查询词典 hyperbolic cotangent

He believes the form he is holding is a hyperbolic paraboloid, a shape well known to mathematicians - or something very close to that - but he wants to be able to prove this conjecture.

他相信他手中的摺纸形式是一种数学家所熟知的双曲线抛物面，或是某种非常接近的形式，於是他想要验证此推测。

The authors show that the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

作者证实：单叶双曲面和双曲抛物面是直线曲面。

This can be a least-squares plane or a plane passing through the center of gravity of the corners and is parallel to the mid-rulings of the hyperbolic paraboloid determined by the corners.

这可以是一个最小平方平面或者是一个通过拐角的重心并且平行于由拐点决定的双曲线抛物面的半轴的平面。

On the basis of these theories, The specific project—the hyperbolic paraboloid shell structure named Shijingshan Gymnasium is introduced, and the finite element model is established, including calculation of load, simplification of node nature and simplification of support.

在这些理论的基础上，引入工程实例——石景山体育馆双曲抛物面网壳结构，建立有限元模型，包括使用荷载的计算、节点性质的简化、支承的简化等。

We discover that under a general configuration the twist system of this mechanism belongs to the seventh special three-system, and all the twist axes are distributed on a hyperbolic paraboloid that is special and unusual and rarely studied. Under original configuration it belongs to the fourth special three-system.

我们发现：该机器人在一般位形下，它的所有运动螺旋轴线在空间分布的二次曲面是比较特殊的，罕见的，是过去理论上研究很少的双曲抛物面，属于第七种特殊三系，在起始位置时属于第四种的特殊三系。

The main research contents are stated asfollow: 1. Simplified analysis method of space grids structuresDouble-layer space grids have been assumed as sandwich plate, and are analyzed bythe nontraditional theory of plate with consideration of shear deformation and threegeneralized displacements. Using the theory of energy variation, simplified methodsfor bending, stability and vibration analysis of double-layer space grids have been putforward based upon the idea of split rigidity. The formulas for calculating internalforces, displacements, critical load and natural frequency have been given out. Set thestable cables and bearing cables in hyperbolic paraboloid cable nets are all replaced bytruss-cable to form truss-cable nets structures. Natural vibration analysis method fortruss-cable nets structures has been put forward using the energy variation method andRayleigh method.

主要内容包括： 1、空间网格结构静动力简化分析方法把网架结构简化为夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析，基于分解刚度思想利用能量变分原理提出了网架结构弯曲、稳定与振动分析的简化计算方法，给出了位移、内力、屈曲临界荷载和固有频率的计算公式；将双曲抛物面索网中的稳定索与承重索均用劲性索代替形成劲性索网结构，基于能量变分法和Rayleigh法给出了劲性索网结构固有振动分析的简化计算公式。

Using Beltrami-Klein coordinate system, convexity and motion of ellipse in hyperbolic plane is considered.

在双曲平面中，利用Beltrami-Klein坐标系对椭圆的凸性和运动做出细致考察。

Indeed, the reader who is slightly familiar with tessellations of the sphere, the Eaclidean plane and the hyperbolic plane, can easily prove the following result

事实上，稍微熟悉球面、欧几里得平面和双曲平面的分格的读者，都能容易地证明出下面的结果。

The third chapter discusses and proves Il"yashenko"s Theorem, that is, if every vertex on the polycycle of an analytic vector field in the real plane is hyperbolic, then limit cycles cannot accumulate on this polycycle.

第三章详细讨论和证明了Il'yashenko定理，即平面解析向量场的多边环上每一顶均为双曲奇点，则此多边环附近不能结集无限多个极限环。

Given a hyperbolic plane H2(-1)=,whose sectional curvature k is function K is the Gaussian curvature of the conformal metric g = e2ug ,then K satisfies the conformal Gauss curvature equation .

设H~2(-1)=是具常截面曲率k==1的双曲平面，其中B={∈R~2：x~2+y~2＜1}是单位圆盘，g=4(dx~2+dy~2)/(1-x~2-y~2)~2是所谓的Poincaré度量。考虑H~2(-1)上的共形形变度量？

He's a pretty westernised kind of guy.

他是一个非常西化的人。

National spirit is the moral kingpin for a nation to realize common ideal and goal.

一、中华民族精神的基本内涵党的十六大报告指出：在五千多年的发展中，中华民族形成了以爱国主义为核心的团结统一、爱好和平、勤劳勇敢、自强不息的伟大民族精神。