阶数

In TFDE, the first-order timederivative is replaced by a fractional derivative, making the problem global in time.

对于前者，时间上的一阶导数被分数阶导数所代替，使得问题在时间上是全局的。

Fractional integral is an essential branch of fractal theory. In this paper, the authors adopted fractional integral in the evaluation of time series dimension, which has a higher accuracy than other methods such as box dimension, gauge method and so on.

分数阶积分是分形理论的一个重要分支，应用分数阶积分进行时间序列维数估计，其精度比box维数、量规法等方法高。

By means of the Hermite interpolation formula with second derivative,a type of integrating formulas with second derivative is derived.

利用带二阶导数的Hermite插值公式，导出一类具有二阶导数的求积公式。

The Taylor formula holds the very important status in the differential calculus, especially in solves in some concrete problems to have the extremely important application, for instance the proof inequality, the judgment improper integral collects the divergence, asks the function the limit, asks the function the higher order derivative, determines certain complex progressions to collect the divergence, solves certain differential equation, as well as approximate calculation in and so on application, therefore this article will do the thorough research to these seven aspects.

摘 要：泰勒公式在微分学中占有非常重要地地位，尤其在处理1些具体的茄题中有10分重要的应用，比如证明不等式，判断广义积分的敛散性，求函数的极限，求函数的高阶导数，判定某些复杂级数的敛散性，求解某些微分方程，以及近似计算等中的应用，因此本文将对这七个方面做深入的研究。关键词：泰勒公式；不等式；广义积分；极限；高阶导数；复杂级数；微分方程

In this paper, we provide a new method using the DQ method based on the interpolation of the highest derivative for the differential equations. The original function is then obtained by integration.

这种方法的出发点是通过对未知函数最高阶导数进行插值，然后积分得到对低阶导数和原未知函数的逼近。

Put forward a new method by transforming the second-order hyperbolic equationinto a first-order system of equations and derived the H_0~1 -norm and the L~2 -norm error estimates.

12提出一种新方法，通过转化双曲型方程中二阶时间导数项得到关于一阶时间导数的耦合方程组，然后进行离散，得到一个两层交替方向有限元格式，并得到H_0~1-模和L~2-模误差估计。

This paper has utilized the mathematic inductive method and Leibniz theorem to study the unity advanced derivation of complex-special Function and original function, acquired their united expression.

用数学归纳法和莱布尼兹公式对一类复杂函数的高阶导数与原函数的统一性进行了研究，获得了该类函数的高阶导数及原函数的统一表述公式。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

The results showed that there were three minimum values in the second derivative spectrums of normal person, in contrast there were four minimum values in most diabetic second derivative spectrums, the diabetic urine had one minimum value more than normal urine during the range from 550 nm to 570 nm.

发现健康人的二阶导数光谱都有三个极小值，与之形成对比的是绝大多数糖尿病患者的二阶导数光谱却有四个极小值，糖尿病患者的尿样在550 nm～570 nm区间范围内比健康人多出一个极小值。

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。