查询词典 implicit differential equation

Governing equation s adopted are Stokes equation for momentum and Laplace equation for energy.

由于研究对象是小液滴缓慢的热毛细迁移过程，因而所采用的控制方程中动量方程为StokeS方程、能量方程为Laplace方程。

Making use of the fundamental solution of Laplace equation, we change the nonhomogeneous Helmholtz equation with veriable coeffients into integral equation.

利用Laplace方程的基本解，将变系数非齐次Helmholtz偏微分方程的边值问题化为积分方程问题。

First the topological relations between the unknown points and known points are built as a linear constrain, then the DSI equation group is formulated by combining Laplace equation with the linear constrain equation.

首先由待插值点与已知点之间的拓扑关系建立线性约束，进一步结合位元场满足Laplace方程，建立离散光滑插值联立方程组，采用预条件共轭梯度求解该方程组。

By the least common denominator of all denominators in the equation to transform it into an integral equation;（2）Solve the integral equation

一次函数y=kx+b有下列性质：当k＞0时，y随x的增大而增大，这时函数的图象从左到右上升：当k＜0时，y随x的增大而减小，这时函数的图象从左到右下降。

The adsorption of Lutetium on the peat is studied under static conditions. The adsorption ratio and adsorption rate for Lutetium onto peat are so high that the surface complex reaction reaches equilibrium. The adsorption of Lutetium is not pH and ion strength dependent. The kinetic process of adsorption can be described by the Elovich equation excellently among five kinds of classical kinetic models, and the adsorption isotherm fits both the Langmuir equation and Freundlich equation very well by means of regression analyses.

静态条件下泥煤对溶液中Lu(上标 3+)的吸附率较高，而且吸附速度较快，镥与泥煤能迅速发生表面络合反应达到平衡。pH值和离子强度对低浓度镥吸附动力学影响不大。5个经典动力学方程中Elovich方程能较优地描述泥煤吸附Lu(上标 3+)的过程。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

Integrate the load transfer principle and shearing displacement method to set up the load transfer equation between the pile of soil, using the discrete and fitting methods to solve the equation so as to educe the pile displacement of arbitrary section as well as the analytical solution. Comparing the results with the soil settlement solved by the Mair equation, the relative displacement can be gained.

1结合荷载传递原理和剪切位移法的思想建立隧道开挖作用下的桩土荷载传递方程，采用离散和拟合两种方法来对该一元二次非齐次微分方程进行求解，可分别得到桩身任意截面处的桩体位移以及桩身位移的解析解，并与基于Mair公式求得的地面下任意深度处的土体沉降进行比较，即可求出桩与桩侧土之间的相对位移。

The percolation equation of the natural gas and the rock body deformation equation have been discreted respectively to obtain their corresponding functional equation while the calculation method was derived and the coupled solution method was presented bas...

对天然气渗流方程和岩土体变形场方程分别进行离散，得到其相应的泛函方程。根据有限元法原理推出其计算方法，并给出耦合求解方法，这对于真实模拟气藏的开发，指导气田生产具有重要的意义。

The first kind is 0-equation model. It only includes mass and momentum conservation equations. Great progresses have been made in improving this model. It has successfully been applied to many natural rivers with complicated boundary geometry. The second kind is κ-ε model. The κ equation and ε equation are needed, besides mass and momentum conservation equations. Many researchers have studied the depth-averaged mathematical models of turbulence in recent years. However, the models were used mostly in regular artificial canals or natural water areas with simple boundaries.

对于宽浅型河流，采用深度平均法进行流场计算时，用得较多的有两类模型：一类是不增加任何脉动量的偏微分方程的模型，这类模型已在适体坐标下运用得较多且较成功；另一类是κ-ε二方程模型，它是近几十年来广泛应用的一类湍流模型，并发展了许多具体的形式，但大多数只对顺直河道进行了研究，对弯曲较大的河道研究不多，本文运用适体坐标，采用正交交错网格及非正交交错网格，把此模型运用到了弯曲较大的河段及具有汇流的河段，取得了较大的成功。

McRae equation and Nicol equation describing solvent effects on absorption wavelength have been compared, and it is found that McRae equation is more suitable here.

比较了两个典型的用来描写溶剂对吸收波长影响的McRae方程和Nicol方程，发现前者在这里更为适合。

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。