A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.     

Coordinating inventory control and pricing strategies: The continuous review model

We analyze an infinite horizon, single product, continuous review model in which pricing and inventory decisions are made simultaneously and ordering cost includes a fixed cost. We show that there exists a stationary (s,S) inventory policy maximizing the expected discounted or expected average profit under general conditions.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

Allocating unfunded liability in pension valuation under uncertainty

This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works.     

简并光学参量振荡器混沌反控制

提出一种实现简并光学参量振荡器混沌反控制的方法，用正弦信号调制简并光学参量振荡器的基模衰减率，使简并光学参量振荡器从定态输出转化为混沌态.数值模拟结果表明，选择不同的调制幅度和调制角频率，只要满足系统的最大李雅谱诺夫指数大于零，即可实现不同的混沌轨道重构.通过比较最大李雅谱诺夫指数λ_max随调制幅度和调制角频率变化曲线， 指出系统从周期态调制到混沌态比从无亚谐波输出的定态调制到混沌态更容易，有更宽的调制幅度和调制角频率选择范围. 关键词： 简并光学参量振荡器 混沌反控制 调制     

Particle systems on flows

We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

类锂离子与软X射线激光研究有关的跃迁波长和振子强度

本文用多组态HXR自洽场方法和优化以Slater径向积分法相结计算了类锂离子(Z=13～17,19)1s~2nl~2LJ(2≤n≤5,0≤l≤4)能级之间的跃迁波长和振子强度,并和实验进行了比较。就软X射线激光跃迁4f—3d而言,本文计算的波长值比其它文献的计算值更接近于观测值。     

Equivariant mappings: a new approach in stochastic simulations

Stochastic simulations on manifolds usually are traced back to ⁿ via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry.