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This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

In order to overcome the deficiency that initial points should be strictly feasible in interior point methods, a primal-dual infeasible-interior-point algorithm for the second-order cone programming is presented.

为了克服内点算法中初始点是严格可行的这一缺点，给出二次锥规划的一种原-对偶不可行内点算法。

E.This order must be fil led within five weeks, otherwise we will have to cancel the order.

此订单须在5周内交货，否则我方将不得不撤销此单。

Also you can order lists by file name, size, modification date orother criteria in the ascending or descending order.

你还可以按照文件名，文件尺寸，修改日期或者其它标准，以升序或者降序排列定制列表。

This concept is similar in practice to the filler order number found in Chapter 4, Order Entry.

这个概念与第 4 章中填充符命令号码的实际操作相似。

In fact, this analysis is also fit to analyze the stability of two-order charge-pump PLL loop by simply setting the value of shunt capacitor of two-order filter to zero.

实际上本分析方法也可以用来分析二阶电荷泵锁相环的稳定性，这只需要假定二阶滤波器中的旁路电容为零即可。

In order to solve the problem,starting from the analysis of the simplest plane wave numerical theory,we derived the formula of relative phase velocity and group velocity under the condition of arbitrary high-order finite-difference approximation,and gave the computational method for acquiring the optimum Courant number,and then analyzed the anisotropic effects due to finite difference approximation.

针对此，从最简单的平面波数值理论分析出发，推导了任意高阶有限差分近似条件下相对相速度和相对群速度的计算公式，给出了求解最佳Courant数的计算方法，分析了差分近似造成的各向异性效应。

With the help of the fundamental theory to singular measure differential system, Green's function matrix expression of solution and well-posed boundary condition are given, together with discussing the properties of the Green's function matrix under the influence of impulsive effect In section 5, based on Lyapunov function method, we investigate that the existence of the first boundary value problem to second-order singular system by macthing the solutions to the second boundary value problem; and the existence and uniqueness of three-point boundary value problem to third order singular system by macthing the solutions to two-piont boundary value problem.

第五部分借助Lyapunov函数法，通过将第二类边值问题的解对结成第一类边值问题的解，得到了二阶广义系统的第一类边值问题解的存在性；通过将两点边值问题的解对结成三点边值问题的解，得到了三阶广义系统的三点边值问题解的存在性和唯一性。

The first order derivative transfer was carried out in the spectrum data.The first order derivative feature is analyzed.It is shown that:The vegetables can be divided into two groups according to their reflectivity during 400nm to 679nm.

研究表明，在波长400~679 nm的范围上，可以根据其反射值的高低，将蔬菜分为两组，一组为大白菜、豌豆、牛皮菜和青菜，另一组为葱、大蒜和香菜。

This paper points out that as the peak of the first order wind spectrum situated at a region of very low frequency, the contribution of the sum_frequency part to the second order wind spectrum is no longer negligible.

本文指出，由于风速谱与波浪谱不同，它的能量峰值位于极低频率处，因此二阶风速谱中和频项的贡献不能忽略，为此本文首先导出了保留和频项情况下的二阶风速谱表达式，并将和频项与差频项在数值上作了比较。

Green function defined inphase space differs from one in coordinate space by its struc-ture which exhibits nonlocatity in coordinates and oscillatorybehavior with respect to momenta.

在相空间中定义的Green函数不同于通常坐标空间的Green函数，在结构上显示出对坐标的高度非局域性，而对动量则显示出振荡行为。

The upper front part of a saddle;a saddlebow.

前鞍桥马鞍前面的上部分；前鞍桥