查询词典 transformation equation

Use samiliar reciprocal transformation on Lax pairs of DGH equation, we obtain a new integrable system through introducing appropriate potential function.

把类似的倒数变换应用到DGH方程的Lax对中，通过引入恰当的势函数得到了一组新的可积系统。

In order to study the numerical method to solve the viscous incompressible flow with free surface, the 3-D mathematical model for steady and unsteady hydrodynamic problem had been established and closed by k-εbuoyant turbulence model. The algebraic coordinate transformation method was used to fit the free surface, the Runge-Kutta method of three step and second precision was devised to simulate the time step. A high precision up-winding compact scheme was studied for the convection term, and the generalized conjugate residual method was set to solve the Poisson equation.

为了研究粘性不可压缩三维问题的数值求解方法，本文从基本的Navier-Stokes方程出发，采用代数拟合方法处理自由表面，用三级二阶Runge-Kutta方法对时间步进过程进行了模拟，并且对对流项的高精度迎风格式进行了研究，给出了求解压力Poisson方程的广义共轭剩余法，从而建立了能够模拟有自由表面的粘性不可压缩问题的定常、非定常三维水动力学模型，并采用k—ε浮湍流模型对其进行封闭。

Firstly, based on the force acting on a single-particle, establish a discriminant formula of the sand threshold, and prove that the sand threshold belongs to the cusp catastrophe. Then establish the basic equation of the cusp catastrophe using coordinate transformation and catastrophe theory. Finally, while particle Reynold number and equivalend diameter are the state variables and Shields parameter is the control variables, we can obtain the model of cusp catastrophe of sand threshold, putting those variables into the basic equations of the cusp catastrophe. The model is derived from the mathematics, which has a certain mathematical theory foundation.

首先从单颗沙粒受力分析出发，建立沙床沙粒起动条件判别公式，进而证明了风沙起动属于尖点型突变；然后通过坐标变换和突变理论建立了尖点突变的基本方程；最后本文选择颗粒雷诺数和等效粒径作为控制变量，希尔兹参数作为状态变量，并把它们代入尖点突变的基本方程，经过拓扑变换得到风沙起动的尖点突变模型，并与前人的公式及实验数据进行比较。

In order to prove the existence of the periodic boucing solutions, firstly we will introduce a new coordinate transformation, transform the system from right half plane to the whole plane. And give the relation of the eigenvalues of Hill's equation and the rotation numbers, using this approach and Pioncar -Birkhoff twist theorem, we proved the existence of the periodic bouncing solutions for asymptotical linear oscillator.

对于周期解的存在性证明，我们引进新的坐标变换把右半平面上的碰撞问题转化到整个平面上，给出旋转数与Hill方程的特征值的关系，并以此来度量渐近线性振子，再应用Pioncaré-Birkhoff扭转定理得到周期碰撞解的存在性。

For example, it is stall need to study the thermal equation-of-state, to find a proper methodology for calculating self-diffusivity, to propose a better potential model for mullite and sillimanite, to calculate mechanical properties at high temperature, and to analyze the structural transformation at high temperature.

本研究所建立的研究方法与流程适合应用在陶瓷材料的模拟与分析，而我们已经探讨了莫来石的缺陷对晶体结构、晶格常数、热膨胀、体模数、缺陷能、氧扩散的影响，接下来可以朝向以下几点深入研究，包含研究热状态方程式、找出最适当的方法来计算扩散系数、提出更好的分子势能模型、研究莫来石在高温下的相变化与力学性质。

By using a similarity transformation, the Navier-Stobes equations in the cylindrical co-ordinates for the steady incompressible flow are reduced to an ordinary non-linear differential equation of the third order.

利用相似转换，将不可压缩流体，定常运动，柱坐标形式的纳非尔-斯托克司方程组简化为一三次非线性常微分方程，运用小参数法及适当边界条件求出此方程的解，结果表明，吸吮或吹注对流动的速度分布，沿流程压力下降和摩擦系数均有显著影响，其影响的大小，依赖于吸吮或吹注的性质，程度及二圆管的相对尺度。

By expressing 4-angular momentum of the high-speed particular in the form of tensor ,and by Lorentz transformation,we can get the conversion equation of 3-dimension angular momentum and auxiliary vector.

高速运动质点的4-角动量表示成张量Jμv 的形式，通过对Jμv进行洛伦兹变换可以得到3维角动量L的变换关系以及辅助量G的变换关系，在经典过渡下，前者与角动量的伽利略变换相符合，后者恰好反映加速度a是伽利略变换的不变量。

This equation describes the transformation of the determinant 9 from one reference frame to another.

这个方程式给出了从一个参照标架转到另一个参照标架时行列式9的变换式。

Chapter 4 mainly deals with the Painleve property and Backlund transformation of nonlinear partial differential equation.

第四章考虑非线性偏微分方程的Painleve性质和Backlund变换。

This example is carried through equation transformation, whose last expression is compared with potential function of cusp catastrophe model.

概述了突变理论的几种简单突变模型，通过举例进行方程转化并利用尖点突变模型，对系统进行了脆性分析

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。