沪深港股市相关性的小波分析

主要使用离散小波变换(DW T)对沪深港股市的相关性进行研究.小波可以把方差和相关系数在不同尺度上进行分解,以便更仔细地研究时间序列的波动性在不同尺度上的相关程度.研究发现:三地股票市场的波动性都随着小波尺度的变化而变化;沪深股市与香港股市相关性非常低,而且在不同尺度上相关程度有较大差别.     

一类广义指派问题的有效解法

提出一类广义指派问题,这类问题研究的是m个人执行n项任务,每个人执行的任务数、执行每项任务的人数以及总的指派人项数均有限制,要求最优指派.对这类广义指派问题建立了数学模型,并找到一种转换方法,将这类问题转换为平衡指派问题,从而用传统方法,如匈牙利法求解.最后用一个箅例来说明这种转换方法的简便和有效性.     

Stationary optimal control of a stochastic system with stable environmental interferences

In this paper, we consider a class of nonstationary control systems. We obtain some conditions for stationary optimal controls of such systems. The results are then applied to a linear-quadratic system.     

Ergodicity of asymptotically mean stationary channels

Some equivalence conditions for an asymptotically mean stationary channel to be ergodic are given. Incidental results on asymptotically mean stationary measures are also given. Absolute continuity of measures plays a crucial role.     

Decaying states of perturbed wave equations

We study the solutions of perturbed wave equations that represent free wave motion outside some ball. When there are no trapped rays, it is shown that every solution whose total energy decays to zero must be smooth. This extends results of Rauch to the even-dimensional case and to systems having more than one sound speed. In these results, obstacles are not considered. We show that, even allowing obstacles, waves with compact spatial support cannot decay, assuming a unique continuation hypothesis. An example with obstacle is given where nonsmooth, compactly supported, decaying waves exist.     

Generalizations of P. Lévy's inversion theorem

We extend the Lévy inversion formula for the recovery of a bounded measure over $\text{R}$ from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for $\text{R}$.     

Subordination,rank, and determinism of multivariate stationary sequences

Necessary and sufficient conditions for an arbitrary q-variate stationary sequence x_t, t ∈ $\text{Z}$, to be deterministic are presented. A characterization of the rank r(x) of x_t, t ∈ $\text{Z}$, and a method to construct the Wold-Cramér decomposition for x_t, t ∈ $\text{Z}$, are given. Subordination of q-variate bounded orthogonally scattered vector measures is considered.     

Molecular level study of the crystallization of a thermoplastic polyimide by infrared spectroscopy

The crystallization process of the thermoplastic polyimide derived from 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA) and 2,2-dimethyl-1,3,-(4-aminophenoxy) propane (DMDA) is studied at the molecular level by utilizing infrared spectroscopy's sensitivity to local molecular environment. Assignments of the unique spectral features appearing upon crystallization are made with additional verification from crystalline model imide compounds. A direct comparison of an annealed polyimide film studied by both infrared spectroscopy and x-ray diffraction shows fairly close agreement in the amount of crystallinity obtained. The unique crystalline infrared spectral features provide insight into the molecular mechanism involved with the crystallization process. Spectral shifts occurring upon crystallization reflect intramolecular rotations toward increased coplanarity as well as intermolecular chain packing of certain molecular groups at specific sites of the chain backbone. The site specific information is then used to study the relative kinetic behavior of the intramolecular and intermolecular effects occurring during crystallization. © 1994 John Wiley & Sons, Inc.     

On maximizing the average time at a goal

In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary decision sets (gambles or actions), there is always available a Markov strategy which uniformly (nearly) maximizes the average time spent at a goal. If the decision sets are closed, there is even a stationary strategy with the same property.Examples are given to show that approximations by discounted or finite horizon payoffs are not useful for the general average reward problem.     

Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation

An original method to detect images in defocused scenes by means of a binary joint transform correlation is presented. Defocused images are described in frequency domain as the product between the Fourier transform of the in-focus scene by the optical transfer function of the imaging lens. This function, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm. Information provided by the algorithm allows to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.