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And the numerical solutions of difference equation are regarded as the approximate solutions for the differential equation.

文中首先对对称正则长波方程提出了一个两层和两个三层的有限差分格式。

And solutions given by the"exact"infinite series solution are compared with solutions calculated by the approximate formula.

比较了"精确的"无穷级数解法和高频近似解。

In Section 1, without assuming operators to be continuous and cones to be normal, we use the Monchs compactness condition to study the existence and iterative approximation theorem of solutions and coupled minimal and maximal quasi-solutions for a class of nonlinear operator equations x = Ax, x under more extensive and weaker conditions than those used in [18] in ordered Banach spaces.

践一节中，利用M加ch的紧性条件，在比文献［18］更广泛的较弱的条件下，在不假潞子连续和拄酬的前提下，研究了Ball''crl空间中一描F线腑子方程X—川巳F）的解和最小最大耦合解的存在与迭代跳定理，并应用到Ban呐空间中非线性VOlterra型积分方程和常徽分方程的初值问题。

Argosy University's Master of Business Administration Program is focused on identifying solutions, putting the solutions to work, and evaluating the consequences of those actions.

康特大学工商管理硕士课程的重点是找出解决办法，把工作的解决方案，并评估这些行动的后果。

Experimental synchronous rotor internal mixer and two kinds of 55L synchronous rotor internal mixer, consulted a number of published articles at home and abroad, then, for the first time, formed four kinds of physical model and the corresponding mathematical model which related to the mixed stock between the mixing chamber side and the top of the rotor wing, to the mixed stock between the two rotors and to the mixed stock at the various temperatures of the mixing chamber. And from the character of model, the author gave the relevant analytic solutions and finite element approximation arithmetic solutions during the experimental process of the synchronous rotor internal mixer.

因此，本文作者在XM—1.7实验用同步转子密炼机和两种50L同步转子密炼机上进行了大量的实验，并参阅国内外已发表的文献和资料，首次建立了同步转子密炼机混炼过程中，胶料在转子棱峰与密炼室壁之间、胶料在两同步转子之间和密炼室中混炼胶温度变化的四种物理模型及其相应的数学模型，并根据所建模型的特点，分别给出了相应的解析解或有限元数值解。

This text studies the obstacle problems associated with nonhomogeneous elliptic equation, gives the definition of solutions of second order degenerate nonhomogeneous obstacle problems, and making use of the Poincaré inequality and others,acquire some properties of these solutions and their lead number,filling up the blank of an nonhomogeneous obstacle problem research.

本文研究了非齐次椭圆方程的障碍问题，给出了二阶非齐次障碍问题解的定义，利用Poincar啨不等式，获得非齐次障碍问题的解及其导数的一些性质，填补了对非齐次障碍问题研究的空白。

Solutions of the network are represented by the eigenvalues and eigenvectors of the symmetric matrix, and the asymptotic behavior of the solutions is analyzed.

这一表达式是由对称矩阵的特征值与特征向量表达的，因而非常清晰。利用解的解析表达式分析了网络的解的全局渐近行为。

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论，研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性，其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

By utilizing the auxiliary ordinary differential equation and its solutions, the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method, and abundant new exact solitary wave solutions were obtained under certain conditions.

利用该方程及其解，采用改进的tanh函数展开法研究了第1类和第2类变系数KdV方程，获得了在一定条件下的若干新精确孤波解。

The auxiliary equation is directly applied to solve the (2+1)-dimensional dispersive long wave equations and the solitary wave solutions and triangular periodic wave solutions are obtained.

利用该辅助方程直接求解了(2+1)维色散长波方程，结果获得了一些孤立波解和周期解，其中包括一些新解。

He's a pretty westernised kind of guy.

他是一个非常西化的人。

National spirit is the moral kingpin for a nation to realize common ideal and goal.

一、中华民族精神的基本内涵党的十六大报告指出：在五千多年的发展中，中华民族形成了以爱国主义为核心的团结统一、爱好和平、勤劳勇敢、自强不息的伟大民族精神。