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Suppose G is a finite group, then QG is a semisimple Q-algera, obviously ZG is a Z-order of QG,we denote the maximal Z-order by ?.If G is not abelian, it is not an easy thing to determine г; if G is an abelian group, then QG is isomorphic to the direct sum of a finite number of number fields, and r is the direct sum of these rings of algebraic integers of those number fields, but which elements of QG belong to r is not clear.

设G是一个有限群，那么QG是一个半单代数，ZG是QG的一个Z-序，设Γ是QG的一个极大Z-序，当G是一个非交换群时，Γ的求解是困难的问题；当G是一个交换群时，QG同构于有限多个数域的直和，Γ相应的就是各数域代数整数环的直和，但Γ具体是QG中那些元素不清楚。

To make paper more systematic and practical, this paper has first introduced the development history of CT equipment, then, elaborate construction of system and theworking principle of CT equipment systematically, including the property of X-ray, the absorption law of X-ray for materials, the reconstruction principle of CT image, the structure of software and hardware for CT equipment. Finally, with 2 CT systems that we used, statistic and analysis of all the malfunctions which have carried out in passed 10 years was given, and according to the systematic parts of fault located, classify the malfunctions, then elaborate their working principle one by one, analyze the regularity and the characteristic of each malfunction, and put forward specific prevention method and measure for the malfunction.

为了使论文更具系统性和实用性，本论文首先介绍了CT设备的发展史，然后比较系统地阐述CT设备的工作原理及系统结构，包括X射线的特性和物质对x射线的吸收规律，CT图像的重建原理，CT设备的软、硬件结构等，最后以我们所使用的2台CT为例，对10余年来所出现的故障进行了全面的统计分析，并按故障所处的系统部件进行分类，然后逐个阐述其工作原理，分析其故障的特点和规律，并就这些故障提出具体的预防方法和措施。

First, one. analyzes the eigenstates-from reachable sets and seeks the one which the target state belongs to. Then using the Grover iteration to amplify the probability amplitude of the desired eigenstate (the modul square of which is the probability of the corresponding eigenstate that the system will collapse to when it is measured). By measuring, the system will then collapse to the desired eigenstate with a probability of almost unity. Finally, one can use the admissible control to drive the system from the eigenstate to the target state.

该策略的核心思想是对本征态能控的系统，通过分析控制目标态与本征态的关系，寻找给定目标态所属的本征态可达集，然后利用量子非结构化搜索的Grover算法，将任意给定的系统初始态经过一定次数的Grover迭代，放大该本征态所对应的概率幅(概率幅的模方对应测量时波函数塌缩到对应本征态的概率)，然后对迭代后的态进行一次测量操作，使系统以接近1的概率塌缩到所需的本征态(前面分析得到的本征态可达集所对应的本征态)，最后用容许的控制将系统从该本征态控制到期望的目标态。

Then there is the story of this woman, a girlfriend now wife of an Air Marshal who complained to the Department of Homeland Security she was followed, photographed, and investigated by the Air Marshals, all because she says her then-boyfriend had a workman's comp claim.

这里有关于这位女性的故事，她是一位空警的女朋友，现在是他的妻子。她向国土安全部投诉称，她被中将跟踪并拍照，原因是她当时的男朋友有一张工人免费票。

Fuzzy controller is designed according to human"s controlling experience of systems. After reducing the operator"s controlling experience to a set of qualitatively descriptive conditional statements, and then quantifying them by using the theory of fuzzy set, the controller can transform the natural language of human"s controlling strategies into the algorithmic language acceptable for the computer, then the controller can receive human"s experience, and imitates humans operating strategies and effectively control some objects that can not be constructed into the mathematical model.

模糊控制控制器是以人对被控系统的控制经验为依据而设计的，它把操作人员的控制经验归纳成定性描述的一组条件语句，然后运用模糊集合理论将其定量化，把人的控制策略的自然语言转化为计算机能够接受的算法语言所描述的控制算法，使控制器得以接受人的经验，模仿人的操作策略实现对一些无法构造数学模型的被控对象进行有效的控制。

Yanowitz algorithm which interpolates the image grey by gradient imformation. Then it can get water meter frame information by horizontal and vertical projection, and extract line by improved Hough transform. Finally, the image can be corrected by affine transform.

