2) analytical approximation
解析逼近
1.
By combining the Newton method with the method of harmonic balance(HB),we have established improved analytical approximations to the period and the corresponding periodic solution to the non-linear Jerk equations.
将牛顿线性化方法与谐波平衡法组合起来建立一类非线性Jerk方程周期及周期解的改进解析逼近。
2.
Based on the analytical approximations to period of nonlinear oscillators with even potential functions,a new analytical approximate period to nonlinear oscillators with general potential functions is established.
利用具有偶势能函数非线性振子周期的解析逼近,建立具有一般势能函数的非线性振子周期的解析逼近,所构造的解析逼近不仅收敛速度快,而且能够建立具有一般势能函数的分段非线性振子周期的解析逼近。
3.
The new analytical approximations for the buckling load and the largest deflection of the Euler\'s column show an excellent agreement with the numerically exact ones,and are valid over nearly the whole range of the independent variable.
基于Euler杆大挠度屈曲的控制方程,构造了屈曲载荷及最大挠度的高精度解析逼近解。
4) smoothing of production
逼近周期循环法
1.
Derived from the concept of smoothing of productions new method,approach-cycle,is put forward.
提了出一种能保证得到多品种混流生产线产品投产顺序优化方案的新的编排方法——逼近周期循环法,较好地解决了生产比例数法和逻辑运算法所存在的问题。
5) asymptotically periodic solution
渐近周期解
1.
We study the periodic solutions and the asymptotically periodic solutions of difference equations with continuous variables, and sufficient conditions for the existence of periodic solutions and asymptotically periodic solutions are obtained.
研究了具连续变量的差分方程的周期解和渐近周期解,并分别获得了周期解和渐近周期解存在性的几个充分条件,我们的结果推广了Agarwal等人的相应结果。
6) the approximate periodic solution
近似周期解
1.
The article mainly discuss the existence and the stability of the approximate periodic solutions for strongly nonlinear quasi-conservative autonomous systems +g(x)=εf(x,).
主要讨论了强非线性拟保守自治系统+g(x)=εf(x,)的近似周期解及其稳定性,并应用以能量函数为基础的摄动法,分析了两个强非线性方程的近似周期解。
补充资料:周期变换逼近
周期变换逼近
approximation by periodic transformations
周期变换逼近[aPpro劝m浦皿by peri威c transf(贫~ti哪:刽口平留。..侧..叫训卿职暇。曰派,二甲“两叩~翻M“」遍历理论(e rgxlic thcory)中的一种方法.具有测度拼的Lebesgue空间X的任意一个自同构T,均可在自同构组成的空间吸内,以自然弱或均匀拓扑,通过一列周期自同构双的极限求得(【11).为了定量地刻画逼近度,不仅要考虑自同构双,还要研究羊舌只否孪的X的有限可测分解(finite measurable decomP‘万itions),即将X分解为有限个互不相交的可测集C。,,,‘’‘,C。,;。,它们在双的作用下,彼此互换.数 乳 d(双Tn;亡。)二艺风TC月.,么Tn瓜,) 资=l给出了关于七。,Tn邻近(proximity)于T的一种估计,这里△是对称差(s帅metrie differenCe) A△B=(A\B)U(B\A)· 假如吼给定,那么可以选取否。和双(具有以上诸性质),使得d(T,兀;亡,)为任意小(Il]).自同构T的度量不变量是明显的,如果我们考虑无限序列双和亡,,使得对每个可测集A,均有一列集人,这里每个人均为某些C,,的并,在 lim风A胡。)=0的意义下逼近A(分解古,收敛于在点上的分解).如果d(T,双;古,)
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