四元

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。

Recently, a lot of studies have been focused on the anisotropic finite element method, and there appears many relative papers(see [26,27,53,54]). However, the main attention of those were paid to the study of conforming Lagrange elements and the interpolation error analysis on the second order or fourth order elliptic boundary value problems.

近年来，各向异性有限元方法已成为有限元领域的热点问题，陆续出现了许多有关此方面的理论及应用研究成果，见[26，27，53，54]，其中大部分工作主要是针对二阶或四阶椭圆边值问题协调与非协调元的插值误差估计进行的。

In order to enlarge the application scope of our algorithm, the expansions of eLiveSet on four ways are studied, that is, the gradient of multi-relation, the constraints on the gradient cell, the gradient in the interval and the different gradient function.

为了扩大了算法处理问题的范围，给出了eLiveSet算法在多种关系间的梯度、梯度元组约束条件、区间上的梯度、不同的梯度函数四个方面的扩展，这些扩展可以通过修改算法的相关部分来实现。

Using the Mindlin theory, the four-node finite element shell modal of healthy and damaged structure is formed; Using Green Function theory, the fluid around the structure is considered to be inviscid, irrotational and incompressible, and then the effect of fluid to structure is translated to the added mass matrix compared with global mass matrix using BEM.

基于Mindlin理论，本文建立了描述健康和损伤的四结点有限元板壳单元模型；基于Green函数理论，将结构所处的流体环境考虑为无粘、无旋、不可压缩的理想流体，推导了三维问题拉普拉斯方程的基本解，并利用边界元方法将流体对结构的影响归结为对结构整体质量矩阵的影响；针对各向同性损伤单元，采取刚度各向整体弱化的方法分析；对于各向异性损伤单元，采用Kachanov理论，引入了x和y两个方向的弹性损伤折减系数。

Their works had a big influence on the development of landscape painting in the later Ming and Qing dynasties.

"元四家"的作品对相继的明清山水画发生了巨大的影响。

Because of the condition of 〓 for two neighbour parametricspline surfaces is too strong,here,instead of it,some simple and practicableconditions of 〓 resulted from the general theorem obtained by Prof.LiuDing Yuan in Chapter 1 were proved,and three 〓 triangular splinesurfaces schemes wre presented:one is piecewise cubic spline surface patcheshaving local 〓 and whole 〓 continuity based on the refined HCTtriangulation,another is the same degree spline surface patches but based onthe refined Powell-Sabin triangulation,the third is piecewise quartic splinesurface patches having local 〓 and whole 〓 continuity based on therefined P-S triangulation.

由于对参数曲面，一阶导数连续的要求较强，我们采用第一章从刘鼎元定理导出的简单实用的几何连续条件，讨论了基于HCT加细三角剖分和P-S加细三角剖分上的两种局部达一阶导数连续而整体有一阶几何连续的分片三次样条曲面构造算法，一种局部达二阶导数连续整体有一阶几何连续的分片四次样条曲面构造方法。

Second, third and fourth place contestants each receive a cheque for $5,000 from Magna.

第二，第三和第四位参赛者分别获得奖金5000元由麦格纳。

To elucidate the relationship between otolith microstructure and microchemistry and the life history events of the grey mullet Mugil cephalus in the early stage, the daily growth increments, growth check, Sr/Ca ratios and trace elements in otoliths of the juvenile mullets collected from the four estuaries from NE to SW Taiwan coast from 1996 to 2004 were examined by using the light and electron microscopes, electron probe microanalyzer and laser-ablation inductively coupled plasma mass spectrometry. A transition check was found in otoliths of all mullets.

为了阐明乌鱼耳石微细构造、微化学与其初期生活史事件之关系，本研究於西元1996年至2004年在台湾东北至西南沿岸的四个河口域进行乌鱼稚鱼的采样，然后利用光学及电子显微镜、电子微探仪及雷射熔蚀-感应偶合电浆质谱仪分析稚鱼耳石的日周轮、锶钙比及微量元素组成之变化。

One reason is that the model is an algebra method and it is based on the theory of minimal element. It can give more credible proof. Another reason is that the model tries to prove security of protocols, rather than check them. Thirdly, the model is simple and easy to use, and proof can be finished by manual. Moreover, graphic description makes its proof more comprehensible. Fourthly, there is much research work related to the model, which gives me a good springboard.

首先，该模型是一种代数方法，以极小元等理论为基础，可以给出可信度较高的证明；其次，该模型不是验证协议，而是试图证明协议的安全性；第三，该模型简单、易用，可以手工的方式完成证明，而且图形表示使其证明更加直观；第四，关于该模型有许多相关的研究工作，这为进一步工作打下了良好的基础。

The project plans to always invest 17.5 billion yuan of RMBs, the design is produced can be every months 1000 90, vitreous substrate dimension is 1500mm × 1850mm, include film of array, color, produce working procedure completely into the 4 parts such as box and modular group, the product shows with TFT-LCD with 37 inches of the following TV and computer monitor screen is given priority to.

项目计划总投资175亿元人民币，设计产能为每月90千片，玻璃基板尺寸为1500mm×1850mm，包括阵列、彩膜、成盒和模组等四部分全生产工序，产品以37英寸以下电视和电脑显示器用TFT-LCD显示屏为主。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。