重积分

In this paper, starting from the double integral, double integral first introduced the basic concept and calculation method, the re - Top songs integral cylinder volume and surface area, for example in the application, as well as the double integral in the application of mechanics.

本文从二重积分入手，首先介绍了二重积分的基本概念和计算方法，二重积分计算曲顶柱体体积和曲面面积的在应用举例，以及二重积分在力学中的应用。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

The use of spherical coordinates triple integral calculation IV Application Multiple Integral Weight points at geometry, physics applications.

利用球面坐标计算三重积分第四单元重积分的应用重积分在几何、物理中应用。

It is key to select the suitable coordinate system, the integral order and the limits of integration determination.

三重积分计算的基本思想是化三重积分为三次积分，其关键是选择适当的坐标系、积分次序和积分限的确定。

The triple integral computation's basic philosophy is turns the triple integral into three integrals, its key is the choice suitable coordinate system, the integral order and the limits of integration determination.

重金悬赏：下列中文翻译成英文，还有积分追加摘要：三重积分计算的基本思想是化三重积分为三次积分，其关键是选择适当的坐标系、积分次序和积分限的确定。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道，基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差，并且作为形式简单且恢复函数为多项式的一种信息基算法，其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

Then introduced a triple integral calculation of the basic concepts and methods of calculating the triple integral in three-dimensional volume, as well as the mechanical application of triple integral example .

随后介绍了三重积分的基本概念和计算方法，三重积分计算立体体积以及力学中三重积分的应用举例。

Then introduces the basic concept and triple integral calculation method, the three-dimensional volume and triple integral calculation of triple integral mechanics.

随后介绍了三重积分的基本概念和计算方法，三重积分计算立体体积以及力学中三重积分的应用举例。

Starting from this dowble, firstly introduces the basic concept and the double integral method, double Integral calculation music volume and surface area of top cylinder, and the application examples in the double integral application in mechanics.

本文从二重积分入手，首先介绍了二重积分的基本概念和计算方法，二重积分计算曲顶柱体体积和曲面面积的在应用举例，以及二重积分在力学中的应用。

The basic concept of FOP can be summarized as to further optimize effective prescription according to the standard of curative effects and with the aid of modern science and technology and theories of traditional Chinese medicine.

其基本内涵可概括为：以确有疗效的中药复方为研究对象，以现代科学技术和传统中医药理论为技术支持，以该复方所治病证的药效响应为评价标准，以优化重组疗效更优的新复方为研究目的。

Ever since our world has been a world, native forests have been indiscriminately exploited by man.

自从我们的世界一直是世界原生森林被任意剥削人。