积分公式

Some well-known results on area transformation formula and variant transformation formula of double integral are improved and generalized.

对现有的有关面积变换公式和二重积分变量变换公式的结果作了相应的改进和推广。

The general formula to calculate the rotating surface area which is shaped by rotating the curve c in xoy plane around the L-axis by using curve integral.

依据所证得的通用计算公式推证得到，在某些特定情形下利用定积分计算旋转曲面面积的具有针对性的公式。

A boundary integral formulation describing constant-αforce-free field with finite energycontent in the semi-infinite space above the sun was proposed(Yan,1995), this formulationcontains boundary field and its normal gradient under integral sign.

颜毅华1995年在太阳物理杂志上发表一文，就太阳磁场提出了一个具有有限能量的线性无力场模型，并对磁场给出了一个边界积分表示公式，该公式用边界上的已知磁场值和未知的磁场法向导数值来确定空间任意点的磁场值。

Concrete confined coefficient K by the numerical integral of whole section using strip method is put forward for the bearing capacity formula of eccentrically compressed SRC column.

通过条带法的全截面数值积分对混凝土约束系数K进行分析与探讨，经过试算与分析配有圆钢管的钢骨混凝土柱的应力应变特征，提出核心混凝土极限公式和偏压柱承载力公式。

Append A presents the formula of a singular integral with a complex parameter, by combining of the residual methode and the law of sines.

在附录A，联合使用保角变换法、留数定理和正弦函数的欧拉公式，求出了一类含有复参数的奇异积分的具体计算公式。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

Calculation formulae for real number order derivative and integral of logarithmic functions and power functions have been obtained which are the important references to calculate real number order calculus of any other functions.

计算得出了对数函数、幂函数的任意实数阶导数及积分的完整计算公式，它们是推导其它函数任意实数阶微积分公式的重要参照式。

The gamma function calculation of Pearson type III distribution is investigated,a new approximation method by using cone curve is put forward,and neither numerical integral nor series expansion may be used.

对皮尔逊Ⅲ型分布公式中伽玛函数的计算问题进行了研究，提出了一种新的数值逼近方法，在一定范围内对伽玛函数用圆锥曲线表示，利用递推公式扩大参数范围，免去了数值积分和用级数展开计算的麻烦。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

The good news is that after formatting from the command line to FAT32 (format /fs:fat32 /a:4096 drive:) all but one of the problematic games that I tested work perfectly.

好消息是，从指挥线后格式化了FAT32(格式/曾荫权：了FAT32/答：4096年径：)所有问题，但其中的游戏测试工作，我很好。

In Amsterdam. He is a Dutch painter, draftsman, and etcher of the 17th century, the greatest artist of the Dutch school, a master of light and shadow whose paintings, drawings, and etchings made him a giant in the history of art.

伦勃朗是一位17世纪画家、绘图家、版画家，荷兰学派的最伟大艺术家，他的明暗法的大师，他的绘画、素描和版画使他成为一位艺术史上的巨匠，其画作体裁广泛，擅长肖像画、风景画、风俗画、宗教画、历史画等。