查询词典 quadratic

Then using Positive definite quadratic theory to prove a sufficient condition of Multivariate function's extreme value problem and show some examples about it.

而后利用正定二次型理论，证明了多元函数条件极值的一个充分条件，并给出了其应用的例子。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

Bring forward a kind of learning algorithm fitting on the base of spline function, because the spline function has good flexibility and quadratic smoothing property, the search problem of network weight functions training can be converted into the resoluting extreme value problem of the plurality function through using spline function to represent network input and link weight functions, thus the PNN can be trained with the help of the existing neural network learning algorithms;④build a kind of learning algorithm base on the alternate of Walsh function, the complexity of network computing can be decreased through using the complete orthogonality of Walsh function corollary.

应用结果表明该算法收敛速度快，稳定性好；③提出了一种基于样条函数拟和的学习算法，由于样条函数具有很好的柔韧性和二次光滑性，将网络输入函数和连接权函数用样条函数的形式表示，可把网络权函数训练的函数寻优问题转换为多元函数求极值的问题，从而可借助于现有的神经网络学习算法训练过程神经元网络；④建立了一种基于Walsh函数变换的学习算法，利用Walsh函数系的完备正交性，可大大降低网络计算的复杂度。

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。

In view of trust region algorithm has good global convergence for solving non-linear quadratic programming problem,the effective elastic module s damage factor and the damage distribution function is introduced by FEM updating .

鉴于信赖域算法在求解非线性二次规划问题中具有良好的全局收敛特性，同时结合有限元模型修正技术，引入有效弹性模量损伤因子和损伤分布函数的概念，在Matlab编程环境下调用ANSYS有限元程序中的APDL语言进行桥梁空间结构的有限元建模，利用信赖域算法调整局部单元的参数，通过连续损伤分布插值多项式拟合连续区段各单元的损伤分布曲线，进而实现了对连续梁桥的动力损伤识别。

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。

Firstly, the author establish the functions of stability on the basis of the spline function method ,according to the theory of geometrical nonlinear and the theory of stability, educe the stability equation of structure based on variational principle, then carry through the flexuosity analysis of CFST arch.The big distortion geometrical nonlinear was considered by the stability equation,the author simplified the problem of geometrical nonlinear through ignored quadratic term and reserve the simple term, at last boiled down to solve the linear stability equation of eigenvalue .

利用样条函数方法、根据几何非线性变形理论和结构稳定性理论，先建立起结构稳定的泛函，再由变分原理导出结构的稳定方程，进行钢管混凝土拱屈曲分析；本文所建立的稳定方程考虑了几何非线性的大变形效应，通过忽略几何非线性的二次项，保留一次项，将几何非线性问题简化，最后归结为求解线性稳定问题的特征值稳定方程，建立了结构非线性静力稳定性问题的新算法及失稳类型判别准则。

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％。

Looking to bounce back from defeat against Cesena last weekend, the Calabrian boss will be sticking to his tried and tested 4-3-3, with Lopez and Sedivic joined up front in Giampaolo's absence by either Nanni or Plasmati.

鉴于上周末对切塞纳的比赛中反败为胜，这支南方球队将会更坚持其一贯而有效的4-3-3阵型，洛佩斯和塞德维奇将取代受伤缺席的詹保罗，和纳尼或者帕斯马蒂中的一个搭档锋线。

Meanwhile, their exposure to the more freewheeling ways of the West broadened dramatically.

另外，西方较自由的生活方式对年轻人的影响增大。