基片变形法测量薄膜应力分析

总结了薄膜应力的一些测量方法。分析了利用测量基片弯曲曲率变形分析法的理论依据及其测量原理,计算了激光干涉法,激光束偏转法的测量精度,分析了其优缺点。     

圆锥曲线的渐屈线和曲率圆

曲线C在点P(x0,y0)曲率圆是与该曲线C相切于点P(x0,y0)(凹侧)的最大圆,曲率圆的圆心D的轨迹曲线G称为曲线G的渐屈线.抛物线y2=2px(p>0)、椭圆x2/a2+y2/b2=1和双曲线x2/a2-y2/b2=1的渐屈线方程分别为y2=8/27P(x-p)3、x3/(c2/a2/3=1和x3/(c2/a2/3-y3/(c2/b)2/3=1.抛物线、椭圆和双曲线的最小曲率圆都是它们的内切圆,其方程分别为(x-P)2+y2=p2、(x±c2/a)2+y2=b4、(x±c2/a)2+y2=b4/a2.     

A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.     

关于黎曼流形上Ricci曲率和截面曲率的讨论

从黎曼流形M的第k个Ricci曲率Ric（k）（M）的概念出发,得出：对于m〉k,如果有Ric（k）（M）≥kc,那么一定有Ric（m）（M）≥mc.还证明了：对于一个n维完备的非紧黎曼流形,若对任意r〉0,令Kp（r）=infM／B（pr,）K,其中K是M的截面曲率,下确界取遍M／B（pr,）中所有点的截面,则Kp（r）≤0,并且Kp（r）是关于r的单调函数.     

提高牛顿环仪测量透镜曲率半径精确度的实验研究

牛顿环仪测透镜曲率半径是大学物理实验中基础的光学实验之一。本文通过多次的实验操作,获得多组测量数据,探究影响实验测量的因素,获得提高该实验精确度的方法。     

量子复合时空理论的曲率解释

本文将量子复合时空理论，量子力学交易解释和量子力学曲率解释结合起来，而且将它们推广到广义相对论的弯曲时空框架中，不仅解决了量子场论中的一些重正化问题，而且以黑洞和白洞的时空度规作了新的理解，初步解决了霍全和彭罗斯的量子黑洞问题上的争论，对天体演化和宇宙演化提出了新的观点，有助于量子引力论的进一步发展。     

Projectively flat arctangent Finsler metric

INTRODUCTION In recent years, significant progress has been made in the study of Finsler metris which have straight lines in local coordinates (Hamel, 1903). Finsler metrics with this property are called locally projectively flat metrics. An important fact about these metrics is that locally projectively flat Finsler metrics have scalar flag curvature, a natural extension of the sectional curvature in Riemannian geometry. In general, it also depends on the direction (flag pole) in the se…     

拟常曲率空间中的伪脐子流形

设Mn是拟常曲率空间Nn p中具有平行平均曲率向量的紧致伪脐子流形,论证得到了这种子流形的两个内蕴积分不等式,从而给出了Mn是全脐子流形的两个内蕴充分条件。     

A level set based segmentation approach for point-sampled surfaces

Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry.     

常平均曲率的曲面

给出一种特殊旋转曲面，即常平均曲率的曲面。