一阶导数

In Chapter 2, one kind of rational cubic spline interpolation with linear denominator has been proposed, whose derivatives are replaced with accurate derivative values, difference quotient and arithmetic average difference quotientrespectively.

第二章给出了一类分母为线性的有理三次插值函数，当其导数值分别取为导数的精确值，一阶差商，以及算术均差商时，便得到三种插值格式，分别为给定导数值的有理三次插值函数，基于函数值的有理三次插值函数，以及基于算数均差商的有理三次插值函数。

Reduce the computing complexity of magnetic field integral equation with differential quotient, which makes the computing which combined field integral equation more efficiently.

在AIM算法的实现技术方面作了两个改进：一是采用了新的多极子展开方案，保证了迭代的数值稳定性；二是在差商逼近偏导数的过程中全部采用二阶形式，保证了差商逼近偏导数的精度。

The procedure estimating the regularization parameter is the same as that the adaptive Marquardt algorithm used. The Frechet derivative is directly derived from the forward methods: SAM and FEM. With the theory of SAM and Zhang′s geometric factor, the relationship between the Frechet derivative and the geometric factor is established, at the same time, one useful corollary is given, i.

选取正则化因子时，沿用自适应的Marquardt算法中阻尼因子的选取计算方法；计算Frechet导数时，根据逐次逼近解法和张氏几何因子理论，推导出了Frechet导数与张氏几何因子的关系，得出了Frechet导数为张氏一阶积分几何因子的结论。

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。

"Economic Mathematics" on the function of the limit, derivative and differential, derivative applications, indefinite integral, integral, integral and infinite binary Series and the first order differential equations, and so forth.

经济数学》介绍了函数、极限、导数与微分、导数的应用、不定积分、定积分、二元积分和无穷级数与一阶微分方程等内容。

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。

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings,an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness,real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix.

为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。

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。

This paper discusses the connection of one step or two step right derivative and protruding property of a function.

研究了函数的一阶及二阶右导数与函数凸性的关系，推广了数学分析中的有关结果。

Based on the improved Atiken iterative method and dimidiate method, a new algorithm of searching zero of derivative function is given, the simulation results show that if using the new algorithm to find the zero of derivative function, the convergence speed is faster than the improved Atiken iterative method .

采用二分法预报、改进的Aitken迭代校正的方法，构造了一种求导数零点的一种新算法。新算法在迭代过程中不用计算导数，且二阶收敛。数值试验表明，该算法具有较高的精度和较大的初值选择范

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。