精确解

The method that combines the effective - field renormalization group with the discretized path - integral representation is extenged to study phase transition of the transverse Ising model in a quantum - spin system on the plane triangular lattice.

将离散路径积分表示下的有效场重整化群技巧推广应用于平面三角晶格上量子自旋横向Ising模型的相变研究，在这个方法中，注意区分了两种具有相同配位数而不同几何构形的晶体，并且考虑了起伏的影响，在二阶累积量近似下，得到了接近于精确解的临界值。

Some new exact solutions of the variable coefficient generalized KP equation are obtained by using the extended algorithm.

应用推广后的算法求得了变系数广义KP方程新的精确解。

Seeking the solutions of NLEEs is now a very important subject in Nonlinear Science.The Lie group method is a Powerful tool to study the nonlinear differentical equations.

为了探索这些方程在应用中的价值，求解出各种非线性演化方程或方程组的精确解，是非线性科学中一个很重要的课题。

There have been a lot of studies this aspect when the exact solution u∈H~2 or u∈H~3. [4], [52] and [50]studied the convergence of conforming linear triangle elements with minimal regularity assumptions u∈H~4, here u is the solutions of the second order elliptic problems. However, their is another vital deficiency of the previous studies, i.e., they relies on the regularity assumption or quasi-uniform assumption on the subdivision of meshes.

对二阶问题，构造了一个新的单元格式，当其精确解具有低正则性时，在不要求网格满足正则假设或拟一致假设的条件下，我们得到了最优误差估计，与[33]相比，我们的证明方法较为简单；对于Stokes问题，研究五节点非协调矩形元对它的逼近，通过引入全新的估计方法，给出了关于速度、压力的超逼近性质。

It is very direct and powerful and can be used to construct more new exact solutions of nonlinear evolutionary equations in mathematical physics.

该方法直接而有效，通过适当的变换将非线性发展方程转化为易於求解的微分方程组，从而可用来构造非线性发展方程更多新的精确解。

We also study the property of global tachyon vortex as well as monopole and in the flat spacetime, the exact solutions of them are obtained.

我们研究了整体快子弦和快子单极子的性质，得到了两者在平坦空间下的精确解，发现它们是一类非常弥散的客体，其质量主要分布在核的远处，并且它们的引力效应跟通常的拓扑缺陷也很不相同。

By using the classical or nonclassical Lie symmetry method we can get amount of exact solutions of the nonlinear differential equations.

李群方法是研究非线性微分方程的有力工具，应用经典或非经典李群方法，可得到大量非线性微分方程的精确解。

A closed-form solution of these equations is not available. Therefore, numberical methods are used for their solution.

这些方程的精确解是不可能的，但是可以采用数值方法来计算。

The numerical solution showed that the control strategy in this paper was effective.

数值模拟结果表明，文中的控制策略是可行的，而且可通过文中的方法可得到矩阵黎卡提方程的精确解(在计算机有效精度范围内)。

Ahigh accurate numerical table is obtained and checked by thisprogram.

在这一章，我们完成了上面所遗留的问题，给出了反问题的精确解和它的存在唯一性定理。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。