积分公式

Based on Collins integral formula and the expansion of the hard aperture function into a finite sum of complex Gaussian functions,the approximate analytical expression of the diffraction field of Gaussian beam by a circular disc is derived,and its characteristics are analyzed by the numerical calculation and numerical simulation.

基于圆孔光阑函数展开为复高斯函数和的方法，用Colins积分公式，导出了高斯光束照射下圆盘衍射的光场近似解析表达式，经计算机数值计算，对高斯光束照射下圆盘衍射的衍射特性进行了详细的分析

Based on the Collins formula, the analytical propagation equations for a Gaussian beam through a multiple spatial filter system are derived by using the methods of the matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian function .

以Collins衍射积分公式为基础，利用A0CD矩阵分解与物理实现的技巧，以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，推导出了高斯光束通过多级空间滤波器系统的传输方程，并用数值计算加以说明。

The spatial propagation properties of output annular laser beam from an unstable resonator are studied based on Fresnel diffraction integral.

本文从菲涅耳衍射积分公式出发研究了激光器非稳腔输出环状光束在空间的传输规律。

The Propagating property of flat topped multi-Gaussian laser beams passing through ABCD optical systems is discussed on the basis of generalized Huygens Fresnel Diffraction integral formula.

利用广义惠更斯－菲涅耳衍射积分公式，研究了平顶多高斯光束通过ABCD光学系统的传输特性，推导出光强分布的解析式。

A third order ENO finite volume method for hyperbolic conservation laws on unstructured triangular mesh is introduced.In order to obtain the third order accuracy on spatial discretization,a weighted quadratic interpolation is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on each edge of every triangular mesh and the third order TVD Runge-Kutta method is used for time discretization.The numerical order of convergence and the numerical result of a mesh 3 wind tunnel with one step are given.

摘 要 基于双曲型守恒律方程，对非结构三角形网格给出了一种ENO(Essentially Nonoscillatory Scheme)型有限体积格式，方法的主要思想是先对每一个三角形单元构造一个加权的二次插值多项式，而在计算交界面的流通量时采用了两点高斯积分公式以保证格式的整体精度，时间离散采用三阶TVD Runge-Kutta方法。

Based on the method that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, the propagation characteristics of a Gaussian beam passing through apertured spatial filter systems are analysed and the corresponding analytical formulae are obtained respectively.

根据矩形函数可以展开为有限复高斯函数之和的方法，从柯林斯衍射积分公式出发，对高斯光束通过受限空间滤波器传输特性进行分析，得到了相应的近似解析式。利用Matlab对其解析式进行数值模拟，得出一组直观的结果。

In 1968,J.simons got the integral formulaof the minimal submanifolds of unit sphere S~(1).After that time,many geometrician had got lots of results on the pinching problem of submanifolds.

自从1968年J.Simons给出球面S~(1)中极小子流形的积分公式后，几何学家对子流形的pinching问题研究的很多。

The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field π/2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained.

通过将输入输出光场在相空间中作π/2角旋转，得到了一阶光学系统在频域的传输矩阵和衍射积分公式，进而得到了一阶光学系统在频域的分数傅里叶表示。

A set of analytical integral method of triangular element linear interpolation BEM has systematically been deduced and put forward.

提出并系统推导了一套三角形线性插值边界元的解析积分公式。

We present a new direct boundary integral equation in terms of the boundary magnetic field only.

文中提出了一个新的直接边界积分公式，仅仅由边界上的已知磁场值确定空间点的磁场值。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。