函数的最小

Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the calculus of variations .

众所周知，通过发现切线方法，函数的最大与最小值理论取得了最大进展，这归功于莱布尼茨。他认为上帝在创世中就像一个解决最小值问题--或者用我们当代的术语说，变分法问题--的数学家。

We make the following assumption for When 2 is positive definite matrix, different estimators about matrix of regression coefficients and inefficiency of Least squares estimate have been discussed in many documents. Considered 2 is nonnegative definite matrix, this thesis derives Best linear unbiased Estimate of parameter matrix B and estimable parameter function KBL under the meaning of matrix nonnegative definite and the property of maximum probability of BLUE is investigated.

当∑＞0时，众多文献讨论了回归系数阵的各种估计及LSE的有效性，本文考虑了当∑≥0的情形，给出了回归系数阵B及其可估参数函数KBL的在矩阵非负定意义下的最优估计，研究了它的一个最大概率性质，并且讨论了最小二乘估计成为最佳线性无偏估计的充分必要条件，在此基础上给出了均值矩阵的最小二乘估计与BLUE的偏差估计，定义了LSE相对于BLUE的一个相对效率，并给出了它的界。

Some relations between generalized KT-properly efficient solution and generalized H-local-properly efficient solution are obtained under appropriate conditions.

在实用中，由于在给定的约束条件下求得的目标函数的最优值，有时会不符合人们的要求，因此有必要考虑当目标函数的最优值作适当改进时，如何使约束条件进行极小扰动的问题。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

The stopband error of prototype filter is used to be the objective function for optimization. Instead of the method of least square approximation, this paper introduce the method of best uniformity approximation.

选择低通原型滤波器最大阻带衰减为优化的目标函数，通常的优化目标函数选用最小平方逼近的方法，本文提出了使用最佳一致逼近的方法。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

The mathematical model can work out the minimum zone solution of the cylindricity error with arbitrary position in space, and there are no special requirements in choosing measurement points.

所建立的目标函数基于圆柱度误差最小区域定义，可以评定空间任意位置圆柱度误差的最小区域解，对测点无特殊要求。

Several models of cylindricity error evaluation,such as MZC,LSC,MCC and MIC,were given,a constriction factor model of the Particle Swarm Optimization was introduced.

建立了圆柱度误差评价的最小区域法、最小二乘法、最小外接圆柱法和最大内接圆柱法的数学模型，将一种含收敛因子的粒子群优化算法应用于圆柱度误差的目标函数的优化问题。

The monotony and extremum theory of function are applied to prove the geometrical characteristic of error hand for 2D linear segment uncertainty ε(subscript σ) model in theory. The result shows that the error hand has the geometrical shape of "larger ends and smaller middle" or "one end larger and the other smaller". The minimum width and its exact position of the error hand are calculated too. It is proved that the minimum width position of the error hand is near the end with the smaller mean square error.

运用函数单调性和极值理论，从理论上证明ε模型的误差带的几何特征；得到线元误差带不仅具有&两端大、中同小&，而且也可能具有&一端大、一端小&的几何形状；给出了误差带的最小带宽及其位置；论证了误差带的最小误差带宽的位置靠近中误差较小的一端。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。