Stochastic averaging of quasi-generalized Hamiltonian systems

A stochastic averaging method for generalized Hamiltonian systems (GHS) subject to light dampings and weak stochastic excitations is proposed. First, the GHS are briefly reviewed and classified into five classes, i.e., non-integrable GHS, completely integrable and non-resonant GHS, completely integrable and resonant GHS, partially integrable and non-resonant GHS and partially integrable and resonant GHS. Then, the averaged and FPK equations and the drift and diffusion coefficients for the five classes of quasi-GHS are derived. Finally, the stochastic averaging for a nine-dimensional quasi-partially integrable GHS is given to illustrate the application of the proposed procedure, and the results are confirmed by using those from Monte Carlo simulation.     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

Distributionally robust Optimal Control and MDP modeling

In this paper we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization.     

自催化三分子模型内噪声随机共振

运用化学Langevin方程 ,数值研究了内噪声对单个和单向耦合自催化三分子模型动力学行为的影响 .研究发现 ,对于单个振子体系 ,内噪声可以诱导持续振荡 ,而且随着系统尺度的增大 ,信噪比经过一个极大值 ,从而证明了内噪声随机共振和最佳尺度效应的存在 ;对于单向耦合系统 ,信噪比还随耦合强度的变化而经过极大值 .此外 ,边界条件对耦合体系的内噪声随机共振行为有很大影响 ,非零流条件下 ,耦合可以增强内噪声随机共振 ,而零流条件下 ,耦合会抑制随机共振 ;当耦合强度适宜时 ,每个振子发生随机共振时的尺度几乎相同 ,表明最佳体系尺度和耦合强度有助于体系达到最佳的化学反应状态 .     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

Nanobuffering property of Fe3O4 magnetic nanoparticles in aqueous solution

In the present study, the buffering effect of magnetite nanoparticles (Fe₃O₄) dispersed in an aqueous solution on the local pH$pH$ value is investigated. It manifests itself in the fact that when some amount of acid or base is added to the solution then the solution near the nanoparticles surface becomes, respectively, less acidic and less alkaline than it is expected. It is the result of both the local electrostatic field, which represents the electric double layer at the surface of magnetic nanoparticles and the magnetic field around the nanoparticles. The magnetite nanoparticles exhibit very low toxicity and they are becoming increasingly important for new biomedical applications related to their effects on chemical reactions in body tissues and cells. The question arises, how strong are these effects at the nanoscale? The strength of the buffering property of magnetite nanoparticles is investigated both theoretically and experimentally by the direct measurement of the local pH$pH$ value of a magnetic nanoparticles suspension. The theoretical model is based on stochastic equations describing the ions diffusing in the neighborhood of the electric double layer of the magnetic material. The electric double layer is modeled with the help of the Poisson–Boltzmann model. It is directly shown that both the electrostatic field and the magnetic field are responsible for the observed local changes of the pH$pH$ value with respect to the bulk pH$pH$ value.     

An approximation algorithm for a facility location problem with stochastic demands and inventories

We propose a 2-approximation algorithm for a facility location problem with stochastic demands. At open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. Costs incurred are expected transportation costs, facility operating costs and inventory costs.     

分层关联表中伞形序对无约束问题的检验

概率分布间的随机序是应用概率论与统计推断中的一个重要概念. 基于交叉分类数据的趋势检验问题已被广泛地研究, 并且分层关联表广泛存在于实践中. 似然比检验方法常用于涉及随机序约束问题的检验. 对带序约束的分层关联表, 该文介绍了一种不基于模型假定的似然比检验方法, 并且给出了检验统计量的极限分布.