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In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.

本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。

Spacelike case: Hyperbolic space H2, spacelike plan.? Timelike case: Null scroll- Timelike umbilical surface: de Sitter 2-space S2, timelike plan.

在此基础上，我们给出了伪全脐曲面的一种分类：·类空的情况：双曲空间H~2，类空平面。

Result: Different projection positions of X-ray can evaluate different thoracic small joints. Image diagnosis were space changes, the deflection of the spinous process of vertebral and hyperostosis osteosclerosis. soft tissue lesions near thoracic spinal facet almost was not evaluated. CT plain scan can evaluate every changes of thoracic spinal facet. Image diagnosis were articular process hypertrophy, osteophyte formation, articular surface hyperostosis osteosclerosis, space changes, joint capsule and ligament calcification.

结果：X线平片不同投照体位可以评价不同胸椎小关节，表现为间隙改变、椎棘突偏斜及增生硬化，对胸椎小关节软组织病变基本无法评价；CT平扫对各胸椎小关节改变均可评价，表现为关节突肥大，骨赘样增生，关节面硬化，关节间隙改变，关节囊及韧带钙化。

A fuzzy membership model based on support vector data description is proposed to fuzzify all the training data. Then the model is introduced into least square support vector machines. Data samples in input space are mapped into a high dimensional feature space, and then the smallest enclosing hypersphere is found.

将模糊隶属度概念引入最小二乘支持向量机，提出一种基于支持向量数据域描述的模糊隶属度函数模型，将输入空间中的样本映射到一个高维的特征空间；然后根据其偏离数据域的程度赋予不同的隶属度。

From theoretical viewpoint,Support Vector Machinesolution corresponds to the center of the lar- gest hypersphere inscribed in the version space,and Analytic Center Machinesolution corresponds to the ana- lytic center of the largest hypersphere inscribed in the version space.

1问题的提出支持向量机以其优越的泛化性能在机器学习和优化领域日益受到重视并得到广泛应用，其解对应于样本空间最大超球体的中心。

It helps the student mastery the essential principle and method of projection. Finally it can train student to diagrammatize the space geometry problem, to imagine and ichnography the form and structure on space, to plot with apparatus and computer.

它能使学生掌握基本的投影原理和方法，并以此培养图解常见空间几何问题的能力、空间形体想象和平面图示能力、运用绘图仪器和计算机的绘图能力。

There is a conjecture in physics that the classical gravitation theoryon AdS-space is equivalent to the conformal field theory on the ideal boundary ofAdS-space.

在物理学中有一个猜想：AdS-空间上的经典重力理论与这个空间理想边界上的共形场理论是等价的。E。

Bing no longer restricted to its traditioned role as the presentation of the suspended time and a fleetingly observed sight before the great changes in Western art, perfect theatment of time and space in painting has overwelmingly changed and transcended the traditionally-established means of presenting a three-dimentional illusionism based on a two-dimentional plane,crying for the emergence of pluralist concept and multiple fashions of time-space treatment in painting.

作为绘画表现的一个重要部分的时空表现在现代绘画中也出现了翻天覆地的变化。西方现代艺术变革之前的艺术家将如何在二维的平面塑造物体的三维空间形体，表现凝固的时间或瞬间场景视为绘画的重要方面，而西方现代绘画在继承性的推翻传统的绘画的同时，出现了多元的，丰富的时空表现样式。

With the development of space technology, the data of space remote sensing image are expanded greatly.

随着空间技术的发展，空间遥感图像的数据量呈几何级数增加。

This is a preview of Your blogger image space is your Picasa web album space .

这是一个预览您的Blogger的形象空间，是您的Picasa网络相册空间。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。