Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.     

Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation

In this paper we present the application of a direct demodulation method for the measurement of surface topography by means of Shadow-Moiré. In our set-up, we use three LEDs (with green, red and blue peak wavelengths) to illuminate the grating. Due to the different position of these light sources, a polychromatic Shadow-Moiré fringe pattern is produced, which can be described as the superposition of three monochromatic (red, green and blue) fringe patterns. Taking the image of this polychromatic fringe pattern with a RGB CCD camera, we get a monochromatic fringe pattern stored at each RGB channel of the CCD. The direct demodulation algorithm employed uses these fringe patterns to calculate the wrapped phase map. After unwrapping the phase map using a standard multi-grid technique, we implemented an automatic procedure to detect the area of interest of the phase map by removing low modulation zones and to calculate the absolute value of the phase. In this way it is possible to determine the topography of a surface with a single RGB snapshot maintaining a simple experimental set-up, which is an important feature, especially for the study of dynamic phenomena such as deformations. We present the experimental results obtained after measuring different objects with both smooth and rough surface textures.     

Some global results for eigenvalue problems governed by a variational inequality

In this paper, we use the Leray-Schauder degree theory to obtain some information about the structure of the solution set of a large class of eigenvalue problems governed by a variational inequality. Applications are given to the unilateral postbuckling of a thin elastic plate.     

Degree distribution of the greatest common divisor of polynomials over 𝔽q

We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field ??_q. We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Quantitative and high mass ToF-SIMS studies of siloxane segregation in hydrogel polymers using cryogenic sample handling techniques

This paper examines the capabilities of cryogenic sample handling to examine composition and structure of hydrogel materials where siloxane components are central to the analysis. XPS analysis of multicomponent polymers with cryogenic sample handling following exposure to aqueous environments has revealed the composition and kinetics of near surface reorganization for siloxane and fluorocarbon containing polymers. In this study we report results from a ToF-SIMS protocol for cryogenic sample handling applied to the analysis of surface changes upon hydration/dehydration of hydrogel polymers. Comparison of results from angle dependent XPS and ToF-SIMS are discussed for a range of commercial soft contact lens materials. Both methods detected changes in surface chemistry between the hydrated (frozen) and dehydrated surfaces. Analysis of the hydrated surfaces detected polymer components indicative of the commercial formulation as well as ice clusters. Analysis of the dehydrated materials detected changes in surface chemistry relative to the hydrated surface in addition to loss of water due to sample dehydration. A quantitative standard additions method for ToF-SIMS data was used to determine submonolayer amounts of PDMS impurities at the surface of the hydrogels. ToF-SIMS analysis of a series of seven poly (allyl methacrylate-g-dimethylsiloxane), AMA-g-DMS, graft copolymers in the hydrated state revealed high mass oligomeric ion distributions for systems with bulk PDMS content greater than 25 wt.%. This marks the first time that detection of high mass oligomeric ion distributions from hydrated (frozen) surfaces has been reported. Analysis of the dehydrated surface detected formation of high mass oligomeric ion distributions for systems with PDMS bulk content greater than 15 wt.%, but only detected these ion distributions in wet (frozen) samples when the bulk concentration was greater than 25 wt.%.     

Metal Complexes with Macrocyclic Ligands. Part XXIX.. Structural and kinetic studies of two isomeric Cu2+ complexes with 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetradecane

The synthesis and complexation properties of 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetra-decane ( 2 ) are described. This ligand forms with Cu²⁺ two complexes, one of which has been characterized by X-ray structure analysis. The structural, spectral, and kinetic studies indicate that the two Cu²⁺ complexes are isomers with the macrocycle in the trans-III and trans-I configuration. The rate of the interconversion of the trans-I isomer to the thermodynamically more stable trans-III species is proportional to [OH^?]. A mechanism for this reaction is proposed.