三维的

In 3D scalar Helmholtz equation computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by The GMT.

首次从理论上证明，在三维静电场分析中，存在一种无穷级数收敛，且有一定普遍性的解析解；推导出三维静电场分析的多极理论通解及其使用规则，证明或解释广义多极技术不能证明或解释的若干使用规则，用多极理论求解工程实际中的三维静电场边值问题。

There are fourteen chapters, including introduction, plane stress and plane strain, two-dimensional problems in rectangular coordinates, two-dimensional problems in polar coordinates, photoelastic and moire experimental methods, two-dimensional problems in curvilinear coordinates, analysis of stress and strain in three dimensions, general theorems, torsion, bending of bars, axisymmetric stress and deformation in a solid of revolution, thermal stress, the propagation of waves in elastic solid media, at last there is an appendix on the application of finite-difference equations in elasticity.

全书共十四章，包括绪论、平面应力和平面应变、直角坐标中的二维问题、极坐标中的二维问题、光弹性与云纹实验方法、曲线坐标中的二维问题、三维应力和应变问题、一般定理、简单的三维弹性问题、扭转、杆的弯曲、回转体中的轴对称应力和变形、热应力、弹性固体介质中波的传播，最后有一附录，讲述差分方程在弹性理论中的应用。

The guidance system is built according to the relative relationship in three dimensions. For longitudinal plane, by introducing the subsidiary smooth function, the attraction domain of sliding mode are analyzed and determined, and the stability of the guidance system is proven, considering from the coupling relations of two planes in three dimensions.

根据末端三维弹目相对运动学关系，建立了三维制导系统的数学模型，并以纵向平面模型和变结构控制中到达条件为基础，引入分段光滑连续函数，以三维平面间的耦合关系为出发点，从两个方面分析并确定了过载受限变结构制导律的滑动模态吸引区，证明其制导系统的稳定性。

Five novel torsion-mirror optical actuators including double-beam thickness differential structure with single torsional axis, double flexible folded-beam structure with single torsional axis, double-beam vertical torsion comb structure with single torsion axis, four-beam differential compound-micromirror structure with double torsional axis and the combined structure of the four basis forms above, are brought forward. All of these devices could be fabricated by the same silicon micromachining process we have developed. The deformation compensation design with local enhancement for the thin torsional beam which is the key structure of these devices is also put forward to improve the reliability. The three-dimension solid model and two-dimension reduced order model of the torsion-mirror optical actuator are established and then the numerical simulations for evaluating the device characteristics of the statics, dynamics, electrostatic field, mechanical and electrostatic coupling, fluid and solid coupling are carried out to optimize the structure design. Furthermore, three optical fibre clamping structures which could be integrated monolithicly are designed and analyzed to improve the optical coupling capability. 4. Three flexible process flows combined with bulk silicon micromachining and surface silicon micromachining are brought forward to fabricate these novel single-crystal silicon or polysilicon torsion-mirror optical actuators by using the same lithography masks for both SOI wafer and regular silicon wafer. A series of important process experiments are carried out to optimize the process parameters and the process flows. Some novel and typical process phenomena which occurred during the microfabrication are analyzed and then the corresponding solutions are put forward. 5. A MEMS dynamic testing system which exploit blur image synthetic technique, stroboscopic image matching technique, stroboscopic mirau microscopic interferometry technique and microscopic laser dopper vibrometer technique is set up to measure three-dimension and six-freedom micro motions of any MEMS devices with nanometer resolution.

在对硅微机械扭转镜光致动器的光机电特性系统地理论研究的基础上提出了硅微机械扭转镜光致动器的结构设计准则。3、提出了单轴双梁厚度差分结构、单轴双柔性折叠梁结构、单轴双梁垂直扭转梳齿结构、双轴四梁差动复合微镜结构以及以上四种基本结构组合后的衍生结构等五种工艺加工技术兼容的新型的硅微机械扭转镜光致动器，对器件关键结构薄厚度、高耐疲劳扭转梁进行了局部加强的变形补偿设计，建立了器件的三维实体模型以及两维降阶模型，对提出的新结构硅微机械扭转镜光致动器进行了系统的静力学、动力学、静电场、力电耦合和流体固体耦合的建模仿真与优化设计，同时设计并分析了三种可实现单芯片集成的弹性光纤定位夹紧结构。4、提出了组合体硅微加工技术与表面硅微加工技术、兼容同一套光刻版图、可分别基于SOI 晶片和普通Si 晶片、适应于制造提出的各种新结构单晶硅和多晶硅硅微机械扭转镜光致动器的三套柔性加工工艺流程，开展了一系列重要工艺步骤的单项工艺试验，对工艺流程与工艺参数进行了优化，针对加工过程中出现的具有普遍意义的典型工艺问题进行了讨论和分析，并提出了解决方法。5、创新性地将模糊图像合成技术、频闪图像匹配技术、频闪Mirau 显微干涉技术与显微激光多普勒测振技术有机结合，建立起了一套周期运动测量与瞬态运动测量相结合、单点运动测量与全视场运动测量相结合、满足不同MEMS 器件各种动态测试要求的集成的MEMS 三维六自由度微运动精密测量系统。

Computer guided noninvasive implant: we use Three-Dimensional Computer Tomography for dental use to the pvease location. Under the help of 3D molding software,doctors can use DCT to obtain a visual 3D mode of the Alveolar bone,which facilitate implant placement、previse the Prognosis、and restoration. In this way ,doctors make implant placement and the restoration more safely and more efficiently and perhaps finish the implant therapy in only one vist .

是利用口腔专用电脑三维CT精确定位经DCT断层扫瞄，医生把这些扫描数据输入电脑三维成型软件，就能制作出可在屏幕上直观可视的三维种植体模型，这样就可预知适宜种植的部位及种植深度，预知术后的种植效果以及制作最终修复体，从而确保手术的精确度和治疗过程安全快捷，快速安装最终义齿，一次性完成种植治疗

For a good 3D models retrieval system, the geometrical similarity matching method should be reckonable, and be robust to rotation, noise, model degeneracy.

对于三维模型检索系统，三维模型几何相似性比较算法要有较好的可计算性，具有较好的噪声鲁棒性，较好的网格简化鲁棒性，以及三维模型的坐标系旋转鲁棒性。

The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial maps are discussed and proved.

从理论上分析并证明了三维多项式映射满足等变的条件，精确地给出了关于正四面体群和正八面体群具有旋转不变对称性的两类三维等变映射的具体公式，在此基础上讨论并证明了三维多项式映射的广义Julia集所具有的性质。

It can measure peak particle, peak displacement, peak particle acceleration, frequency at the peak velocity and the resultant peak partide velocity, peak sound , and frequency at the peak sound in three dimensions.

NCSC 5300是便携式固化计算机控制的测震仪，可以调出测点的三维振动速度、振动加速度、质点振动位移、振动频率和噪声强度、噪声频率，打印出测试结果及振动频率与三维振动速度的关系图、三维振动波形图，是理想的爆破测震仪器

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

We construct the algorithm of three-dimensions model surface reconstruction in three stages: first, we use Oct-tree to describe scatter data points in space, second find adjacent points and tangent plane and use the triangulation method to realize 3D surface reconstruction in the end, in research on algorithm of three dimensions model surface reconstruction based on scatter data points.

在"基于散乱数据三维表面算法的研究"这一章中，首先通过八叉树的数据结构的算法对三维散乱数据进行处理，然后再确定邻点和微切平面，最后用三角网格化的方法完成三维物体表面重构。

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