Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations

Let {X_k}_k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?→? define Y_k=X_g(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Y_k} is studied when X_k has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Y_k} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd.     

A Liouville type theorem for polyharmonic elliptic systems

In this paper, we consider the polyharmonic system m(−Δ)U=Vq,m(−Δ)V=Up in RN, for m>1, N>2m, with p?1, q?1, but not both equal to 1, where m(−Δ) is the polyharmonic operator. Set α=2m(q+1)/(pq−1), β=2m(p+1)/(pq−1), for α,β∈[(N−2)/2,N−2m), we prove the nonexistence of positive solutions.     

Approximation of signals from local averages

This work is concerned with approximation of a signal from local averages. It improves a result of Butzer and Lei [P.L. Butzer, J. Lei, Approximation of signals using measured sampled values and error analysis, Commun. Appl. Anal. 4 (2000) 245–255].     

UNIQUENESS PROBLEM WITH TRUNCATED MULTIPLICITIES OF MEROMORPHIC MAPPINGS FOR MOVING TARGETS

In this article,two uniqueness theorems of meromorphic mappings on moving targets with truncated multiplicities are proved.     

Interactions between kinetic and radiative processes inside moving absorbing fluids

The aim of this paper is to present several features of the couplings occurring between radiative transfer and the kinetics of a moving dielectric. After determining how the velocity field affects the apparent thermo-optical properties of matter, the energy transport problem is investigated in instationary regime and the general form of transient radiative transfer equation inside a moving medium is built. Then, the model is applied to the particular case of turbulent flows: a system of two equations for mean and fluctuating radiative energies is presented, and the resolution of this system is finally carried out.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Novel simulated moving-bed adsorber for the fractionation of gas mixtures

The separation of propylene-propane mixture is an energy intensive operation commercially practiced using cryogenic distillation. The separation by pressure swing adsorption has been studied as an alternative. A fixed-bed pressure swing adsorption yields the heavy component as a pure product. The product recovery and the productivity are not high. In a moving-bed process, because of the counter-current solid-gas contact, the separation achieved is similar to that of the fractionation by distillation. Although the moving-bed operation offers the upper limit for the performance of a cyclic adsorptive process, due to mechanical complexities in the handling of solids the 'simulated' moving-bed is preferred. By moving the inlet and outlet ports of streams located along the length of the bed, a moving-bed process can be realized in a fixed bed. We describe here a 'moving-port' system which permits injection or withdrawal of the fluid along the axial direction in a fixed bed. A fixed bed embedded with the moving-port systems emulates a simulated moving-bed adsorber. The proposed adsorber can fractionate a binary gas mixture into two product streams with high purities. It is similar to the Sorbex process of UOP but does not have the eluent as an additional separating agent. A parametric study indicates that high purity products and a higher productivity by an order of magnitude can be achieved with simulated moving-beds compared to the fixed beds.     

Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares

Changeable size moving window partial least squares (CSMWPLS) and searching combination moving window partial least squares (SCMWPLS) are proposed to search for an optimized spectral interval and an optimized combination of spectral regions from informative regions obtained by a previously proposed spectral interval selection method, moving window partial least squares (MWPLSR) [Anal. Chem. 74 (2002) 3555]. The utilization of informative regions aims to construct better PLS models than those based on the whole spectral points. The purpose of CSMWPLS and SCMWPLS is to optimize the informative regions and their combination to further improve the prediction ability of the PLS models. The results of their application to an open-path (OP)/FT-IR spectra data set show that the proposed methods, especially SCMWPLS can find out an optimized combination, with which one can improve, often significantly, the performance of the corresponding PLS model, in terms of low prediction error, root mean square error of prediction (RMSEP) with the reasonable latent variable (LVs) number, comparing with the results obtained using whole spectra or direct combination of informative regions for a compound. Regions consisting of the combinations obtained can easily be explained by the existence of IR absorption bands in those spectral regions.     

Controllability of the wave equation with moving point control

This paper deals with approximate and exact controllability of the wave equation in finite time with interior point control acting along a curve specified in advance in the system's spatial domain. The structure of the control input is dual to the structure of the observations which describe the measurements of velocity and gradient of the solution of the dual system, obtained from the moving point sensor. A relevant formalization of such a control problem is discussed, based on transposition. For any given timeinterval [0,T] the existence of the curves providing approximate controllability inH _D ^–[n/2]–1 ()×H _D ^–[n/2]–1 () (wheren stands for the space dimension) is established with controls fromL ²(0,T; R ⁿ +1). The same curves ensure exact controllability inL ²() × H^–1() if controls are allowed to be selected in [L (0,T; R ⁿ+1)]. Required curves can be constructed to be continuous on [0,T).This work was supported in part by NSF Grant ECS 89-13773 and NASA Grant NAG-1-1081.     

动态单滴法研究乳状液液膜的稳定性

乳状液液膜作为化学分离的一种手段,自七十年代发现以来已有了许多进展,但是如何将其工业化还有许多课题有待于进一步研究.目前,除了乳状液液膜的水静态渗透性质以外,对乳状液液膜的稳定性和溶胀性质的研究主要采用搅拌法.虽然得到较好的规律性,但是搅拌法具有乳状液滴粒径分布广的弱点,对于不同的搅拌方式及条件,乳状液液膜的有效面积不同,对液膜作用的机械强度不同,因此结果会有很大差别.我们自行设计的动态单滴法实验装置,可定量地研究乳状液液膜的溶胀、稳定性及水渗透性质.