Asymptotic behavior of M-estimator and related random field for diffusion process

The M-estimate which maximizes a positive stochastic process Q is treated for multidimensional diffusion models. The convergence in distribution of the process of ratio of Q's after normalizing is proved. The asymptotic behavior of M-estimates is stated. We present the asymptotic variance in general cases and in estimation by misspecified models.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

Banach空间四阶周期边值问题正解的存在性

讨论了Banach空间E中的四阶周期边值问题:( u(4)(t)??u00(t)+′u(t)= f(t; u(t));06 t 61; u(i)(0)= u(i)(1); i =0;1;2;3正解的存在性,其中f :[0;1]￡ P ! P连续, P为E的正元锥,?;′2 R且满足0<′<(?2+2?2)2;?>?2?2;′?4+??2+1>0:通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果.     

Existence of solutions for a nonlinear system with a parameter

In this paper, the existence of solutions for a system of nonlinear equations is considered. n² nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.     

The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval

As an important iteration, the Mann and Ishikawa iteration has extensive application in fixed point theory. In 1991, David Borwein and Jonathan Borwein proved the convergence of the Mann iteration on a closed bounded interval in their paper. In this paper, we will extend their result to an arbitrary interval and to the Ishikawa iteration, indicating the necessary and sufficient condition for the convergence of Ishikawa iteration of continuous functions on an arbitrary interval.     

Long alternating paths in bicolored point sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length . We disprove a conjecture of Erd?s by constructing an example without any such path of length greater than .     

A two-level hedging point policy for controlling a manufacturing system with time-delay,demand uncertainty and extra capacity

This paper focuses on the production control of a manufacturing system with time-delay, demand uncertainty and extra capacity. Time-delay is a typical feature of networked manufacturing systems (NMS), because an NMS is composed of many manufacturing systems with transportation channels among them and the transportation of materials needs time. Besides this, for a manufacturing system in an NMS, the uncertainty of the demand from its downstream manufacturing system is considered; and it is assumed that there exist two-levels of demand rates, i.e., the normal one and the higher one, and that the time between the switching of demand rates are exponentially distributed. To avoid the backlog of demands, it is also assumed that extra production capacity can be used when the work-in-process (WIP) cannot buffer the high-level demands rate. For such a manufacturing system with time-delay, demand uncertainty and extra capacity, the mathematical model for its production control problem is established, with the objective of minimizing the mean costs for WIP inventory and occupation of extra production capacity. To solve the problem, a two-level hedging point policy is proposed. By analyzing the probability distribution of system states, optimal values of the two hedging levels are obtained. Finally, numerical experiments are done to verify the effectiveness of the control policy and the optimality of the hedging levels.     

Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving gronwall's inequality in banach spaces

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α ∈ (n-1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Gronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.     

Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings

We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction.This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space.     

一类单调算子的新不动点定理

利用单调迭代法、数学归纳法以及序差距的性质,在半序Banach空间中探究不具有紧性、连续性以及任何凹凸性的单调算子不动点存在以及惟一性问题,得出其新不动点定理,这些结果对相关结论进行了推广,使其适用范围更广,同时将该结论应用于求解Volterra型积分方程组问题中.