三次方程

By virtue of method of continuum approximate limit, we obtained the solitons of the vibration of lattice in one-dimensional harmonic and inharmonic chains of polarized molecule, under the conditions considering and inconsidering the interaction of exciton with phonon, through solving moving equations of exciton and phonon.

运用连续极限近似方法，通过求解声子和激子的运动方程，得到了在不考虑激子与声子的相互作用和考虑激子与声子相互作用两种情况下的极性分子简谐链和非简谐链中晶格振动的孤子解，并得出了激子与声子的相互作用的非线性效应类似于晶格三次势的非线性效应，以及相同的非线性效应不论是同时作用还是单独作用都具有相同的非线性效应的结论。

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

The results indicated:① In general,the changes of soil moisture conte...

用SPSS统计软件进一步对土壤水分与土层深度的关系进行拟合，结果表明土壤水分与土层深度的关系具有极强的相关性，其关系方程为拟和三次抛物线型。

This paper studies a class of cubic system with planar polynomial.We use the qualitative theory of ordinary differential equations method of analysis, reached the following conclusions of four parts: First, we analyze the quality of all critical points of the system,and draw the conditions of existence of singular integrals for the system , in front based on the analysis, using Pioncare form series method to calculate the focal value of o(0,0). Finally, we also study the behavior of critical points at infinity.

中文摘要：本文研究了一类平面三次多项式系统，我们采用常微分方程的定性理论的分析方法，得出如下四个部分结论：第一部分，分析系统所有奇点的性态，并得出系统存在奇异积分直线的条件；在前面分析的基础上，用Pioncare形式级数法，计算出了系统在奇点o(0，0)的三个焦点量；最后，研究了系统无穷远奇点的性态。

Based on vector expression of parametric equation of a third－order Bezier curve, Bezier curve interpolation algorithm is proposed in order to imitate tabulation curve.

为了描述列表曲线，本文从三次Bezier曲线参数方程的矢量表达式出发，推导出CNC系统三次Bezier曲线插补法。

Understand 3 times, the development history.2 of formula of 4 equation extract a root.

了解三次、四次方程求根公式的发展历史。2。

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。

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。

This thesis will be expanded from two aspects: first, delta-sequence obtained by cubic spline interpolation cardinal function showed the properties of symmetry, Riesz basis and interpolation. Non linear convection diffusion equation (Burgers′equation) was used as an example. Then we modified this delta-sequence to improve the attenuation, the same example was used in numerical application.

在小波方法与PDE算法相结合方面，本文主要从两方面入手：首先是以样条插值基函数为基础构造δ-序列核，以非线性对流扩散方程为例给出了一种数值算法；进而对三次样条插值基函数进行改进，构造新的具有更快衰减性质的δ-序列核，同样以非线性对流扩散方程为例验证了新函数在数值求解中的有效性。

A set of quadruply coupled equations (fluid flow, convection-diffusion, energy conservation and mechanical equilibrium) with a number of cross-couplings and coupled constitutive relations is formulated to quantify the multi-physics of oil displacement by CO2 injection, implemented into and solved by using FEMLAB. FEMLAB is the first engineering tool that performs equation-based multi-physics modeling in an interactive environment. With FEMLAB, the coupled multi-physics model can be solved simultaneously. The applicability of this model has been demonstrated through an example of simulations for a two-dimensional reservoir of size 1000 m×1000 m with one injection and one production wells. Model results illustrate the significant importance of the cross-couplings between individual (thermal, hydrological, chemical and mechanical) physics.

首先，建立一套流、固、热、多相流等多场全耦合控制方程组及其相应的耦合本构关系；然后，采用FEMLAB为工具来模拟三次采油阶段CO2驱油过程中的流、固、热、物质守恒等多场之间的全耦合作用，是第一个人机交互式的基于偏微分方程组的多物理场耦合分析的工程工具，利用FEMLAB，该4个耦合方程组成的方程组可以一次同时被求解出来：最后，应用该模型来求解一个二维油田的驱油情况，数值计算结果表明，原位应力、注入温度、注入压力等因素对CO2的地下贮存效率、驱油速度等有重要影响。

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。