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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？

Based on the priori knowledge of a point scattering - hyperbolic feature of subsurface objects in GPR B-Scan images, a method of ROI extraction with Neural Network is presented.

在分析了均匀介质中的目标回波特征一双曲线形态的产生机理和基本特征的基础上，提出了一种利用神经网络进行ROI提取的方案，根据GPR数据解译的特点，本文设计了相应的B-Scan图像预处理方法和神经网络结构、训练及测试方法，使用塑料管及其他目标的B-Scan实测数据对神经网络进行训练与测试。

Finally, we get local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems by the properties of bounded solutions to nonlinear nonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

Finally,we get local stable manifolds andlocal unstable manifolds of near hyperbolic equilibrium point of nonlinearautonomous dynamical systems by the properties of bounded solutions to nonlinearnonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

In this paper, we consider neutral functional differential equations and study the global existence of their solutions, stable subspaces and unstable subspaces of linear autonomous dynamical systems, local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems, periodic solutions and oscillation of the neutral equations.

本文主要研究中立型泛函微分方程解的整体存在性，自治线性动力系统的稳定子空间与不稳定子空间、自治非线性动力系统在双曲平衡点的局部稳定流与局部不稳定流，周期解与解的振动性。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。