几何基础

Firstly, this paper introduces the model-line of the scroll expander in detail and deduces integrally the geometrical theory on the scroll expander. Basing on the transparent geometrical relation of the scroll expander, force analysis of the immobile and the rotary turbination are showed in the paper.

首先，本文比较详细的介绍了涡旋机械的型线构造，之后对涡旋式膨胀机的几何理论进行了比较全面介绍和推导，在明晰涡旋膨胀机基本几何关系的基础上，对动、静涡盘进行了受力分析。

So, the aromaticity of acenaphthenyl groups in C_2 gum should be the least. In order to explain the reason, quantum chemical calculation is utilized. The optimized geometrical structrures of condensed aromatics in C_1 gum, C_2 gum and C_3 gum are calculated at B3LYP/6-31G* levels. We find that some phenyl groups in acenaphthenyl groups are coplanar and have the largest conjugated structure.

为了解释其原因，我们利用量子力学方法进行了计算，研究了三种稠环基团在B3LYP／6-31G*基组水平下优化得到的几何结构，发现苊式多苯基苯基中的萘环和中间的苯环共面，电子离域性最大，而其他二者所有苯环都不共面，发生了明显地扭曲；同时，在优化几何结构的基础上，对三种化合物进行了前线分子轨道的分析，利用密度泛函理论方法(density function theory，DFT)计算了稠环基团的最高占有轨道和最低未占轨道之间的能量差，即能隙，发现C_2胶上苊式多苯基苯基的Eg最小，解释了C_2胶具有最好的辐射保护效果的原因。

A new method to recognize some special features such as thin-wall features and bar-shaped features which could be reduced dimensionally is also developed.

本文在研究几何模型边界元素的细微度量化方法的基础上，提出了实体模型的细微特征识别和分解方法，实现几何模型的自动简化。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

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。

4Have done a great deal of research work, while on the stiffened ones, Wanget al. [5, 6, 7] have also done a series of research work. But up to now, tothe author's best knowledge, there have been no papers reported in the openliterature on the stability analysis of the laminated composite shells of revo-lution, both unstiffened and stiffened, by the finite element method.

在SABA族元素[1]的基础上，把复合材料各向异性的弹性性质考虑进去，把纵向筋条处理成为空间梁，计入梁偏心的影响，由梁的基本弹性和几何刚度矩阵出发，经过一系列变换，推导出与SABA元素相协调的新的弹性和几何刚度矩阵，从而较为精确地得到了复合材料叠层及加筋的稳定性分析结果。

After verification of the program, the mathematical models of the suspension bridges were studied by means of the program, as well as the determination of the main cable's shapes and its internal forces at different stages, the calculation of the cable's unstrained length and the analysis of the construction processes, of which some new approaches were presented in the mean time. Thus makes the structural analysis results of suspension bridges more reliable and in accordance with reality.

在用算例验证了程序分析结果正确性的基础上，应用该程序对悬索桥的数学模型、各阶段缆索几何形状及内力状态的确定以及缆索无应力长度的计算和施工过程分析进行了研究，提出了确定缆索在成桥状态下的几何形状及其内力状态以及缆索无应力长度计算的新方法，使悬索桥的结构分析结果更加符合实际情况。

The appearance of paradox of set theory makes this problem more poignant.

欧几里得几何是第一个公理化体系，非欧几何的出现促使人们对它的基础作了严格审视，其中希尔伯特公理化方法最为成功；但它的相容性问题一直没有解决，集合论悖论使得这个问题更加尖锐。

A method of computing certain inaccessible distances or heights based on similarity of geometric figures and attributed to Thales presaged more abstract approach to geometry taken by Euclid in his Elements , one of the most influential books ever written.

一种方法计算某些无法距离或高度相似性的基础上几何数字和归因于泰勒斯预示较抽象的做法所采取的欧几里得几何的元素，其中最具影响力的书籍写。

The typified programming technique for numerical control, described in this paper, is established on the basis of characteristic analysis of geometric configurations and dimensions of any two-dimensional patterns.

本文提出的数控编程典型化技术，是在对任意二维空间图形的几何形状及几何量进行特征分析的基础上建立起来的。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。