形式上

The Laplace matrix is an active and important subject in Algebra Graph Theory. It is a discrete form of the Laplace operator on the compact Rimannian manifold acting on the graphs. It has been widely used in many fields such as Physics, Chemistry, Biology, Computer net science and Information theory ,etc. Some results on the Laplace matrix are given in this thesis.

本文主要研究了代数图论中的一个课题：单圈图的Laplace谱，它是黎曼流形上的拉普拉斯算子在图上的离散形式，Laplace矩阵在物理、化学、生物和计算机通信网络研究等学科中有着广泛的应用。

Painting which is the mainstream of the western art is extremely representational in the aspect of the space concept. But relieves combine the paintings'complanation with sculptures'extensity .so we decide to research the process of the evolvement and the interaction between paintings and sculptures. We expect to discuss the space and art expression in the western art and relieve ,so I can have a further comprehension about the space of optical art. The comprehension can not only help us understand the traditional western paintings and relieves better, but also make us comprehend the space concept of modern art better, to set the artistic creations of contemporary paintings and relieves into action.

油画，作为西方绘画的主流形式，在空间形态的表现上极富代表性，而浮雕兼具绘画的平面性与雕塑的实体空间性，因此，我选择研究油画与浮雕在空间上的演变过程及其相互影响，以期可以从一个侧面来探讨西方绘画与浮雕中的空间观和艺术形态表现，从而对视觉艺术的"空间"有更深一个层次的了解，这不仅有利于我们理解传统的西方油画和浮雕，也能使我们更好地理解现代艺术的空间观念，进而更好的推动当代的油画和浮雕创作。

In philosophy,we used it to name the doctrine of Confucious,because they had the same template.

在美学上，它是一条普遍的最具和谐性的形式法则；在哲学上，它与中国两千多年前孔子的"中庸"和合思想遵循同一模式。

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

MICE Tourism is a new kind of traveling form which has good report of "the gem in the tourism imperial crown"in the international area.

有"旅游皇冠上的宝石"美誉的会展旅游是国际上新兴的一种专项旅游形式。

This result is a higher-dimentional analogue of the Fundamental Theorem of Calculus: it expresses the integral over D of some kind of derivative of P and Q in terms of an integral of P and Q over the boundary of.

格林公式建立了曲线积分和二重积分的关系 O 这是微积分基本定理在高维情形的推广：它将上P、Q某种形式的导数的积分用的边界上 P、 Q 的积分表示出来。

Transform : Applies a specified function object to each element in a source range or to a pair of elements from two source ranges and copies the return values of the function object into a destination range.

该算法有两种形式：一种采用的是一元函数，作用到区间中的每个元素上；另一种采用的是二元函数，同时作用到两个区间中相互对应的元素上。

On the political front, the United States played a pivotal role and has far-reaching influence;On the economic front, the potential problem is the integration of Latin American too dispread;On the social front, the rising of left-wing forces to bring the people a ray of hope, as well as an increase of more uncertainty.

在政治上，美国扮演起关键性的角色，牵一发，动全身；在经济上，拉美各国的整合形式过於分散，是一大隐忧；在社会上，左派势力的兴起带给人民一丝希望，同时也增加了更多不确定性。

At the same time, the four different genesis types of the sequence interfaces are divided: orogenic erosive sequence unconformity interface, uplift erosive sequence unconformity interface, transgression onlap sequence unconformity interface, exposural sequence unconformity interface; simultaneously the ten concrete mineral showing forms are summarized, i.e. paleo-weathering crust, drossy layer, river rejuvenation surface, paleo-karst surface, slope gravity current erosion surface, intrabasin turbid flow erosion surface, volcanic events surface, lithologic and lithofacies conversion surface, onlap surface and maximium sea flooding surface.