Yanowitz算法，能够很好的分割目标和背景；再利用水平和竖直投影提取水表表框信息；然后再利用改进的Hough变换提取表框范围内直线，对结果进行统计分析，求出水表的倾斜角度；最后采用逆仿射变换的方法，对表框图像进行双线性插值旋转，得到表框的矫正图像。

Presence of multiples leads to poor quality in main stages of offshore seismic data processing, such as velocity analysis, stacking and imaging. Three basic multiple attenuating methods are reviewed; and a more effective multiple attenuator is achieved by joining them. As the first step, shot or receiver records are extrapolated by wave-equation datum algorithms. The extrapolation will establish a model of waterbottom multiples. Waterbotton multiples will then be removed by subtracting the extrapolated records from the original records. After that, predictive deconvolution is used to attenuate the multiples created by source ghost. Finaly, RADON transformation is adopted to separate peg-leg multiples and residual water-bottom multiples from the original data in the τ-p domain.

地震勘探尤其是海上地震勘探中存在着各类多次波，由于多次波的存在严重影响了速度分析、叠加、偏移成像等地震资料处理，海上多次波主要有全程多次波和层间多次两大类，为了压制海上不同类型的多次波，本文首先分析波场外推、预测反褶积和拉东变换衰减不同多次波的理论基础，然后联合采用这些方法，分别衰减全程多次波和层间多次波；即：首先对炮记录或者接收点记录进行波场外推，建立海底多次波模型，预测并减去全程多次波，然后利用预测反褶积衰减掉周期性明显的多次波，最后将数据转换到τ-p 域，用拉冬变换根据同一时间多次波和有效波在速度等方面的差异，进一步分离层间多次波和剩余的全程多次波，并在该域中切除分离出的多次波，从而实现联合多次波衰减处理。

The method first embeds watermark into the geometric invariant Fourier-Mellin domain of an image to weaken the geometric distortion, brought by printing process, of the watermark in presswork, and the image is then used to create presswork via a legal printing process. Secondly, the method rectifies rescanned image from the presswork by using Radon transformation and the embedded watermark in it is detected. Since there is an obvious difference between the destruction degrees of the watermark caused respectively by legal and pirated printing process, we can judge whether a copy of presswork is valid or not just by computing the ratio of the successfully derived watermark and comparing it with a predefined threshold.

该方法先将水印嵌入到具有几何不变性的Fourier-Mellin域中，以削弱正版印刷过程中的几何失真对水印的破坏；再利用Radon变换对由扫描印刷品所获得的图像进行矫正，并从图像中提取嵌入的水印信息；由于正版和盗版印刷过程对水印的破坏程度区别明显，该方法最终通过计算水印提取的正确率来度量这种破坏，并将其与预先制定的阈值进行比较来判定印刷品的正伪。

To get to the festival back then many people took stagecoaches pulled by horses; a few years later, they arrived by train on the new railroad. By the 1940s automobiles were common, and that's how most people got to Florence. By 1960, automobiles were so popular that the festival began to feature a show for fancy sports cars.

以前的人们会搭乘马拉的驿马车来参加此一盛会，但几年后，由於新铁路完工，人们於是改搭火车前来；到了1940年代，汽车普及后，大部分人就以此交通工具代步，出发来到佛罗伦斯。1960年后，汽车普及，因而该节日开始以拉风跑车秀来做为号召。

To get to the festival back then many people took stagecoaches pulled by horses; a few years later, they arrived by train on the new railroad. By the 1940s automobiles were common, and that's how most people got to Florence. By 1960, automobiles were so popular that the festival began to feature a show for fancy sports cars.

以前的人们会搭乘马拉的驿马车来参加此一盛会，但几年后，由于新铁路完工，人们于是改搭火车前来；到了1940年代，汽车普及后，大部分人就以此交通工具代步，出发来到佛罗伦斯。1960年后，汽车普及，因而该节日开始以拉风跑车秀来做为号召。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。