On Approximations of First Integrals for Strongly Nonlinear Oscillators

In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations. In particularthe generalized Rayleigh oscillator equation will be studied in detail, and it will beshown that at least five limit cycles can occur.     

Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails

We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation.     

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses values of linear functionals (integrals over hyperspheres) and is exact for all -harmonic functions, and consequently, for all algebraic polynomials of variables of degree .

     

强耦合混沌系统中的近似同步

以单向驱动耦合Lorenz振子一维链为研究对象，研究振子间的混沌同步行为. 数值计算结果表明，对于变量y驱动x的耦合方式，在合适的耦合强度下，会出现第一个振子和第二个振子不同步，而与次近邻非直接连接的振子(如第三个振子)近似同步. 进一步研究表明，出现这一现象的原因是在大耦合强度下，对于这种驱动方式，第一个振子和第二个振子间出现驱动单变量近似同步；虽然它们之间未出现所有变量的完全同步，但是驱动信号事实上已经传递下去了. 关键词： Lorenz振子 混沌同步 近似同步     

利用弹簧振子演示李萨如图形

介绍了利用光滑导轨、弹簧振子、高亮发光二极管演示李萨如图形的方法.     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

Mn22+离子1s22s-1s2np的偶极跃迁能和振子强度

用全实加关联方法计算了类锂Mn22 离子1s22s-1s2np(2≤n≤9)的偶极跃迁能和振子强度.1s2np(2≤n≤9)态的精细结构通过计算自旋-轨道与自旋-其他轨道相互作用算符的期待值确定.依据单通道量子亏损理论,确定了Rydberg系列1s2np的量子数亏损.从而可以用这些作为能量的缓变函数的量子亏损,实现对任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离阈附近束缚态-束缚态跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将Mn22 离子的这一重要光谱特性的理论预言外推到整个能域.     

三维各向同性谐振子波函数的递推关系(英文)

本文应用拉普拉斯变换得到了三维各向同性谐振子波函数边界的精确解,同时,利用同种方法还得到了利用产生算符和湮灭算符表达的该波函数的递推关系.     

超辐射机制相对论返波管的数值计算

 运用相对论返波管非线性理论，推导出描述相对论返波管束波互作用的非线性自洽方程组；数值求解了该非线性自洽方程组，揭示了相对论返波管中由非稳态束波互作用产生的超辐射现象的基本规律：输出超辐射波峰值功率大约与参与互作用电子总电荷量的平方成正比。并将超辐射和由稳态束波互作用所产生的受激辐射作了相关比较,结果表明：超辐射是短电子束脉冲产生非稳态束波互作用的结果，而受激辐射是长电子束脉冲产生稳态束波互作用的结果；不断增加电子束脉冲宽度，辐射机制由超辐射转变为受激辐射。     

Constructing the time independent Hamiltonian from a time dependent one

In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.