微分几何

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

Gauss（1777—1855）; intrinsic differential geometry ; non-Euclidean geometry ; Gaussian curvature ; Gauss-Bonnet Theorem

高斯（C.F.Gauss ； 1777—1855）；内蕴微分几何学；非欧几何；高斯曲率；高斯-博内定理

Gauss （ 1777-1855 ）; intrinsic differential geometry; non-Euclidean geometry ; Gaussian curvature ;Gauss-Bonnet Theorem

高斯（C.F.Gauss，1777—1855）内蕴微分几何学非欧几何高斯曲率高斯-博内定理

Gauss(1777—1855);intrinsic differential geometry;non-Euclidean geometry;Gaussian curvature;Gauss-Bonnet Theorem

Gauss，1777-1855；内蕴微分几何学；非欧几何；高斯曲率；高斯-博内定理

Asimple necessary and sufficient condition for global controllability will bepresented. The analysis method is based on some basic facts in planartopology such as the Jordan curve Theorem, and in the geometric theoryof ordinary differential equations including the Poincare-Bendixson Theo-rem.

分析方法主要是基于平面拓扑中的一些基本事实，比如Jordan曲线定理，以及常微分方程几何理论中的几个基本定理，如Poincare-Bendixson定理，指标定理等。

At the same time, considering the jumpiness or incline caused inaccuracy and pretermission when the capsule moving ahead, two couples of infrared ray and electron transducer were designed to detect the light signal of the corresponding parts of the capsule. After the addition operation compensation and differential coefficient, turning the little different simulation signals of the body and cap of the capsule into digital signals for detection. It is more accurate for detection and stable to the disturbance. Step electromotor was used for the capsules direction turning which solved this problem efficiently. The capsules were ranged in order according to their colors with the cap at the same direction.

同时考虑到胶囊行进过程中跳动、倾斜及随机干扰造成的误判、漏判，设计了两对红外光电传感器用以同时检测胶囊上下两个边缘部位的光信号，两个检测信号经加法运算补偿、微分运算处理，将体现胶囊的帽、体微小几何尺寸差别特征的弱模拟信号直接转变成数字量检测，提高了检测的准确率及抗干扰能力，并由步进电机控制胶囊掉头，有效地解决了胶囊体、帽的位置调整，分色调头排列，达到帽、体一致。

The principle of minimum potential energy was used to derive the governing differential equation and corresponding boundary conditions.

分析了压杆屈曲时的几何变形条件，导出了压杆的曲率、变形能和各项外力势的表达式，用最小势能原理导出压杆失稳的微分方程和边界条件。

Delay differential equations; variational structure; Minimax theory; Morse theory; multiple periodic solutions; subharmonic solutions; Z_p geometrical index

基础科学，数学，数学分析时滞微分方程；变分结构；极小极大理论； Morse理论；多重周期解；次调和解；广义Z_p几何指标

A global gravity field recovery based on energy balance approach using CHAMP kinematic orbits is presented. A method combining the Newton's numerical differential formula and the remove_restore procedure for determining kinematic velocities is developed.

介绍了利用CHAMP几何法轨道恢复地球重力场模型的基本原理和算法，提出了基于牛顿数值微分公式并辅助移去-恢复方法计算卫星速度的算法。

A geometrical method of judging whether nonlinear differential equation of oscillation has stable solution—phase plane method, is applied to analyze operation stability for the first time.

首次将研究非线性振动微分方程稳定解判据的几何研究方法——相平面法——用于脉冲燃烧运行稳定性研究。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。