查询词典 particular solution

However, the second associated Legendre function is too complicated to compute, so a simple and practical ellipsoidal harmonic series expansion is introduced, and the series solution and integral solution of the Dirichlet boundary value problem and the Neumann boundary value problem under ellipsoidal boundary are given.

鉴于展开式中第二类缔合勒让德函数的计算较为复杂，接着引入一种形式简单、实用的椭球谐级数展开，介绍了椭球界面下Dirichlet边值问题和Neumann边值问题的级数解和积分解。

Algorithm application of neural networks.Ⅲ Implementation of neuro-computers. The main contribution of the dissertation can be summarized as follows: 1 Hopf bifurcation of three kind of neural networks are discussed in detail, including type of discrete time delay, type of time delay with weak kernel and strong kernel as well as the proof of existence of bifurcation. Other problems such as asymptotic stability of bifurcation periodic solution, algorithm of determining the bifurcation direction, asymptotic stability and style of periodic solution are also studied. The average time delay is chosen as the bifurcation parameter, phenomena pertinent to system states of the continuous time delay network with strong kernel evolving from stable to oscillating, then back to stable again are observed.

论文的主要创新之处可以归纳如下： 1）针对目前国内外对神经网络的分岔研究较少的情况，论文中详细讨论了带离散时延神经网络、带弱核的连续时延神经网络、带连续分布时延且具有强核的神经网络的Hopf分岔现象，从理论上证明了Hopf分岔的存在性，并研究了分岔周期解的渐近稳定性，得到了确定周期解的渐近稳定性、分岔方向、周期解的渐近形式的算法；用平均时延作为分岔参数，发现带强核的连续时延神经网络中存在着系统的状态由稳定变化到振荡现象，当继续增加平均时延参数时，又从振荡变为稳定这一特殊的动力学现象。

Basing on this, the formal asymptotic expansion of solution for the original problem is obtained. Finally, under suitable conditions, existence and its uniform validity of asymptotic expansion of solution for the initial boundary value problem are proved,by using theory of differential inequalities.

在这基础上得到了原问题解的形式渐近展开式；最后，在适当的条件假设下，利用微分不等式理论，证明了原初边值问题解的存在性及其渐近展开式的一致有效性。

This paper, considers conservative equation with periodic boundary value problem, and construct a difference scheme, Uses the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, proves that the scheme converges uniformly to the solution of differential equation with order one.

研究守恒型奇振动方程的周期边界问题，构造一个差分格式，利用分解解的奇性项的方法，结合问题的渐近展开，证明所构造的差分格式为一阶一致收敛。

The uniformly valid asymptotic expansion of the solution to a class of time delay differential equations with damping term and general forcing term was obtained and a simple analytic approximate expression for the resonance solution was given.

对于一类带阻尼和一般力的时滞微分方程问题求得一致有效渐近展开式，给出了共振解筒洁的近似解析表达公式。

Based on the solution for incompressible materials, the asymptotic solution of the order up to ∈~2 is obtained.

第一种方法以学术界普遍接受的高玉臣与Rice等的不可压缩(ν=1/2)理想弹塑性扩展裂纹尖端场为基础，以ε=1/2-ν为小参数作摄动展开，得到了直到ε~2阶的渐近解。

The new method has advantage of asymptotic solution, numerical solution and BVT method. It is useful and efficient in practical application.

混合算法结合了渐近解、数值解和BVT法的优势，是一个实用、有效的算法。

A class of SIR model with transportation is studied. We studied the unique existence of solution and the asymptotic behavior of its stationary solution.

研究一类具有迁移的无垂直传染的SIR模型，讨论了其解的存在惟一性和拟稳态解的渐近性态。

Using the fixed point principle and the theory of differential inequality, we prove the existence of the solution and an uniformly valid asymptotic expansions of the solution is given as well.

利用不动点原理及微分不等式理论，我们证明了边值问题解的存在性，并给出了解的一致有效渐近展开式。

With the controller, the closed-loop system has a unique solution and the trivial solution is asymptotically stable.

简单的数值例子表明了方法的可行性。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48