫铝材实验为基础，通过获得不同实验阶段的泡沫铝样品，以及对实验样品切面或断面进行观察和分析，描述了在熔体发泡法制造泡沫铝过程中TiH2加入熔体后的分解过程，原始气泡的形成方式以及产生的气泡和未分解TiH2的存在状态；解释了气泡进一步长大的原因和未分解的TiH2如何释放气体；表述了气泡的合并和无泡层的形成。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。