阶数

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

Let be a function whose st derivative exists for each in an open interval containing.

如果函数在含有的某个开区间内具有直到阶导数，则对任意，有

And the expression of its subdifferential is developed in the case that the effective domain of the optimal value function is a non-empty convex set.

最后利用方向导数和次微分导出了广义半无限极大极小规划的一个一阶最优性条件及其等价形式。

Based on the analysis and summary of basic ideas and methods,this thesis proposes two new estimation of error of higher order approximation.

方法二是在等距分布的条件下，基于三次样条插值函数的三弯距算法，通过利用节点处弯距的加权和近似计算区间中点处的二阶导数。

Theorem(Stokes's Theorem) Let be a piecewise smooth oriented curve in three-space, be a piecewise smooth oriented surface with boundary curve .The surface and the curve are related by a right-hand relationship, i.e., if the fingers of the right hand are cupped in the direction of ,then the thumbpoints in the direction of orientation of .,, have continuous first partial derivatives on and ,then

定理 设为分段光滑的空间有向闭曲线，是以为边界的分片光滑的有向曲面，的正向与的侧符合右手规则(即如果右手大拇指表示曲面的方向，则弯曲四指表示曲线的方向)，函数，，在曲面上具有一阶连续偏导数，则有下述公式成立

For polydisperse systems at large Péclet number, we establish the systems of differential equations describing the leading term and the second term of the pairdistribution function via regular perturbation method.

针对高Péclet数情形，通过正则扰动法我们建立了决定对分布函数的微扰展开的主导项和一阶项的联立方程组，并用由此算出的对分布函数的数值解计算了系统的沉降系数。

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn't use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy.

构造求解两点边值问题的一种Hermite型五次元高精度有限体积法，其中试探函数空间取Hermite型五次有限元空间，与Hermite型三次元相同，未引入更高阶导数作为插值条件，检验函数空间取分段线性函数空间，这样构造的格式求解精度更高。

Chapter 4 gives a micellar electrokinetic chromatography method for the quantitative analysis of seven podophyllum lignans in podophyllum emodi wall.

第四章：建立了胶束电动毛细管色谱法分离测定抗癌药物桃儿七中七种主要有效成分的新方法；利用二阶导数电泳图定量测定低含量和在实际样品没有达到基线分离的组份。

Results By using containing ethanol-2mol·L -1 lithium chloride-water(2∶1∶5)solution,there is a very good secondary derivative differential pulse polarogram peak at -1.703 V.

结果 ：秦皮甲素在乙醇- 2mol·L- 1 氯化锂-水(2∶1∶5 )的底液中，于- 1.70 3V处出现一良好的二阶导数差示脉冲极谱法峰，其峰幅值与秦皮甲素在 0 。2～ 1.6mmol·L- 1 范围内呈良好的线性关系(r =0 。9998)，检测限为 5 0nmol·L- 1 。

Objective: To establish a simple rapid method for determining Kjeldahl nitrogen content by 1st order differential coefficient single sweep polarography.

建立用一阶导数单扫描极谱法测定食品中凯氏氮含量的简单、快速的方法。

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。