几何学的

In the vast cosmic exchanges the universal life goes and comes in unknown quantities, rolling entirely in the invisible mystery of effluvia, employing everything, not losing a single dream, not a single slumber, sowing an animalcule here, crumbling to bits a planet there, oscillating and winding, making of light a force and of thought an element, disseminated and invisible, dissolving all, except that geometrical point, the I; bringing everything back to the soul-atom; expanding everything in God, entangling all activity, from summit to base, in the obscurity of a dizzy mechanism, attaching the flight of an insect to the movement of the earth, subordinating, who knows?

在宇宙广袤无边的运动中，无量数的空间活动交相往来，把一切都卷进那神秘无形的散漫中，并也利用一切，即使是任何一次睡眠中的任何一场梦也不放弃，在这儿播下一个微生物，在那里撒上一个星球，摇摆，蛇行，把一点光化为力量，把一念变成原质，散布八方而浑然一体，分解一切，而我，几何学上的这一点，独成例外；把一切都引回到原子棗灵魂，使一切都在上帝的心中放出异彩；把一切活动，从最高的到最低的，交织在一种惊心动魄的机械的黑暗中，把一只昆虫的飞行系在地球的运转上，把彗星在天空的移动附属于棗谁知道？

In the vast cosmic exchanges the universal life goes comes in unknown quantities, rolling entirely in the invisible mystery of effluvia, employing everything, not losing a single dream, not a single slumber, sowing an animalcule here, crumbling to bits a planet there, oscillating winding, making of light a force of thought an element, disseminated invisible, dissolving all, except that geometrical point, the I; bringing everything back to the soul-atom; expanding everything in God, entangling all activity, from summit to base, in the obscurity of a dizzy mechanism, attaching the flight of an insect to the movement of the earth, subordinating, who knows?

在宇宙广袤无边的运动中，无量数的空间活动交相往来，把一切都卷进那神秘无形的散漫中，并也利用 www.8 t t t8。 com 一切，即使是任何 dd dtt。 com 一次睡眠中的任何 dd dtt。 com 一场梦也不放弃，在这儿播下一个微生物，在那里撒上一个星球，摇摆，蛇行，把一点光化为力量，把一念变成原质，散布八方而浑然一体，分解一切，而我，几何学上的这一点，独成例外；把一切都引回到原子棗灵魂，使一切都在上帝的心中放出异彩；把一切活动，从最高的到最低的，交织在一种惊心动魄的机械的黑暗中，把一只昆虫的飞行系在地球的运转上，把彗星在天空的移动附属于棗谁知道？

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

That our civil rights have no dependence on our religious opinions, any more than our opinions in physics or geometry; that therefore the proscribing any citizen as unworthy the public confidence by laying upon him an incapacity of being called to offices of trust and emolument, unless he profess or renounce this or that religious opinion, is depriving him injuriously of those privileges and advantages to which, in common with his fellow citizens, he has a natural right; that it tends also to corrupt the principles of that very religion it is meant to encourage, by bribing, with a monopoly of worldly honours and emoluments, those who will externally profess and conform to it; that though indeed these are criminals who do not withstand such temptation, yet neither are those innocent who lay the bait in their way

我们世俗的权利并不依赖于我们的宗教见解，正如不依赖于我们在物理学或几何学上的见解一样；所以，如果一个人不声明支持或放弃这个或那个宗教观念，就以不值得公众信任为由将其置于不适合被选举为信任和有薪的职位而排斥他，这有害的剥夺了他的基本人权和利益，而对于这些人权和利益，和他同胞一样，他也拥有自然的权利；同时也趋向于败坏真正的宗教原则，这意味着贿以世间荣誉和报酬的独占权来鼓励那些表面上支持和遵守它的人；这些经不住诱惑的人固然是罪人，然而在他们路上安置诱饵的人也不能说是无罪

And iswithdrawing from the ministry those temporal rewards, which proceeding from anapprobation of their personal conduct, are an additional incitement to earnestand unremitting labours for the instruction of mankind; that our civil rightshave no dependence on our religious opinions, any more than our opinions inphysics or geometry; that therefore the proscribing any citizen as unworthy thepublic confidence by laying upon him an incapacity of being called to officesof trust and emolument, unless he profess or renounce this or that religiousopinion, is depriving him injuriously of those privileges and advantages towhich, in common with his fellow citizens, he has a natural right; that ittends also to corrupt the principles of that very religion it is meant toencourage, by bribing, with a monopoly of worldly honours and emoluments, thosewho will externally profess and conform to it

同时夺走了这位牧师应得的世俗报酬，而牧师们正是通过这些人们赞许的表示而继续从事他们身体力行的牧养，这些报酬可以鼓励更多的为人类教育而热忱并不懈的工作；我们世俗的权利并不依赖于我们的宗教见解，正如不依赖于我们在物理学或几何学上的见解一样；所以，如果一个人不声明支持或放弃这个或那个宗教观念，就以不值得公众信任为由将其置于不适合被选举为信任和有薪的职位而排斥他，这有害的剥夺了他的基本人权和利益，而对于这些人权和利益，和他同胞一样，他也拥有自然的权利；同时也趋向于败坏真正的宗教原则，这意味着贿以世间荣誉和报酬的独占权来鼓励那些表面上支持和遵守它的人

