阶数

In Chapter 3, we study the semilocal convergence for the method appeared in Chapter 2 under Lipschitz continuous condition of the second Frechet derivative, and get the corresponding error estimation by majoriz-ing function technique. And also, an application of the theorem to a non- linear equation is given.

在第三章中，研究了复合型Newton-Steffensen迭代方法在算子的二阶导数满足Lipschitz连续条件时的半局部收敛性，并利用优函数技巧得到了其在该条件下的误差估计，最后给出了这个定理的一个应用。

In this paper, one corollary has been derived, i. e., the Frechet derivative which is necessary to the resistivity inversion, is the first order of Zhang's integrated geometric factor.

针对阵列电位电极系测井正演与反演研究，我们得到另一结论：反演过程中必然用到的Frechet导数为张氏一阶积分几何因子。

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

The dissertation focuses on performance gradient estimation and SRO algorithm of DES aswell as other related topics,such as modeling of DES and discrete event simulation,performancemeasure Hessian matrix estimation,Stochastic Approximationand so on.General Semi-Markov Processis adapted to describe behaviour of DES and discrete eventsimulation.A general result is obtained and applied to analyze strong consistency of performancegradient Perturbation Analysisestimator.Conditions for effectiveness of InfinitesimalPerturbation Analysisare also discussed.New PA algorithms,such as server PA,PA usingDirac generalized function,job sequence PA etc.,are proposed to deal with discreteparameters.Furthermore,strategies of combining PA algorithms with certain iterative rules areanalyzed widely in order to optimize DES parameters and some SRO algorithms are constructed toslove DES optimization problems.

论文将DES性能分析领域中性能梯度估计和单运行仿真优化作为主要的研究对象，探讨了与性能梯度估计有关的DES和离散事件仿真过程建模、高阶导数估计以及随机逼近等理论和方法；建立了具有一般性的DES和离散事件仿真的广义半Markov过程模型；获得了分析性能梯度估计量强相合性的理论结果和无穷小摄动分析算法应用的条件；提出了诸如服务台数目的摄动分析、奇异摄动分析、串联生产线和加工车间中工件加工序的摄动分析等一系列摄动的思想和算法，对连续参数和离散参数都进行了深入的研究；对摄动分析算法同优化规则结合实现仿真优化的策略也进行了广泛的分析，构造了新型的变界截尾的随机逼近算法，并用于DES的单运行仿真优化研究；最后，给出了DES性能分析方法的实证性研究结果。

The present work proposed a simple computation of the second horizontal derivatives of gravitational potential fieldsusing a digital filter of five operators that is designed to fit the data in the least-square concept.

从目前的研究来看，二阶垂直导数的求解方法较简单，它采用的五个因子的数字滤波的最小二乘法来优化数据。

The Hankel transformation method has been used to turn the basicdisplacement equations and displacement-stress constitutive equations intoa system of first order non-homogenous ordinary differential equations inwavenumber domain,and by us of the matrix method,the transfer matrix ofthe medium layered is established.

利用Hankel变换，将轴对称静力问题的位移基本方程和位移应力本构方程转化为波数域内非齐次一阶常微分方程组，利用矩阵法，建立了介质层的传递矩阵，导出了层状弹性半空间轴对称静力问题奇异解的一般解析表达式。

Rather than discussing higher derivative gravity (where our lunch discussion took off) I would like to discuss a much simpler system.

而不是讨论高阶导数引力我要讨论一个非常简单的系统。

As the cam profile with constant-velocity-constant-acceleration ramp feature and with continuous higher derivative lift feature is widely adopted in the advanced high-speed internal combustion engines, the cam ramp profile is fitted with a reasonable function and the cam-lift profile is fitted with a polynomial function.

考虑到高速内燃机的凸轮大多采用具有等加速-等速特征的缓冲段和高阶导数连续特征的工作段型式，用等加速-等速函数拟合缓冲段实测升程数据，用整体式高次多项式函数拟合工作段实测升程数据。

A quasilinear equation is one in which the highest -order derivative appears linearly.

最高阶导数线性地出现的那种方程是准线性方程。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。