Hyperspaces of Normed Linear Spaces with the Attouch–Wets Topology

Let Cld _AW (X) be the hyperspace of nonempty closed subsets of a normed linear space X with the Attouch–Wets topology. It is shown that the space Cld _AW (X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then Cld _AW (X) is homeomorphic to a Hilbert space with weight 2 ^w(X).     

Gaussian Chaos Laws on Banach Function Spaces

We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ _∞ ⁿ 's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces. __________ Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005.     

Boundedness of Multilinear Operators on Herz Type Spaces： Extreme Cases

In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases.     

Stable nonequilibrium probability densities and phase transitions for meanfield models in the thermodynamic limit

A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.     

The moduli space of flat SU (2) and SO (3) connections over surfaces

All the connected components of the moduli space of flat connections on SU (2) and SO (3) (trivial and non-trivial) bundles over closed oriented surfaces are determined. The symplectic structure and volumes of the non-maximal strata of the moduli space are also determined.     

随机化交通灯的二维元胞自动机交通模型

元胞自动机交通模型以简单的规则反映交通系统中的多种因素，可以分析各种交通现象，且可在计算机上方便、高效地运作·Ｂｉｈａｍ－Ｍｉｄｄｌｅｔｏｎ－Ｌｅｖｉｎｅ模型（ＢＭＬ模型）实现了二维交通问题的元胞自动机模型的模拟研究·本文对ＢＭＬ模型作了改进，解除了该模型中关于交通灯同步变化的限制·在新模型中，每个路口的交通灯可以自由选定起始工作时间和变化节奏，于是可以更全面、准确地反映交通灯对交通系统性能的影响·本文还对新模型中出现的若干新效应作了解释·     

A highly selective solid phase extraction sorbent for pre-concentration of sameridine made by molecular imprinting

Summary A novel approach to solid phase extraction, based on the use of a highly selective molecularly imprinted polymer, is presented. The versatility of this type of sorbent for solid phase extraction was demonstrated in a model batch-wise pre-concentration of sameridine prior to gas chromatography. Problems associated with leakage of remaining imprint molecules during the desorption phase could be eliminated by the use of a close structural analogue of sameridine as the imprint species. It was found that a major benefit of the imprinted polymer was its specificity, which lead to distinctly cleaner chromatographic traces and ability to improve sensitivity by extracting sameridine from larger sample volumes.     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Sets of sampling and interpolation in Bergman spaces

Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip (1993). Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk.