椭圆系统

In a kind of quasi dissipative systems the disappearance of some elliptic periodic orbits and the elliptic islands around them via a collision with the discontinuous border of the system function can be observed.

在一种类耗散系统中观察到了椭圆周期轨道及其周围的椭圆岛与映象不连续边界碰撞而消失的现象。

In using the elliptic curve cryptosystem, it is important to select a secure elliptic curve.

在使用椭圆曲线密码系统时，挑选一个安全性高的椭圆曲线是很重要的。

The solution of the equation and the period of the particle motion for a non-pertubated system are expressed exactly by means of Jacobian elliptic function and the 1-st kind elliptic integral.Melnikov function of the rotated periodic orbit is constructed,and also bifurcation of the system is analyzed by the method.

利用Jacobian椭圆函数和椭圆积分给出了系统的解和粒子运动周期，用Melnikov方法构造了旋转型周期轨道的Melnikov函数，并用这个方法分析了系统的局部分叉性质。

Phase plane properties of an electron in Wiggler field are analysed by using Jacobian elliptic function and elliptic integral based on the pendulum equation for FEL.

从自由电子激光器的摆方程出发，利用Jacobian 椭圆函数和椭圆积分分析了系统的相平面特征，并利用加速器概念和束流动力学方法，讨论了系统的稳定性、增益和临界特征等问题。

The speed of point addition on elliptic curve is critical in elliptic curve application cryptosystem design based on FPGA device.

提高椭圆曲线上点加运算的速度在整个基于FPGA设计的椭圆曲线密码应用系统实现中极为关键。

The mathematics principles of elliptic curve cryptosystem are systematically explained, including the addition rule for elliptic curve point defined over finite field.

系统研究了椭圆曲线密码系统的数学原理，研究分析了椭圆曲线密码体制的点加、倍点和点乘运算。

For a monotone twist map the well-known Birkhoff fixed point theoremsays that the circles with rational rotation number will break up whence a finitenumber of pairs of periodic points arise,half of which are elliptic and the othershyperbolic.Moreover,around each elliptic periodic point a few of new invariantcurves will appear and make a picture of phase space with a self-similar structure.Again one may ask is there a similar picture for higher dimensional Hamiltoniansystems?

对于单调扭转映射，著名的Birkhoff不动点定理指出，在通有情况下旋转数为有理数的不变曲线一般会破裂，在原来的不变曲线附近会产生有限多对周期点，其中一半是双曲的，一半是椭圆的，而在椭圆型周期点的周围又会产生一圈圈的不变曲线，使得椭圆周期点附近的动力学行为和整个相空间的动力学行为十分相象，换句话说，整个相空间具有无限嵌套的自相似结构，自然又产生了一个问题：对于自由度数目大于2的高维哈密顿系统，其相空间是否有类似的图象？

This article mainly elaborated numerical control lathe,milling machine utilizing the macro-program processing ellipse frustum of a cone,the surface craft route and essential method.

主要阐述了数控车床、铣床运用宏程序加工椭圆台、面的工艺路线和基本方法，结合实例分别分析了数控车床与数控铣床在椭圆加工过程中程序编制思路，并给出了FANUC系统常用车、铣椭圆粗、精加工宏程序。

To seek new infinite sequence exact solutions to nonlinear evolution equationsNEE(s, the formula of nonlinear superposition of the solutions of the second kind of elliptic equation are given, infinite sequence exact solutions to combined KdV with varible coefficients and forcible term is constructed with the aid of symbolic computation system Mathematica, which include Jacobi-like elliptic function solutions, infinite sequence soliton-like solutions and infinite sequence triangular function solutions.

为了获得变系数非线性发展方程的无穷序列精确解，给出第二种椭圆方程解的非线性叠加公式，借助符号计算系统Mathematica构造了带强迫项变系数组合KdV方程的无穷序列精确解。这里包括无穷序列类Jacobi椭圆函数解、无穷序列类孤子解和无穷序列三角函数解。

Then the system parameters were gain from solving non-linear equation. First, the figure which the circle projecting on the CCD plane by the camera led is proved as an ellipse, and find out the reference point coordinate by calculate the canters of ellipses. Then the system parameters were gained from calculating the formulas in two pictures.

首先证明了参考圆在合适条件下经过相机镜头所成的像是椭圆，通过椭圆的中心求出参考圆的中心，就得到了各个参考点的位置；然后通过各个参考点分别在两个相机坐标系中的位置来确定相机之间位置关系参数，就完成了系统的标定。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。