separation of variables造句

• 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
• 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。
• Third , the mode solution is obtained using the separation of variables . the last , the mode transition property is discussed when the plane wave transmit in the step - index optical fiber
  再次，利用分离变量法推导出平面波在阶跃光纤中传播的模式表达式，讨论了光波在光纤中传播的模式特性。
• 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) 。
• 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。
• The tu ' s scheme is extended to the generalized dirac spectral problem with an arbitrary function , the generalized kaup - newell spectral problem and the new 3x3 spectral problem with five potentials such that their lax integrabie integrabie hierarchies of equations and liouville integrabie hamilton structures are obtained . chapter 7 is devote to higher - order constraint flow , involutive system , lax representation , r - matrix and the separation of variables
  第六章研究了lax可积的新的方程族和liouville可积的n - hamilton结构方面的问题：将屠格式推广到新的含有任意函数的广义dirac族的谱问题、广义kaup - newell谱问题及含有五个位势函数的3 3谱问题，研究了它们的lax可积的方程族和liouville可积的hamilton结构。
• In this dissertation , with the aid of many types of constructive transformations and symbolic computation , some topics in nonlinear waves and integrable system are studied , including exact solutions , painleve integrability , backlund transformation , darboux transformation , symmetry ( similarity reduction ) , conditional symmetry , lax integrable hierarchy , liouville integrable n - hamilton structure , constraint flow , involutive system , lax representation , r - matrix , separation of variables and integrable couplings . chapter 2 and 3 are devoted to investigating exact solutions of nonlinear wave equations : firstly , the basic theories of c - d pair and c - d integrable system are presented
  本文以构造性的变换及符号计算为工具，来研究非线性波和可积系统中的一些问题：精确解(如孤子解、周期解、有理解、 dromion解及compacton解等) 、 panileve可积性、 backlund变换、 darboux变换、对称(相似约化) 、条件对称、 lax可积族、 liouville可积的n - hamilton结构、约束流、对合系统、 lax表示、 r -矩阵、变量分离及可积的耦合系统
• 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。
• 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。
• There are many kinds of ways to solve the electrostatic field of two - dimensional laplace ’ s equation or the poisson ' s equation , like the separation of variables , green ’ s function or alternative means . but if their boundary shapes are quite complex , it is extremely difficult to use these usual methods , and , in general , it is impossible to work out even there is such peculiar instance as analytic solution , or obtains the approximate solution
  对二维拉普拉斯方程或泊松方程的平面场的解法有多种,如分离变量法、格林函数法或者其他方法,但如果它们的边界形状比较复杂,用这些通常的方法求解会非常困难,即使对于存在有解析解的特殊情况,一般说来也不可能求出,而且求得的只能是近似解。
• 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。