Dr Perelman proved Poincaré's conjecture by taking an equation normally used to model heat dissipation in three-dimensional objects, known as Ricci flow.
佩雷尔曼博士利用广为人知的“瑞奇流（Ricci flow）”这样一个热方程来证明了庞加莱猜想。
The equation smoothes out the irregularities of an object, transforming it mathematically into something that looks like a uniform three-dimensional sphere.
这个方程能消除物体间的差异，并能把物件精确的变形为一个统一的三维球体。
I now would like to write down, in most general form the equation for the position and the velocity as a function of time for a one-dimensional motion whereby the acceleration is constant.
我来把更一般的形式，写出来吧，在一维空间中，位置和速度，作为时间函数的，一般形式，这里的加速度是一个常数。
At the same time, based on the result, it is concluded that the upwind finite difference scheme for solving the one dimensional heat transfer equation for SG is stable.
同时，根据这个结果分析得到了求解蒸汽发生器一维传热方程的逆风有限差分格式是稳定的。
The three-dimensional heat conduction equation for steady state operating conditions of bipolar microwave power transistors has been solved.
本文对双极性微波功率晶体管(以下简称微波功率晶体管)求解了稳态工作条件下的三维热传导方程。
It is briefly introduced that three-dimensional finite difference numerical equation is built according to Darcy's law and water equilibrium principle.
又简介根据达西定律和水均衡原理，建立了三维有限差分数值方程及其解法。
First, the neutron diffusion equation is converted to three coupled one dimensional partial flux equation through transverse integration.
首先通过横向积分将中子扩散方程化为三个互相耦合的一维偏通量方程。
One dimensional overpotential distribution equation along the direction of the bed thickness is formulated.
建立了固定床内超电位沿床层厚度方向的一维分布方程。
Many of the exact solutions of (3 + 1) dimensional breaking soliton equation are obtained by using a simple transformation relation and solving the ordinary differential equation.
首先通过变换关系和求解简单的常微分方程，得到了(3 +1)维破裂孤子方程丰富的孤立波解和周期波解。
The equation of lattice vibration of one-dimensional monatomic lattice and the equation of longitudinal vibration of a uniform bar are discussed.
一维单原子链晶格振动与均匀杆自由纵振动的运动方程在数学上存在内在的联系。
Based on control equation of three dimensional elasticity in cylindrical coordinate system, the state equation is derived.
根据圆柱形坐标系的三维弹性力学控制方程，导出其状态方程。
The transfer equation for dust given in this paper is a equation of two dimensional airflow diffusion transport.
建立的粉尘在巷道中的传递方程是一个二维平流扩散输运方程。
The discrete ordinate approximation method of three dimensional radiative transfer equation in absorbing scattering medium is expounded.
阐述了含吸收散射性介质三维空腔内辐射传递方程的离散坐标解法。
By making use of the Vlasov distribution theory and the three dimensional wave equation of waveguide modes, the dispersion relation of scattered waves in Compton region is deduced.
利用电子束的弗拉索夫分布函数理论和三维波导模的波动方程求得在康普顿区域中的散射波色散关系。
Taking one-dimensional diffusing equation as the object of study, a method of undetermined coefficients was given. Then gave two examples and analyzed their stability and truncation error.
针对一维扩散方程，给出一种新型差分格式的待定系数法，并以两种新型差分格式为例进行稳定性和截断误差分析。
In this paper, a finite difference domain decomposition algorithm on an unstructured triangular mesh for numerically solving the two-dimensional heat equation is studied.
本文讨论了一类在无结构三角网上数值求解二维热传导方程的有限差分区域分解算法。
The present paper studied the global existence of nonnegative solutions of one-dimensional Newtonian filtration equation with more general boundary fluxes term, reaction, diffusion and convection.
讨论具有一般形式的对流项、扩散项、边界流项以及反应项的一维牛顿渗流方程初边值问题非负解的整体存在性。
A three-dimensional Langevin equation with covariant form is applied to describe the asymmetric nuclear fission.
采用一个具有协变形式的朗之万方程组来描述不对称热核裂变。
The application of the steady-state equation in one-dimensional transport processes of gas is discussed and the physical meaning of the equation is analyzed.
分析讨论了气体输运过程的稳定态方程的物理内涵，以及在气体一维输运过程中的应用方法。
The initial boundary value problem for nonlinear hyperbolic equation in three dimensional domain with moving boundary is studied.
研究具有变动边界的三维区域上的非线性双曲型方程的初边值问题。
So this method is effective in soluting two-dimensional parabolic equation and can be widely used.
该方法是求解二维抛物型方程的有效方法，必将得到更广泛的应用。
Based on two-fluid model of ion and electron and Maxwell equation, the two-dimensional magnetohydrodynamic (MHD) model of vacuum arc was obtained.
以离子与电子的双流体模型以及麦克斯韦方程为基础，推导得到了真空电弧的二维磁流体动力学(MHD)模型。
This model is based on a one - dimensional heat conduction equation, an equilibrium press- temperature relation, energy and mass conservation relations.
喷墨过程的数值建模是建立在一维热传导公式，温度-压强关系式和能量、物质转换关系的平衡的基础上的。
Using the theory of wave propagation, one-dimensional wave equation and inverse problem of damaged medium was established and analyzed.
利用波传播理论，建立损伤介质的一维波动方程及反问题分析理论。
The slip coefficient B is introduced in momentum equation of one dimensional nucleating flow.
本文在一元蒸汽凝结流动量方程中引入了滑移系数B，考虑两相滑移的影响。
The variable separation approach is used to obtain coherent soliton structures of a new (2 + 1) dimensional evolution equation.
用分离变量法研究了新(2 +1)维非线性演化方程的相干孤子结构。
The function of the dimensional equation in identifying the relationship between physical quantities is also mentioned.
论述了量纲式配合普遍形式的物理方程在辨识物理量之间关系时的作用。
In this paper, for solving the parameter problem of two dimensional wave equation, the method of Finite Element and the Pulse Spectrum Technique, i. e. the iterative process are used.
本文针对求解二维波动方程的参数问题，利用有限元方法把波动方程反问题转化为有限元反问题，并利用脉冲谱技术，即一个迭代过程进行求解。
In this paper, we consider two dimensional singular integral equation with two shifts.
本文研究带两个位移的二维奇异积分方程。
In this paper, we consider two dimensional singular integral equation with two shifts.
本文研究带两个位移的二维奇异积分方程。
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