导数

In this paper,the existence of commmon Borel point of algebroidal function and its derivatives in the unit disc is proved.

证明了单位圆内代数体函数及其导函数至少存在一个公共Borel点，结果和Valiron在1928年提出的关于亚纯函数及其导数是否存在公共Borel方向这一问题是相关的。

One bases on function value and another bases on arithmetic average difference quotient. In this paper, the author mainly studies the approximation properties of both the function value and the derivative of two kinds of splines interpolation mentioned before, and the optimal error constants are obtained finally.

文中分别就这两类插值样条的函数值及一阶导数的逼近性质展开讨论，相应得出这两种插值函数在被插函数分别为一阶连续可导和二阶连续可导情况下的最佳误差常数。

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。

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

Based on the chain rule techniques, AD seeks first or higher order derivatives of functions represented by a group of dependent program procedures and extended files, the so-called original model, through a number of code-to-code transformings under a series of differential rules.

基于链式求导法则的自动微分方法通过改写原程序模式代码，依赖机器自动构造不同的微分模式，来分析求解函数的一阶或高阶导数，即在一系列预定微分规则下对不同程序对象做从代码到代码的自动微分转换。

Theorem 1 Let be continuous on the closed interval and let be a point in.

如果函数在区间上连续，则积分上限函数=在上可导，并且它的导数是

When using restricted maximum likelihood for parameter estimation, we need to get the minimum of a function. But if the expression of the function is complicated, it is difficult to obtain the derivatives of the function. We introduced conjugate direction method which avoided the derivatives.

在用限制极大似然法估计参数时，需解决函数的极小化问题，而当函数的表达式较为复杂时，将难以获得其偏导数，本文给出的共轭方向法，避开了求导问题。

On the basis of method of derivative on the left and the right of separable function,the derivability of separable function on demarcation point was simply distinguished,and derivative continuity on demarcation point discussed.

运用研究分段函数的导函数的左、右极限的方法，简便地判明分段函数在分界点处的可导性；同时讨论了分界点处导数的连续

According to the studies for this zero-order differential operator to make an expansion of a function, it can restrain border effect and control Gibbs effect.

并进一步构造了1阶和2阶导算子，对它们的导数矩阵的特性进行了研究，实现了用这样的导算子对微分方程的求解。

Gravity anomaly of sea surface, vertical gradient of gravity anomaly, downward continuation, cylinder method, geometry method

地表重力异常及其梯度本质上都是位的派生物，重力异常是其径向的一阶导数，垂直梯度是其二阶导数，它对接近地表的扰动物质更为敏感。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。