查询词典 gauss curvature

The model for calculating the stability of the resonator containing a laser rod with curvature ends was developed,which was based on the transfer matrix theory of Gauss beam. The results from the numerical simulations on some typical resonators indicate that the laser rod with curvature ends can expand the stable region of plano-plano,plano-concave and plano-convex cavity notability;despite the laser rod with curvature ends can improve the stability of above mentioned cavities,it costs the effective mode volume.

计算结果表明，对于几类典型的谐振腔如平平腔、平凹腔，球面端面激光棒可以显著的扩展强热聚焦作用下的稳定工作范围；球面端面激光棒在提高约束稳定性和热稳定性的同时，通常是以牺牲有效模式体积为代价的。

This paper reported a new method using tangential curvature to establish a mathematical model of the anterior cornea and an analysis of the regularity of the distribution of the asphericity Q. The curvature in the horizontal meridians is a prolate ellipse. The curvature in the vertical meridians is an oblate ellipse. The curvature of the horizontal meridians is important for anterior corneal asphericity.

本研究分析了运用正切曲率半径值建立人眼前表面角膜数学模型的科学性，显示角膜前表面水平子午线方向非球面性趋向于长椭圆，垂直子午线方向非球面性趋向于扁椭圆，说明人眼角膜的非球面性特性主要由水平子午线实现。

In addition, we made account for the selection of inverted bending curvature of pipe axis and the length of equal curvature region, and pointed out that we can only equalize the curvature in the equal region and carrying out straightening really is in the region of unequal curvature. This is the development and perfect of bending straightening theory and this method can spread to bar straightening machine.

此外，还对反弯曲线曲率和等曲率区长度的选取作了说明，指出在等曲率弯曲区只能使曲率均匀化，而真正实现矫正是在后部的非等曲率弯曲区，这是对矫正理论的深入和完善，并且这一研究方法也可推广到棒材矫正机。

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。

In this paper, a "rigid bar relative movement model" was established to illustrate the traces of the helices in wire ropes. The angular speed of a moving particle of the model was relatives to curvature tensor to derive the curvature components and torsion of helices in multi-layer wire ropes. According to long and thin rod theory of Love and Yen-Chen's theoretical model considered the contact force and frictional force, the force-deformation or force-strain relative of wire in curved wire ropes subjected axial force is derived from the curvature components and curvature increment.

本研究改以刚杆相对运动模型，直接描述钢索中钢绞线轨迹，并且透过角速度类比曲率张量之概念，推导圆弧型多层钢索内部之钢铰线之曲率分量与扭率；之后再依据Love的细长杆理论，辅以Yen-Chen在考虑接触力及摩擦力下所修正之理论模型，以曲率及曲率增量来探讨圆弧型钢索受静态荷重作用下，钢绞线之受力与变形或应变关系。

Researches the submanifolds in nested space,for constant curvature Riemannian submanifold in quasi-constant curvature manifold and pseudo-umbilical submanifold with parallel mean curvature vector in constant curvature Riemannian submanifold,presents three sufficient conditions for this pseudo-umbilical submanifold to be total-umibilical submanifold,generalizes the result of JI Yongqiang.

对于拟常曲率流形中的常曲率黎曼子流形以及常曲率黎曼子流形中具有平行中曲率向量的紧致伪脐子流形，给出了这种伪脐子流形是全脐子流形的3个充分条件，推广了纪永强的相关结果。

The equations of the curvature, curvature radius, main curvature and main curvature radius on hypocycloid抯 and epicycloid抯 theoretical tooth shape and practical tooth profile are deduced respectively.

根据微分几何知识，分别推导出内、外摆线理论齿形和实际齿廓的曲率、曲率半径、主曲率及主曲率半径的方程式，并绘制了内、外摆线理论齿形和实际齿廓曲线及理论齿形的曲率半径变化曲线。

The computer software is worked out to calculate numerically the geometric drive properties: normal curvature, geodesic curvature, induced normal curvature, induced geodesic curvature, lubrication angle, contact line and meshing area, etc.

本文首次建立了在双自由度运动状态下，用直线型切刀包络加工圆柱蜗杆传动的啮合原理数学模型；并编制了相应的计算机软件，对其几何传动特性：法曲。。。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。