ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

Assembly of bifunctional receptors via the melamine-barbiturate structural motif

An assembly of cation receptor 1 and anion receptor 2 via the hydrogen bonding melamine-barbiturate structural motif complexes sodium thiocyanate, sodium iodide, and sodium azide in apolar solvents.     

Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers

We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self-induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two-dimensional spatial optical solitons. We apply the matrix criterion for stability of these two-parameter solitons, and verify it by direct numerical simulations.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .     

Fractal character of effective Hall properties of a three-dimensional disordered composite

The dependencies of the effective Hall properties on a scale, obtained by means of an iterative averaging method, manifest their fractal character. The influence of an intensity of the Hall effect on the fractal character of the Hall properties was considered. Scale ranges and dimensional characteristics of the effective Hall properties behavior were calculated and discussed.     

Limit theorems for partially hyperbolic systems

We consider a large class of partially hyperbolic systems containing, among others, affine maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms. If the rate of mixing is sufficiently high, the system satisfies many classical limit theorems of probability theory.

     

Quantization of lie Bialgebras via the Formality of the operad of Little Disks

We give a proof of the Etingof–Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck–Teichmüller group acts non-trivially on the corresponding quantization functors. Partially supported by an NSF Grant and A. Sloan Research Fellowship Received: November 2004 Revision: April 2006 Accepted: May 2006