阶数

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程，直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散，得到分数阶松驰方程一个数值方法，并给出了相容性，收敛性和稳定性的证明。

This article discusses the use of the theorem of the residues to calculate Cauchy's Principal values of the improper integral, where auxiliary function has poles of higher order on the real axis and proposes a new theorem of culcuation.

在复函中应用留数定理计算广义积分的科希主值时，许多著作仅讨论了辅助函数在实轴上有一阶极点的情形[1-3]，有的则认为：辅助函数"在实轴上的奇点不能是二阶或二阶以上的极点["4，5]。

By transforming high - grade gentle lack one type linear differential equation into the linear differential equation of successive integral, the theory and method for the general solutions of this kind of equation are determined.

方程'+=f是高阶线性微分方程，(约定尹0)=刃，是两项和的形式，其特征是含有相同的底，导数的次数相差一阶，因此不妨定义该方程为：高阶和式次数差一型线性微分方程。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

In this paper,based on an improved orthogonal expansion in an clement , using the new idea of Ref.[3] ,a new error expression of n-degree Hermite finite element approximation to one-dimensional 4-degrec 2-point bounded problem and 2-degree ordinary differential problem, and then optimal order superconvergence for their first derivatives is obtained.

本文针对在改进的单元正交性估计的基础上，利用文[3]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u_h∈C~1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。

The model of programmed crystallization of SPM was proposed based on the moment transformation of the population considering the agglomeration. The optimal temperature-time curves in a batch crystallizer which maximized the terminal mean size and mean weight size can be determined from the application of the Pontryagin Maximum Principle. The calculated crystallization results heating under optimal temperature were compared with ones under linear or natural heating temperature.

根据第四章所得到的螺旋霉素晶体二次成核和晶体生长和布朗扩散引起的聚集动力学，利用第六章所描述的晶体尺寸分布的各阶矩对时间的一阶导数所构成的自封闭的一阶常微分方程组，采用庞得里亚金极大值原理，以温度为控制变量，在满足某些约束条件下，以最大平均尺寸和最大晶体重量平均尺寸为性能指标，计算出了螺旋霉素间歇结晶的最优温度—时间曲线，并同线性加热和自然方式进行了比较。

First, based on the analysis of the grid Reynold number, the necessity for adopting high order scheme is emphasized when there is the complex flows with strong separation and high parameters gradient regions. Then, according to the entropy increased condition, the third order ENN scheme is constructed. Meanwhile, a fast, effective, and simple implicit numerical method called hybrid flux splitting method is developed. After that, the one dimensional model problem with many extrema and Burgers equation are simulated. Through the comparisons with exact solutions, the accuracy and effectiveness of the ENN scheme are confirmed.

首先通过对网格雷诺数的分析，论证了在求解含分离及较大参数梯度的流动时，采用高阶格式的必要性，然后从熵增原理出发，提出了建立三阶ENN格式的准则，同时发展并建立了一种快速、有效的简单隐式算法"混合通量分裂法"，通过对一维模型问题及Burgers方程的数值试验，检验了三阶格式的计算精度。

The necessary and sufficient conditions for convergent of characteristic domain and the conditions for tangent plane continuity are obtained. The conditions for having limited value of the second order of differential at the convergent point are shown as well.

给出了任一特征域收敛的充要条件；给出了曲面在任一极限收敛点上达到一阶几何连续的条件；分析了极限收敛点处的二阶连续，给出了二阶导数有界的条件。

In model experiments, we find that the deviation of the first derivative calculated by Fourier transform is very large to comparing with the theoretical derivative, but the fitting effect of the derivative of anomalies calculated by cosine transform is very good. The calculation accuracy of data are all very high except that errors of several data on the boundary are large because of the residual Gibbus effect induced by finite truncation of gravity anomalies. Errors are -009%～5%.

模型实验中发现，用Fourier变换计算的一阶导数与理论导数偏差很大，而余弦变换计算的导数与理论异常导数拟合效果非常好，除边界几个数据因重力异常的有限截断产生的吉布斯效应残留使误差较大外，数据的计算精度均很高，误差为-009%～5%。

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

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。