重积分

Intergral approximate calculation is widely used in many practical projects.

0引言积分的近似计算是实际工作中最常碰到的数学问题之一，例如在原子能科学技术领域和武器装备论证时会出现许多复杂的单重与多重积分。

Aiming at the engineering application of the two-layer fuzzy integration, we established the concepts of "two-layer measurable function on domain" and "two-layer measurable function for the monotone class".

针对二重模糊积分工程实用化，建立了备域上二重可测函数、单调类上二重可测函数的概念。

In recent years, Feng Kang has advanced a more natural and direct redu-ction, i. e. the reduction via Green's formula and Green's function.

近年来冯康又提出一种更自然而直接的归化，即从Green公式及Green函数出发将微分方程边值问题化为边界上的含有广义函数意义下发散积分有限部分的奇异积分方程，这种归化在各种边界归化中占有特殊地位，被称为正则边界归化，本文将这一理论应用于重调和椭圆边值问题，研究了其正则归化的性质，并通过利用Green函数、Fourier分析及复变函数论方法等不同途径求出了在上半平面、单位圆内部、单位圆外部三种区域的Poisson积分公式及正则积分方程，其离散化可用于实际计算。

The Galerkin's method solution of electromagnetic field integral equations for e lectromagnetic scattering problems of perfectly conducting object requires calcu lation of singular double surface integrals.

利用电磁场积分方程的伽略金法求解理想导体电磁散射问题时需要计算奇异性的二重面积分(即4维积分)。

By using integral periodogram to estimate the spectral functions of a stationary time series, the invariance principle for the error process has been demonstrated either for Gaussian or non-Gaussian series.

用积分周期图估计平稳时间序列的谱函数，不论是高斯序列还是非高斯序列，其误差过程的不变原理都已被证明￣（［1］，［3］），许重光￣［5］采用自迥归谱估计的积分估计谱函数也证明了误差过程的不变原理成立。

By constructing a new Lyapunov-Krasovskii function, using free-weighting matrix and triple integral approach, a controller design scheme is proposed in terms of linear matrix inequalities.

通过构造新的Lyapunov泛函，引入自由权矩阵和三重积分，以线性矩阵不等式形式给出了控制器的设计方案。

Holds true whenever the diameter of the largest subregion is less than, then A is said to be the triple integral of function over the region ,written

任给， 存在，对的任意一个分法，设小区域为，它们的体积用表示，在每个中任取一点，当小区域的最大直径小于时，不等式成立，则成为在D上的三重积分，记作，或。

Triple integral equation.

三重积分方程

We shall study double integrals over more general sets in the plane.

我们将研究定义在平面上更一般的集合中的二重积分。

On the basis of the investigation of different moments, the concept of generalized moments is firstly defined and then, an abstract algorithm framework for computing the accurate generalized moments is presented. The framework replaces integrals on 2-dimensions space by summations on 1-dimension ORBIR list without introducing the error incurred by discrete sampling, and therefore, reduces the computation complexity for moments generation.

矩在工程实践中的应用非常广泛，在考察矩的实质的基础上，定义了泛化矩的概念，并研究泛化矩的生成框架，该框架在不引入离散化过程中存在的采样误差的前提下，将矩生成过程中需要的二重积分运算转化为在一维的ORBIR矩形序列上的求和，因此降低了矩生成的计算复杂度。

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。