Quaternions for GUTs

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyze possible quaternionic groups for GUTs.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.     

Gevrey properties of real planar singularly perturbed systems

By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions.     

Nonlinear optical properties of regioregular main‐chain polyesters

We have prepared new polyesters containing quadratic, nonlinear optical (NLO) active chromophores covalently incorporated into the main chain. In these polymers, the sequence of the chromophore units along the main chain is rigorously head to tail. All the polyesters are processable, both in the melt and in solution. For one polyester, a full second‐order NLO characterization has been performed. An out‐of‐resonance d₃₃ coefficient of 21 pm/V at 1368 nm has been measured. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2719–2725, 2007     

Carbide precipitates in solution-quenched PH13-8 Mo stainless steel: A small-angle neutron scattering investigation

This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.     

Performance evaluation of fiber Bragg grating sensors by digital holographic technique, strain gauge measurement

In view of the growing interest for non-destructive tests of materials, geodynamical monitoring and in general remote sensing, there is a great effort to bring practical optical sensors from research labs to industrial and environmental applications. In this paper, we employ digital holographic technique as an efficient tool for evaluating the strain measurement capability of fiber Bragg gratings (FBG). A cantilever beam has been employed as a test structure under loading test. The strain measurements results obtained by fiber-based sensors have been compared to those obtained by using full-field digital holographic technique and point-wise strain gauge sensors glued on the same cantilever beam. A simple theoretical model is also presented to interpret and compare the experimental results coming from different techniques.     

A Tin(IV) Porphyrin with Two Axial Organometallic NCN‐Pincer Platinum Units

A tin(IV) porphyrin was combined with two axial NCN‐pincer platinum(II) fragments by utilizing the oxophilicity of the apical positions on the tin atom and the acidic nature of the NCN‐pincer platinum derived benzoic acid. The solid‐state structure determined by X‐ray crystallography revealed some close contacts between the pincer complexes and the meso‐p‐tolyl subsitutents of the porphyrin. It was shown by ¹H NMR spectroscopy that these close contacts were not present in solution and that this compound can potentially act as a novel building block for supramolecular architectures.     

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.     

On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002