同时归纳出了4种不同的层序界面成因类型：造山侵蚀层序不整合界面、升隆侵蚀层序不整合界面、海侵上超层序不整合界面和暴露层序不整合界面等；同时总结出10种具体的物质表现形式，即：古风化壳、渣状层、河流回春作用面、古喀斯特作用面、斜坡重力流冲刷侵蚀面、盆地内浊流侵蚀面、火山事件作用面、岩性、岩相转换面、上超面和最大海泛面。

It solves the problem that the unitary contour presentation can not correctly extract face contour in a face image which suffers from scale, rotation etc. The definition of the internal and external energy function is provided. At the same time, the global matching algorithm and local matching algorithm is given. The experiment shows that this presentation and the accompanying matching algorithm can be used to extract the face contour very well. So the image segmentation can be implemented by using it.②By analyzing the recognition principle of PCA method, we can conclude that the face images coming from different surrounding consist of different face image space. This is the essential reason that makes the generality of PCA method worse. Also, we give a measurement means to measure the distance from different face image space, so we can analyze face image space more conveniently.③We also construct various scale models and rotation pose models to detect the scale and rotating angle of face image to be recognized. The experiment results show that the detecting precision is very high. So it is good for face image feature extraction and face image representation.④Similarly, we construct local feature models of face image and utilize them to detect the local feature of face image. At the same time, we put forward a novel face image local feature detection algorithm, locating step by step. The experiment results show that this method can accurately detect the location of local face feature in a image.⑤A novel face image presentation model, dual attribute graph , is put forward. Firstly, it utilizes attribute graph to present the face image, then exact the local principal component coefficient and Gabor transform coefficient of thc pixels which corresponds to the nodes of the graph as the attribute of the nodes. This representation fully makes use of the statistical characteristic of the local face feature and utilizes Gabor transform to present the topographical structure of face image. So DAG has more general property.⑥Based on the DAG presentation, we give a DAG matching function and matching algorithm. During the design of the function and algorithm, the noise factor, e. g., lighting, scale and rotation pose are considered and tried to be eliminated. So the algorithm can give more general property.⑦A general face image recognition system is implemented. The experiment show the system can get better recognition performance under the noise surrounding of lighting, scale and rotation pose.

本文在上述研究的基础上，取得了如下主要研究成果：①构造了一个通用的人脸轮廓模型表示，解决了由于人脸图象尺度、旋转等因素而使得仅用单一轮廓表示无法正确提取人脸轮廓的问题，并给出了模型内、外能函数的定义，同时给出了模型的全局与局部匹配算法，实验表明，使用这种表示形式以及匹配算法，能够较好地提取人脸图象的轮廓，可实际用于人脸图象的分割；②深入分析了PCA方法的识别机制，得出不同成象条件下的人脸图象构成不同的人脸图象空间的结论，同时指出这也是造成PCA方法通用性较差的本质原因，并给出了不同人脸空间距离的一种度量方法，使用该度量方法能够直观地对人脸图象空间进行分析；③构造了各种尺度模板、旋转姿势模板以用于探测待识人脸图象的尺度、旋转角度，实验结果表明，探测精确度很高，从而有利于人脸图象特征提取，以及图象的有效表示；④构造了人脸图象的各局部特征模板，用于人脸图象局部特征的探测；同时提出了一种新的人脸图象局部特征探测法---逐步求精定位法，实验结果表明，使用这种方法能够精确地得到人脸图象各局部特征的位置；⑤提出了一种新的人脸图象表示法---双属性图表示法；利用属性图来表示人脸图象，并提取图节点对应图象位置的局部主成分特征系数以及Gabor变换系数作为图节点的属性，这种表示方法充分利用了人脸图象的局部特征的统计特性，并且使用Gabor变换来反映人脸图象的拓扑结构，从而使得双属性图表示法具有较强的通用性；⑥在双属性图表示的基础上，给出双属性图匹配函数及匹配算法，在函数及算法设计过程中，考虑并解决了光照、尺度、旋转姿势变化等因素对人脸图象识别的影响，使得匹配算法具有较强的通用性；⑦设计并实现了一个通用的人脸图象识别系统，实验结果表明，该系统在图象光照、尺度、旋转姿势情况下，得到了较好的识别效果。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。