Through simulation of the real process of thomcolumbar burst fracture and use of modem dynamics techniques, the present study was (1) to investigate the kinetic relationship between structural damage and impact energy absorption and dynamics mechanism of thoracolumbar burst fracture by quantitative analysis of various injured segments;(2) to explore the instability mechanism of L1 vertebral burst fracture and its injury threshold by three-dimensional analysis of the injured segment with stereophotogrammetry in combination of transient physical parameters, anatomy and image;(3) to explore the corresponding relationships between impact energy, geometry parameters and biomechanics by geometry and biomechanical analysis of thoracolumbar burst fracture, which may provide an objective standard for evaluation of spinal injury severity and experimental evidence for adoption of biomechanical treatment in clinic;(4) to evaluate the fixation effect of different instruments and the effect of intervertebral bone graft on segment fixation by analysis of the threedimensional stability of different internal fixation instruments and their decompression of the spinal canal, which may provide experimental evidence for therapeutical selection for thoracolumbar burst fracture in future; and finally to investigate the effect of various instrument fixation on dynamical characteristics by comparison and quantitative analysis of frequency and amplitude responses, which may provide certain theories and experimental evidence for application of vibration test to judge the stability of the spine.

本研究从胸腰段脊柱爆裂骨折发生的实际过程出发，以现代动力学检测及计算机多通道高性能数据采集分析系统等高新技术为基础，实时量化分析损伤节段的工程参数，揭示了结构破坏与能量吸收的变化规律，探讨了胸腰段脊柱爆裂骨折的瞬态损伤机制；利用三维立体摄像技术，对不同损伤程度的节段进行三维运动分析，结合瞬态物理参数、影像学和病理解剖，明确了〓椎体爆裂骨折的失稳机制及损伤阈值；通过对胸腰椎爆裂骨折的几何学变化及生物力学分析，明确了撞击能量与几何参数、几何参数与生物力学的相应关系，为评判脊柱损伤程度提供了客观标准，为治疗中采取适宜的生物力学方法提供了实验依据；通过对比分析不同内固定器械的三维稳定性和对椎管的减压作用，评价不同器械的复位固定作用，同时比较椎体间植骨对节段固定作用的影响，为今后临床胸腰段脊柱爆裂骨折的治疗选择提供依据；利用振动测试与分析技术，比较及量化分析了不同致伤状况的频幅响应特征，比较分析了各种器械固定对动力学特性的影响，为今后临床建立基于振动测试与分析技术判断脊柱稳定性的诊断方法，提供了一定的理论和实验依据。

He had begun an investigation, as he imagined, with the severe equal integrity of a judge, desirous ssbbww.com of truth, even as if the question involved no more than the air-drawn lines figures of a geometrical problem, instead of human passions, wrongs inflicted on himself.

照他自己的想象，他是以一个法官的同等的严峻与公正来开始一次调查的，他只向往真理，简直把间题看得既不包含人类的情感，也不卷入个人的委屈，完全8 t tt8。 com 如同几何学中抽象的线和形一般 SsbbwW.com 。

"As mentioned by Bak in this debate, the SOC hypothesis has been suggested, on the one hand, on the basis of the observation of power law distributions, such as the Gutenberg-Richter law for earthquakes and the fault length distribution, and of the fractal geometry of sets of earthquake epicenters and of fault patterns, and on the other hand on the study of highly simplified models with somewhat similar scale-invariant properties."

&如同Bak在这场辩论中已提到的那样，一方面，在对动力法则分布进行观测的基础上，如用于地震和断层长度分布的Gutenberg-Richter定律，以及对震中的破裂几何学内容的观测和对断层图案的观测，以及另一方面对带有某种程度类似标度不变性质高度简单的模型的观测基础上，提出了SOC〔'自组成危险性'〕假说。&

The wetFoam geometry likened by Podborsek and Snooks to the gradient of a milkshake in which the bubbles enlarge and multiply towards the surface is used to create two separate but mutually dependent spaces as the lattice of the walls thicken out to form a second inhabitable space.

&潮湿泡沫&几何学--与 Podborsek 及 Snooks 所提出的的渐变的奶昔泡沫有关，泡沫在渐变的过程中增大并且向着表面增值--被用来创造出两个独立但互助互依的空间，而空间的边缘则作为墙体划分的格子，进而创造出另一个可供居住空间。

We once believed that such things as the growth patterns of tree branches, and the networks of tree roots, the contours of mountain chains, and the directional meanderings of rivers and streams were random, because that was the simplest of explanations.

……我们曾经认为树枝的生长模式、树根的分布网络、山脊的外形轮廓，以及河流的蜿蜒曲折都是随意产生的，因为这是最简单的解释。但随着分形几何（分形几何学fractal geometry，空间具有不一定是整数的维，而存在一个分数维数。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。