曲率

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

PCI can be an alternative method on routine ocular biometry of children instead of A-scan and auto-keratometry.

PCI测量的K值与曲率计测量结果无差异。PCI可以替代A超和曲率计，有望成为儿童眼球生物测量的常规方法。

Firstly, the method fits each vertex and its local neighborhood of the clothing and human models by constructing the biquadratic Bezier surface. It can estimate the Gaussian curvature and the mean curvature of each vertex. Then, the feature points of two mesh models are extracted according to curvatures.

该方法基于双二次Bezier曲面局部拟合服装模型和人体模型的网格顶点及其邻近点，估算出人体和服装模型网格顶点的高斯曲率和平均曲率，然后提取出人体和服装模型两点集的特征匹配点。

According to the boundary curve features of the object, all kinds of boundaries sign patterns of the object are setup and used to train the second RBFNN, so as to tangent points, inflection points with low curvature and boundary types.

根据工件边缘曲线的特征，建立了各种边缘的曲率符号模型，用该模型训练第二个RBFNN，从而识别具有低曲率的切点和拐点及边缘曲线的类型。

In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.

在本文中，我们主要研究了Ricci曲率有下界完备非紧的Riemann流形的拓扑问题，在比较几何的基础上研究了有特定曲率条件的Riemann流形的拓扑，得到了有关其拓扑结构的一些结果。

Curve C at the spot P(x0, y0) curvature is the maximal circle of the curve C tangency at the spot P(x0, y0). Contrail curve G of the center D of curvature circle entitles evolute of curve C.

曲线C在点Px0，y0）曲率圆是与该曲线C相切于点P(x0，y0的最大圆，曲率圆的圆心D的轨迹曲线G称为曲线C的渐屈线。

The paper deals with curvature line and curvature characteristic of developable surface based on differential invariant of developable surface and it details curvature line and curvature characteristic of cone and tangent surface .

本文通过可展曲面的微分不变量，导出可展面的曲率线与曲率特征，并以锥面和切线曲面为例阐明这些特性的几何意义。

First, a special normal transversal at the initial point is constructed and a second-order Taylor's algorithm is used to trace the projections along the aforementioned normal transversal. A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point. Finally gradient based method for correcting iteration errors is put forward.

首先构造初始点处的一条特殊的法截线，并给出沿着该法截线追踪投影点的二阶泰勒迭代方法；然后将给定点向初始点处的法截线的曲率圆作投影，提出基于曲率的步长控制策略，在此基础上给出了基于梯度的迭代误差矫正方法。

Thus, evaluation of the minimum zone circle could be solved effectively.Three methods of assessment of roundness error were proposed in this dissertation. Based on the criteria of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and convex hull, a unified approach was proposed to evaluate roundness error of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle. Evaluation of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was fulfilled with rotation based the contact pattern. The minimum circumscribed circle and maximum inscribed circle were evaluated with curvature and the curvature circle.

本文提出了三种圆度误差评定的方法：根据最小区域圆、最小外接圆、最大内接圆在极坐标系下的判别准则，利用计算几何中的凸壳理论，提出了一种统一的评定方法，实现了对最小区域圆、最小外接圆、最大内接圆的误差评定；基于接触斑点的检验原理，利用旋转法，实现了最小区域圆、最小外接圆和最大内接圆的误差评定；利用曲率和曲率圆，实现了对最小外接圆和最大内接圆的误差评定。

The said Martinez stretcher comprises concave spherical reflecting lens, plane reflecting lens and grating. The said compressor comprises plane reflecting lens, inner right angle reflecting lens and grating, which is characterized by the following: the grating fringe density of the stretcher is larger than that of the compressor.

所述的马丁内兹展宽器由凹球面反射镜、平面反射镜和光栅组成；所述的压缩器由平面反射镜、内直角形反射镜和光栅组成，其特征在于，展宽器的光栅条纹密度大于压缩器的光栅条纹密度；展宽器中的凹球面反射镜曲率半径位0.9～1.2米，光栅距凹球面反射镜的位置为凹球面反射镜曲率半径的1/3～1/2。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。