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Using Fourier expansion, Laplace transforms and Hankel transforms with respect to the circumferential, time and radial coordinates, respectively, the partial differential equations are reduced to a set of ordinary differential equations. Transfer matrices for this situation are derived and explicitly solved.

利用Fourier级数和Laplace-Hankel变换，将该状态变量方程转换为两组一阶常微分方程组，提出了有限层饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到饱和多孔介质空间非轴对称Biot固结问题在状态空间中的解。

It computes wind factors for flight data file, uses differential equations to solve for position and tension vectors as a function of arc length, and uses Runge-Kutta method for integration of ordinary differential equations.

该软件计算用于飞行数据文件的风向因素，使用不同的方程式，比如一个弧线长度函数来解决位置和牵引方向问题，使用 Runge-Kutta 方法解决综合推理差异方程式。

In this work, the equations describing circular Gaussian beams propagating inside absorptive Keer medium have been derived from nonlinear paraxial equation. Based on the equations, an evolution equation of beam waist lias been obtained.

本文从非线性近轴波方程出发，导出了在吸收克尔介质中具有二次位相因子的圆对称高斯光束的传输方程，得到了光束束腰的演化方程。

Content: By learning this course, students should grasp the elementary solution of first order differential equation, the structure theory of linear differential equation or system of linear differential equations and the solution of constant coefficient differential equation or system of constant coefficient differential equations.

主要内容：通过对本课程学习，使学生掌握一阶微分方程的初等解法、线性微分方程的结构理论和常系数方程的解法，对微分方程初值问题的一些基础理论有一定的了解，对

The principle of method,experimental conditions,regression equations and linear equations are discussed.

讨论了方法原理、实验条件，建立了回归方程和线性方程组。

The proposed scheme is developed using the local coordinate system based PML splitting equations and integral approaches of the PML equations under a discretization of triangular grid cells.

本方法的核心是建立局部坐标系下的分裂方程和基于积分近似的微分方程弱形式。

The equations of electromagnetic field are invariant with respect to the Lorentz transformation and the mechanical equations are invariant with respect to the classical transformation.

电磁场方程对于洛伦兹转换是不变的，而力学方程对于经典转换是不变的。

The observational equations have been derived using the three methods above which are based on high-low SST and low-low SST observational data respectively, at the same time, the shortages and merits of these three methods are analyzed. 3The problem of gravity field recovery can be attributed to the solution of over determined system of equations.

本文分别以高低卫卫跟踪和低低卫卫跟踪观测数据为基础，导出了基于上述三种方法的观测方程，并分析了它们的优缺点。3重力场恢复最终归结为超定线性方程组的求解问题。

In the low-low satellite to satellite gravity mission, the intersatellite range and range-rate data are the observable values, while the intersatellite acceleration can be derived from the range-rate through digital differential. Using acceleration data, people can avoid solving the variation equations of the satellite motion and simplify the observation equations. But on the other side, the digital differential will amplify the observation noises and finally affect the solved geopotential accuracy.

低低卫星跟踪卫星的观测量是两低轨卫星的星间距离或星间速度，星间加速度由星间速度通过数值微分导出，用星间加速度作为观测量可以避免解算卫星运动的变分方程，简化观测方程的建立，但数值微分会使观测噪声放大，从而影响重力位的解算精度。

One simple fluid model, magnetohydrodynamics , treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier Stokes equations .

一个简单的流体模型，磁流体，把血浆作为一个单一的流体管理相结合的麦克斯韦方程组和 N - S方程。

This matter overthrew all basises I learned from Sunday school .

这件事把我从周日学校学到的所有道理都颠覆了。

It's one of the cruel ironies of aging: if you want to remember your favorite restaurants, the less you should eat at them.

这是一个老化的残酷讽刺：如果你想记住你最喜欢的餐馆，你应该更少吃到它们。