multiple integral

Multiple Hardy-type Integral Inequality with the Best Constant Factor

一类多重的Hardy型积分不等式及最佳常数

Using DFT to calculate SNR and harmonic distortion of telemetry seismic data acquisition system, if the recording length of data is not integral multiple of sine wave's period, the energy of the fundamental wave and its harmonic will leak to the vicinity region.

在用离散傅里叶变换（DFT）计算遥测地震数据采集系统的信噪比（SNR）和谐波畸变时，如果数据记录长度为正弦波周期的非整数倍，基波及谐波的能量会泄漏到邻近频率。

From this has been constructed a unified theoretical system of Measure Calcalus: multiple integral and integral on manifold have been unified; computation successive changes from higher dimensional into low till definite integral.

由此形成测度微积分的统一理论体系：流形上的积分与重积分融为一体，计算则由高维向低维逐步转化，直至定积分。

In this paper, we derived the discrete Formula of Green and establish formula of from multiple integral to curvilinear integral. By different methods, we derive any polygon area formula.

通过对Green公式的离散变形，建立了重积分到曲线积分的公式，用多种方法推导出任意多形的面积公式。

Using multiple integral to prove a generalization of Pythagoras theorem and to calculate the Moivre integral.

得到了一类多重积分的计算公式,并运用数学归纳法给出了证明.