查询词典 quadratic function

Koblitz curves over a finite field of characteristic 2 and characteristic 3 disassembles k using prime element of simple Euclidean domain.To further improve the efficiency,presents an assumption of disassembling k based on prime element of quadratic Euclidean domain.

特征2和特征3的这类Koblitz曲线是以一次欧式环的素元来分解k，对此设想是否可以二次欧式环的素元为基底来二次分解k从而进一步提高效率。

Some closedforms of formulae are also obtained for the evaluation of the Cauchy prin-cipal integrals over quadratic boundary elements and linear internal cells of2-D problems.

通过采用以上各种技术成功地解决了三维弹塑性有限形变问题边界元法中最关键的数值积分的精度和效率问题。

With the theory of quadratic form, this essay gives out another way to solve the extremum problems of multi-variable functions.

文章以二次型理论为依据，提出了解决多元函数极值问题的另一种方法。

According to the analysis results, the dissertation gives the deformation and plastic zone curves family of the rocks of four different superincumbent depths and makes fitting analysis on the curves to obtain corresponding displacement formulation in quadratic polynomial form.

研究洞群稳定时以分析主厂房的下游边墙关键点位移或围岩塑性区为主，并通过回归分析的数学方法推求各种条件下的洞壁位移预测公式。

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。

The last chapter talks about the H"yashenko"s two-side cycle theorem, that is, every two-side cycle of an analytic vector field in the real plane is the finite polycycle. The quadratic finiteness theorem is a direct corollary of this theorem.

最后一章介绍了Il'yashenko两边形定理，即实平面上解析向量场的任一两边形均为有限多边环，这个定理的直接推论便是二次系统的有限性定理。

The first part discusses about the effects of the five factors:temperature,relative air moisture,rate of frass sifting,density of larvae,fodder water percentage to growth speed and survival rate of older mealworm (Tenebrio molitor L.) larvae through rotational composite design of quadratic regression. Two models were established to describe the effects of the five factors. The models showed that percentage of fodder water is the major factor that has effect on the growing speed of T. molitor larvae,and fodder water is the major factor on death rate. The models also show that temperature on growth speed,temperature and fodder have important effects on death rate,and the significant test showed they have significant difference on 1% or 5% level. From the two models,by frequency analysis,we can get the optimizing rearing condition,in which the mealworm larvae overweight 10% per day,temperature is 25-26 ,frass sifting rate is once 2-4 days,density of larvae is 0.61-0.79 g/cm2,fodder water is 33.27%-39.71%. And the rearing condition,in which total death rate of T.

第一部分：采用五因素二次正交旋转组合设计，以黄粉虫幼虫饲养过程中饲养温度(X_1)相对湿度(X_2)、虫粪筛除频率(X_3)、饲养密度(X_4)以及饲料含水量(X_5)五因素为参试因素，考查它们对黄粉虫高龄幼虫的生长及存活的影响，建立了以黄粉虫幼虫增重率及死亡率为目标函数的回归模型，并进行了简化： Y_增=127.5079+18.6559x_5+2.7894x_3x_4-2.3854x_3x_5-3.0594x_1~2+1.8241x_3~2-3.8559x_5~2 Y_死=1.7459+0.4108x_1+0.0975x_2+0.9025x_4+0.3442x_5+0.0834x_1~2+0.3060x_4~2-0.2623x_5~2 分析结果表明：影响黄粉虫幼虫生长后期增重及死亡的主要因素分别为饲料含水量和饲养密度；饲料含水量和温度对黄粉虫增重有着重要的影响，饲养密度、温度、饲料含水量对黄粉虫的死亡有着重要的影响，其影响均达1％或5％显著水平；黄粉虫幼虫后期日增重率大于10％的饲养条件为：温度26～27℃、筛粪频率2～4天／次、饲养密度0.61～0.79g／cm~2、饲料含水量33.27～39.71％。

We know that the solutions of quadratic, cubic and quartic can be expressed by radicals. As to the solution of the quintic which has became an issue for past two or three hundred years, it was not solved until 1832 a great young Mathematician of French named Galois who recommended group theory that proved a polynomial of degree 5 and over 5 can't be solvable by radicals.

中文摘要我们知道二次、三次及四次的方程式都可以用根式表示，至於五次方程式的解迟迟无法解决，这个问题持续了两三百年，直到1832年，一位法国青年Galois在其决斗前夕，在他的遗书中，这位伟大的青年数学家引进了群的理论，证明了：五次及五次以上的方程式，不可能有公式解。

By the age of 19 Gau had discovered for himself and proved a remarkable theorem in number theory known as the law of quadratic reciprocity.

将number theory 误为"数理"，系不了解专业所致，其实它在数学上是指"数论"，与"数理"是两个不同的概念。

First, by utilizing classical Gauss motion equations, we derived the three separate control laws, which could maximize the time rate of change of a desired orbital element. Then, the separate control laws were blended based on the deficit between current and target value of orbital state. Finally, to obtain the optimal guidance law effectively and reliably, a hybrid method combining genetic algorithm with sequential quadratic programming was used to optimize the weight values.

首先利用传统Gauss型运动方程，推导出三个轨道根数增大最快的独立控制律；然后根据当前根数与目标值的偏差量对独立控制律进行加权组合；最后为高效可靠地获得最优制导律，采用一种遗传算法和逐次二次规划相结合的混合方法对权重进行了优化。

In the chapter 2, the theoretic knowledge about the photosensitive resin and the grinding tools was firstly introduced.

第二章阐述了光固化树脂结合剂磨具的相关理论研究。

Do not use the program's indenting or margin-setting features; these will be added during typesetting.

不要使用缩排，页面边缘设置之类的选项，偶看不大懂。