相似性定理

Based on the resemblance of deflection equation with free vibration equation, the reciprocal theory can be applied to the analysis of free vibration of unidirectional plate,and through which we can easily get the inherent frequency of unidirectional plate with different boundry supporting after assuming the form of free vibration.

利用单向板挠曲面微分方程和振型方程在数学上及力学上的相似性，提出了分析单向板自由振动的功的互等定理法。

Has first produced the matrix in the article and its the similar definition, the theorem and its the nature, the matrix similar condition and so on, and gives the full proof.

在文中首先给出了矩阵及其相似性的定义、定理及其性质，矩阵相似的条件等，并给予充分证明。

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

To fulfill the need of the application of RP technique in medical domain, reverse CAD modeling from medical cross sections is systematically studied in this dissertation. Firstly, Some algorithms related to the research of this dissertation are studied. New algorithms for orientation and inclusion test for simple polygon, an error constrained automatic faring algorithm for B-spline curve and a theorem regarding the termination criterion for subdivision of triangular Bézier patch are proposed. Then based on similarity between contours of adjacent sections, a methodology for surface reconstruction from cross sections is presented. Finally, a virtual measuring method is proposed.

本文针对RP技术在医学领域应用的需要，系统研究了基于医学断层轮廓数据的反求CAD建模理论和方法：(1)在基础算法研究部分，提出了简单多边形方向及点在多边形内外判断的新方法、三角Bézier曲面片离散的误差控制定理和一种带误差约束的B样条曲线的自动光顺方法；(2)提出了一种基于相邻层轮廓相似性的医学断层轮廓数据曲面重构方法；(3)提出了一种称为"虚拟测量"的曲面模型处理方法。

A comparison is made between the electrostatic field and universal gravitation field to find out the very similarities between them.

在比较静电场与万有引力场相似性的基础上，归纳出相似性的本质，进而根据相似性由静电场中已有的公式、定理及解题方法推导出万有引力场中与此相似的公式、定理及解题方法。

In order to solve the similitude problem of shaking table scale modle test of dynamic interaction of pile-soil-bridge structure in ground of soil liquefaction, based on the theorem of Bockingham π widely applied at present, the dimensional analysis method is used, and the constitutive strain-stress relationship of material between model and prototype and the dynamic response similarity of pile-soil interface are considered at the same time.

基于目前广泛应用的Bockingham π定理，主要采用量纲分析方法，并且结合考虑模型与原型之间的材料变形应力-应变本构关系及桩－土接触边界动力响应相似性，求解液化场地桩－土－桥梁结构动力相互作用振动台试验的模型设计相似关系，同时提出人工质量问题的解决办法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。