Nonlinear Amplitude-Phase Effects in Selective Reflection from a Resonance Gas

Selective reflection of a laser wave from a resonance gas is considered for arbitrary intensity, polarization, and angle of incidence on the interface. Variations of the reflection spectra nonlinear in the wave amplitude are studied taking into account the nonlinear increment of the optical phase upon reflection. The result of this increment is a quadrature component of the reflected wave shifted by a quarter period, which may be observed using the homodyning technique (optical mixing). The regularities studied are of interest both for spectroscopy and for nonlinear transformations in the quantum statistics of reflected light.     

Synthesis of ordered Ge-Si heterostructures containing ultrasmall germanium nanoclusters

Different techniques for the fabrication of structures containing ensembles of ultrasmall germanium nanoclusters distributed with a high density over the substrate surface are discussed. How to control the morphology and ordering of these ensembles is also discussed.     

Synthesis and characterization of oxidized cellulose

Samples of oxidized cellulose (OC) with various carboxyl contents and degrees of crystallinity were obtained by the oxidation of native and mercerized cellulose with a solution of nitrogen(IV) oxide in CCl₄. A detailed characterization of these OC samples was performed. The effect of oxidation conditions (concentration of N₂O₄ in the solution and oxidation time) and starting cellulose material on OC characteristics (carboxyl, carbonyl and nitrogen content, degree of crystallinity and polymerization, surface area and swelling, and acidic properties) was investigated. Reactivity in the oxidation process was higher in mercerized cellulose than in native cellulose. The action of dilute solutions (10–15%) of N₂O₄ did not affect the degree of crystallinity of cellulose samples. Under these conditions, the oxidation took place mainly in amorphous regions and on the surface of crystallites. Oxidation in a concentrated (40%) N₂O₄ solution led to the destruction of crystallites, which increased the surface area and swelling of cellulose in water. The surface area and the swelling of OC samples increased with a decrease in the index of crystallinity. The acidic properties of OC were shown to increase with an increase of swelling in water. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4785–4791, 2004     

Deviation inequality for monotonic Boolean functions with application to the number of k‐cycles in a random graph

Using Talagrand's concentration inequality on the discrete cube {0, 1}^m we show that given a real‐valued function Z(x) on {0, 1}^m that satisfies certain monotonicity conditions one can control the deviations of Z(x) above its median by a local Lipschitz norm of Z at the point x. As one application, we obtain a deviation inequality for the number of k‐cycles in a random graph. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

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.