| 1. | Method of separation of variables and boundaryvalue problem of the isosceles - right triangular waveguide
分离变量法与等腰直角三角形波导的边值问题 |
| 2. | By using the method of separation of variables and limited fourier and laplace transform , the analytical results are obtained
运用分离变量法和有限傅立叶变换和拉普拉斯变换，将系统运动微分方程转换为线性方程组，求出挠度和内力解析解。 |
| 3. | According to thinking the joints of plates as elastic boundary supports to plates and by using of the method of separation of variables , betti ' s reciprocal theorem of work , the solution of dynamic equation can be deserved
运用变分法，分离变量法，互等功定理等数学工具求解板的运动方程，可得出弹性地基上考虑接缝传荷能力的道面板在移动荷载下的动力响应(解析解) 。 |
| 4. | By adopting appropriate transformation , this paper transform the heat conduction equation with internal heat source into a non - source heat conduction equation , and then solve the problem successfully by the method of separation of variables
其关键方法是：通过将电场量引入温度场方程，作适当变换，把含内热源的热传导方程转化为不含内热源的热传导方程，然后采用分离变量法进行求解。 |
| 5. | The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils . because " the surface current source is placed at the interface , the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation . by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants , the expressions for the magnetic vector potential of the three regions are solved out
在求解过程中，假定放置式圆柱线圈是由无穷多个对称圆环线圈密饶而成，首先求解含有有限长磁芯的通电对称圆环线圈的电磁场：以有限长圆柱磁芯的侧面和圆环线圈所在圆柱面为分界面将场域划分为三个小区域，由于场源放置在内边界面上，使得关于矢量磁位的非齐次约束方程转化成齐次亥姆霍兹方程，利用分离变量法求解，根据分界面郑州大学硕十研究生毕业论文摘要条件以及无限远条件确定待定常数，从而得到各场区矢量磁位的表达式。 |
| 6. | The governing equations of the problem are derived in hamiltonian form by using variable substitution and variational principle . then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem . the result can be derived by analytical method
在平面弹性问题中，由变量代换及变分原理，方程可导向哈密顿体系，从而通过分离变量法及共轭辛本征函数向量展开法，以解析的方法来进行求解。 |
| 7. | 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。 |
| 8. | 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。 |
