简化方程

This study uses the soil parameter reduction coefficients to model the seismic pile responses affected by liquefied soils. One dimensional wave equation analyses were conducted for the solutions. Based on the bore-hole data and nearby seismic record, the soil parameter reduction coefficients of liquefied layers can be obtained through a pre-analysis for liquefaction potential of the site. The reduction coefficients were used to reduce the soil modulus for liquefied soils, and the lumped mass analysis is performed to obtain the free-field response of the site. The ground deformations are superimposed onto the pile elements for discrete wave equation analysis, and the non-linear pile responses can be simulated through the modified Bouc-Wen model. Thus the deformations and failure mechanism of the pile are able to investigate.

中文摘要本研究之土质参数折减系数模式，系以一维波动方程模拟地盘液化状态下之桩基础动力反应，依据现场土层钻探资料与邻近测站之地震纪录，由土壤液化潜能评估法配合日本相关规范求得液化土层之土质参数折减系数，以此系数对土壤强度模数进行折减，并使用集中质块法求取自由场之地盘液化反应，再以此为前置解作用於桩基础之波动方程求解，桩身刚度以简化之Bouc-Wen模式模拟其非线性行为，以了解液化地盘内基桩之变形行为与破坏机制。

By exploiting the special structure of symmetric circulant system, the problems of solution of these systems can be simplified to change the problems of lower dimension systems.

研究具有对称循环结构的广义大系统Lyapunov方程和Riccati方程的求解化简问题，利用简化的解求得复杂系统的最优控制问题。

In using integral equation, The author brought forth some new idea about the dissection of magnet. The author also made a thorough investigation and study of the fast convergence numeric algorithm of complete and incomplete elliptic integral. In order to make full use of the computer resource, the author considered the symmetry of the magnet structure.

在应用积分方程法设计时，依据设计要求而对源区进行的剖分有独到之处，并对由剖分而引入的各类完全和不完全椭圆积分的快速收敛数值算法进行了深入探讨，还充分利用磁体结构对称性进行简化，以减少计算时间，使得当前的计算机资源能满足积分方程法之所需。

The nonlinear equation of β obtained is subsequently approximated by a cubic equation from which β is solved directly.

利用这一极值原理，得到一个关于β的非线性方程，近似简化后成三次方程，直接求解。

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current.

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。

Considering that the temperature gradient through thickness is much higher than that through width and length of plate, in this model, the governing equation of heat transfer was simplified as a one dimensional differential equation, and the series function solution for temperature is established in Lagrangian coordinate setting.

在该模型中，考虑到轧件厚度方向的温度梯度远大于沿宽度和长度方向的温度梯度，因而将热传导方程简化为一维微分方程，基于拉格朗日坐标建立了温度场的级数解法。

First, theoretical analysis methods were used for the static analysis of the suspension bridge. The formulas for endogen force of the asymmetry suspension bridge through elastic theory were deduced and they were contrasted with those of the normal suspension bridge. The basic differential equation of deflection theory was deduced and the method of getting the roots of the equation was offered, and some simplified methods for deflection theory were presented.

推导了非对称式悬索桥弹性理论的内力计算公式，并对比了其与对称式悬索桥弹性理论的内力计算公式的异同；推导了非对称式悬索桥挠度理论的基本微分方程，并且给出了部分均布荷载作用下基本微分方程的试算方法；提出了挠度理论的几种简化计算方法。

In the method, the equation of vorticity is simplified and combined with the definitions of vorticity and divergence , and then restrained by the equation of continuity to set the system of retrieval equations. Three-dimensional wind vector, vorticity and divergence can be got by solving the system of equations. Preliminary test has proved that it is feasible.

该方法从动力学角度出发，将柱坐标中的垂直涡度方程适当简化后，联系涡度散度的定义式，再以大气连续方程作约束，得到一个反演方程组，求解方程组就可得到不同高度层上的三维风场以及涡度、散度，初步检验证明其是可行的。

In the simplified model, the governing equation of heat conduction is discretized using implicit finite difference method, and the computational domain is discretized using cell centered scheme, and the solution of Maxwell equation is used to determine the distribution of the internal heating sources.

使用的简化模型中热传导方程的离散采用隐式差分法、区域的离散采用内节点法，并以Maxwell方程的解确定内热源分布。

Besides, a nonlinear mathematical model is established on the base of non-equilibrium thermodynamic theory and phase equilibrium principle.

从非平衡态热动力学和相平衡的角度，推出了非饱和多孔介质的热湿迁移的数学控制方程，根据本文所研究的对象，对该控制方程进行了简化，建立了蔬菜热湿迁移的一维非线性数学模型，并给出了求解该数学模型的定解条件。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。