解析函数

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

With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented.

通过将孔径函数展开为有限项复高斯函数之和，得到了高斯光束在受孔径约束的抛物面折射系统中分数傅里叶变换较符合实际的近似解析表达式，并进行了数值模拟。

By using the method of expanding the aperture function into a finite sum of complex Gaussian functions, approximate closed-form propagation equations of TMn0-Gaussian beams diffracted by hard-edged parallelogram aperture s are derived.

通过将硬边光阑函数展为复高斯函数之和的方法，在直角坐标系下研究了TMn0模高斯光束通过有平行四边形光阑的衍射，得到了近似的解析传输公式。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all th...

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory.

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

The main contents of this course include: complex number and planar point set, function of complex variable, complex integral, series, residue, conformal mapping, analytic extension, harmonic function.

本课程的基本内容有：复数与平面点集、复变函数、复积分、级数、留数、保形映射、解析开拓、调和函数。

In order to study the propagation of partially coherent modified Bessel-Gaussian beams passing through a paraxial ABCD optical system with hard-edge aperture,the approximate analytical propagation equation was derived with the hard-edged aperture function expanded into a finite sum of complex Gaussian functions.

为了对部分相干修正贝塞尔－高斯光束通过有硬边光阑近轴4BCD光学系统的传输进行研究，采用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，得到了近似的解析传输公式。

The propagation equations for oblique and off-axial Gaussian beams passing through cat-eye optical lens are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions.

运用矩阵光学理论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，进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式，通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律。

Using the relations between Hermite and Laguerre-Gaussian modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions, the propagation of complex- argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied. An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.

利用拉盖尔－高斯模和厄米－高斯模的变换公式，并使用将二维矩孔光阑窗口函数展开为有限个复高斯函数之和的方法，得到了复宗量拉盖尔－高斯光束通过含矩形硬边光阑近轴ABCD光学系统的变换的解析传输公式，并对复宗量LG光束通过矩形硬边光阑的衍射和聚焦特性进行了研究。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。