However , linearization of the boussinesq equation 624 science in china : series d earth sciences allows the derivation of analytical solutions valid for specific cases . here we follow the methodology of brutsaert 20 22 to linearize the diffusion term in : 22cossin , hkpdhkhnttffxfx where p is the linearization constant taken to be 0 . 5 usually and d l is the mean aquifer depth . the clas - sical separation of variables method for partial differ - ential equations is adopted to give the analytical solu - tion of eq 对于方程2 , brutsaert进行了如下的线性化处理20 22 22cossin , hkpdhkhnttffxfx ? ? ? ? ? ? 3这里p是线性化常数一般取值为0 . 5 20 , 21 ,而d l是整个潜水面的平均厚度的线性化参数,下面采用science in china ser . d earth sciences第4期? ?田向军等:基于boussinesq - storage方程同时考虑水分储存和入渗的地下径流机制377的是偏微分方程理论中比较经典的分离变量法来给出以上这个经过线性化处理后的方程的解析解
Abstract : to facilitate the design , teaching and research of asphalt pavements , the article founded the models of displacement and tensile stress of three - layer system by using separation of variables , analysis and synthesizer . based on the analysis of common pavement structures and their equivalent conversion , the regression formulas of displacement and tensile stress are obtained successfully , furthermore the formulas applied in multi - layer system are checked . a great number of results of regression formulas show good accuracy for engineering application and theory research 文摘:为方便沥青路面结构设计生产、教学、科研之用，本文采用分析综合法与分离变量法建立了弹性三层体系应力位移显式模型；并在分析常见路面结构层厚度及其当量换算和模量变化范围的基础上，成功求得了三层体系路表弯沉、上层滑动应力、上层连续应力、中层应力逼近公式；精度分析表明本文逼近公式精度很好，完全可推广应用于多层体系，满足工程设计和有关理论研究的需要
The vector magnetic potential of a system consisting a line electric current and an infinite long magnetic dielectric column is calculated with the method of separation of variables and method of images , it is pionted out that the vector magnetic potential of a system consisting a line electric current and a magnetic dielectric plane , an ideal paramagnetic column , a superconductor column , and a line electric current in homogeneous magnetic field can all be deduced from our calculation 摘要用镜象电流法和分离变量法计算了线电流与无限长磁介质圆柱系统的磁矢势，指出线电流与无限大磁介质分界平面、线电流与超导体圆柱、均匀外磁场中有磁介质圆柱系统时的磁矢势都可以由线电流与磁介质圆柱系统的磁矢势的极限情形给出。
By using the method of separation of variables , a recursive formula was derived for the electromagnetic fields in a circular coaxial cable with a radial conductor plate and filled with multilayered homogeneous isotropic media , and the relationship between the first and the nth layers of the electromagnetic fields was determined 摘要采用分离变量方法，推导了有径向导体板、填充均匀的多层各向同性介质的同轴线各层电磁场之间的递推关系，得到了第1层与第n层介质中电磁场的关系方程。
