分析几何学

The linear system optimum control theory distributes one of parameter systembasic topics,in domains and so on aerospace,national defense,finance,communicationhas the widespread application prospect.simultaneously, because the research tech-nique involves to foundation mathematics theories and so on the functional analysis,analysis situs,geometry, algebra.

线性系统的最优控制理论是分布参数系统的基本课题之一，在航空航天、国防、金融、通讯等领域有着广泛的应用前景。同时，由于研究手法涉及到泛函分析、拓扑学、几何学、代数学等基础数学理论。

The analytical geometry is used to study the formulas of Moire fringes for the measurement of screen line, to analyze the geometric forms and their properties of Moire fringes , and further discusses the bases of theory for the measurement of screen line.

本文用解析几何学方法研究测量网线的莫尔条纹方程，分析莫尔条纹的几何形状与特性，并且进一步讨论网线测量的理论依据，旨在深刻地揭示测量网线的莫尔条纹原理。

The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.

这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

The computer simulation software was developed for figuring the path curves and instantaneous speed of the lapping process.

文中从运动学和几何学原理出发，建立了工件精密研磨过程的轨迹方程，通过将复杂的研磨运动简化为在中心距一定条件下夹具绕研磨盘中心轴的回转运动及夹具自身的回转运动，对工件上任意点相对于研磨盘的运动轨迹及瞬时速度进行了分析计算，并开发了相应的计算机仿真软件，对其运动轨迹曲线及瞬时速度进行了分析。

Mathematical morphology is developed from set theory and integral geometry, which is concerned with the shape of a signal waveform completely in the time domain rather than the domain frequency.

数学形态学是从集合论和积分几何学发展起来的，它完全在时域对信号的波形进行分析，不涉足频域分析。

Based on the source investigation and the comparative approach of history of mathematics,a historical background of Gauss competition essay and its contribution to intrinsic differential geometry are discussed.

运用文献分析研究和数学史比较研究方法，分析了高斯哥本哈根获奖论文产生的历史背景及其对内蕴微分几何学的贡献。

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。

In this paper, the effects of the rigid body motions and low frequency surface errors on the image quality were analyzed. Quadratic equations were used to build the mathematical model of the Wolter type I and II X-ray telescopes and reduce the computational complexity of ray tracing. With the help of a self-developed optical surface analysis code, the effects of the perturbations of the mirrors on the image quality was analyzed and the growth of the image spot formed by deformed telescopes was calculated, this is important for giving the reasonable fabrication tolerance.

在本篇文章中，详细分析了刚体运动误差和低频表面误差对成像质量的影响；使用空间解析几何学的二次曲面方程建立Wolter I、II型X射线掠入射望远镜镜片的数学模型，降低光线追踪的计算复杂度；借助自主开发的光学仿真软件分析了国内研制的X射线成像望远镜的刚体运动误差和低频表面误差对成像质量的影响，计算出像点艾里斑半径均方根值随误差变化的增长率，对工程上提出合理的制造公差的误差容限有重要的指导意义。

The combination with the Calculus,physics,especially variational principles and geometry is one of the features of tiffs dissertation.

本文在查阅大量原始文献和相关研究文献的基础上，利用文献分析和比较研究方法，以&为什么数学&为切入点，结合微积分学、物理学以及几何学等背景，对变分法的起源和创立进行了系统分析和研究。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失