在详细的数学推导之后，给出了金属疲劳断裂几率即一个变上限复杂积分的近似解析函数表达式，并与计算机的数值曲线进行了比较。
Following a detailed mathematical derivation a new approximate algorithm for the fatigue fracture of metals is given namely a complicate integral having a changing upper limit.
在柱坐标系中，求出了绝对零度情况下近理想玻色气体涡旋态的波函数和能量的近似解析形式。
Approximate analytical solutions of wave function and energy of vortex in the cylindrical coordinates system are obtained for the near-ideal Bose gases at zero temperature.
以高斯光束的变换为例，推导出了一个表示为初等函数之和的近似解析传输公式。
The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived.
在综合大量实例的基础上，提出双高斯函数逼近多模光纤的光脉冲输出的解析近似方法，使时域法确定光纤带宽的精度大为提高。
On the base of a plenty of facts we suggested a method in which bi-Gaussian form is approached the output pulse in multimode fibers The accuracy measuring band in time domain can be improved highly.
讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似。
The non-relativistic approximation of wave functions and energy equation and phase shifts are also studied.
用解析几何作为一种近似的方法讨论了生命能量系统动力学模型中两个典型方程解函数平衡点的求解问题。
Analytic geometry was used as an approximate method to discuss the equilibrium values of two typical dynamic equations of Life Energy System.
当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。
The nonlinear equation of heat conduction is transformed into a Laplace's equation by applying the Kirchhoff transformation, and an analytic approximate solution of the equation is derived.
对势函数采用二阶近似后，求解此方程得到高斯型呼吸模式的光束宽度的近似解析式。
Having adopted the quadratic approximation of potential, we can solve the equation and get the approximately analytical solutions of Gaussian typed breath mode.
本文用适当的多项式函数近似扩散光波导的高斯折射率分布函数，推导了导模有效折射率的解析形式渐近解。
The Gaussian index profile of a diffused optical waveguide is approximated by an appropriate polynomial, and the asymptotic solutions of the mode efficient index is derived in a analytical form.
通过数学运算和近似处理，得到了动态散斑强度涨落的空-时相关函数的解析表达式，从理论上揭示了散斑受超声调制的过程，对散射介质中的声光调制机制做出了新的诠释。
The specific space-time intensity correlation function of dynamic speckle has been derived and opens out the mechanism of the dynamic speckle modulated by ultrasound in scattering medium.
本文基于有限解析法的基本思想，用单元内插值函数近似地代替单元内的近似解析解。
Based on the idea of finite analytic method, an interpolation function is used in place of the analytic solution, and a mathematical model is established.
本文基于有限解析法的基本思想，用单元内插值函数近似地代替单元内的近似解析解。
Based on the idea of finite analytic method, an interpolation function is used in place of the analytic solution, and a mathematical model is established.
应用推荐