Stability and growth estimates for electric fields in non-conducting material dielectrics

Employing results derived by the author for solutions of an abstract integrodifferential equation in Hilbert space, we obtain stability and growth estimates for electric fields in nonconducting material dielectrics. It is assumed that a linear constitutive equation of Maxwell-Hopkinson type relates the electric field and the electric displacement field in the dielectric; specific results for a simple memory function of exponential type are given.     

Cyclotomic Birman–Wenzl–Murakami Algebras,II: Admissibility Relations and Freeness

The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We study admissibility conditions on the ground ring for these algebras, and show that the algebras defined over an admissible integral ground ring S are free S-modules and isomorphic to cyclotomic Kauffman tangle algebras. We also determine the representation theory in the generic semisimple case, obtain a recursive formula for the weights of the Markov trace, and give a sufficient condition for semisimplicity.     

Modelling class hierarchies in the fuzzy object-oriented data model

In this paper we describe a fuzzy logic based approach to modelling uncertainty in class hierarchies. It is shown that the traditional view of class hierarchies is subsumed in this model as a special case. The problem of multiple inheritance in class hierarchies is discussed and analyzed. The membership value derivations in the inheritance hierarchy reflects the degree of fuzziness existing in the data values and the semantics of the situation being modelled. Thus a more realistic modelling of the universe of discourse is possible through this approach. This model is compatible with existing object-oriented data models.     

Group structure and the pointwise ergodic theorem for connected amenable groups

Let G be a connected amenable group (thus, an extension of a connected normal solvable subgroup R by a connected compact group $\text{K =}\text{G}\text{R}$). We show how to explicitly construct sequences {U_n} of compacta in G in terms of the structural features of G which have the following property: For any “reasonable” action G × L^p(X, μ) ↓ L^p(X, μ) on an L^p space, 1 <p < ∞, and any f ∈ L^p(X, μ), the averages

$\text{A}{}_{\mathrm{n}}\text{f=}\text{1}\text{|U}{}_{\mathrm{n}}\text{|}\text{∫}\text{U}{}_{\mathrm{n}}\text{T}{}_{\mathrm{g}}{}^{\mathrm{?1f}}\text{dg (|E|=}\text{left Haar measure in}\text{G)}$

converge in L^p norm, and pointwise μ-a.e. on X, to G-invariant functions $\text{f1}$ in L^p(X, μ). A single sequence {U_n} in G works for all L^p actions of G. This result applies to many nonunimodular groups, which are not handled by previous attempts to produce noncommutative generalizations of the pointwise ergodic theorem.     

Infrared behaviour of propagators and vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by , where Π(k²) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest and neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of via numerical simulations.     

Polyfluorene containing diphenylquinoline pendants and their applications in organic light emitting diodes

We present a short, efficient synthetic route for the preparation of a novel polyfluorene copolymer (PF‐Q) containing two electron‐deficient, 2,4‐diphenylquinoline groups functionalized at the C‐9 positions of alternate fluorene units that form a three‐dimensional cardostructure. The presence of the rigid bulky pendent groups leads to a polyfluorene possessing a high glass‐transition temperature (207 °C) and very good thermal stability (5% weight loss observed at 460 °C). A photoluminescence study revealed that the Förster energy transfer from the excited quinoline groups to the polyfluorene backbone is very efficient; it also demonstrated that the commonly observed aggregate/excimer formation in polyfluorenes is suppressed very effectively in this polymer, even after it has been annealed at 150 °C for 20 h. A light emitting diode (LED) device prepared with PF‐Q as the emitting layer exhibits a stable blue emission with a maximum brightness of 1121 cd/m² at 12 V and a maximum external quantum efficiency of 0.80% at 250 cd/m². We also used PF‐Q, which contains diphenylquinoline units that behave as electron‐transporting side chains, as a host material and doped it with 2.4 wt % of a red‐emitting phosphorescent dye, Os(fppz), to realize a red electroluminescence with CIE color coordinates of (0.66, 0.34). The doped device exhibits a maximum external quantum efficiency of 6.63% (corresponding a luminance efficiency of 8.71 cd/A) at a current density of 47.8 mA/cm², together with a maximum brightness of 10457 cd/m². © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 859–869, 2005     

On the modeling and simulation of induced anisotropy in polycrystalline metals with application to springback

The presence of initial, and the development of induced, anisotropic elastic and inelastic material behavior in polycrystalline metals, can be traced back to the influence of texture and dislocation substructural development on this behavior. As it turns out, via homogenization or other means, one can formulate effective models for such structure and its effect on the macroscopic material behavior with the help of the concept of evolving structure tensors. From the constitutive point of view, these quantities determine the material symmetry properties. Most importantly, all dependent constitutive fields (e.g., stress) are by definition isotropic functions of the independent constitutive variables, which include these evolving structure tensors. The evolution of these tensors during loading results in an evolution of the anisotropy of the material. From an algorithmic point of view, the current approach leads to constitutive models which are quite amenable to numerical implementation. To demonstrate the applicability of the resulting constitutive formulation, we apply it to the case of metal plasticity with combined hardening involving both deformation- and permanently induced anisotropy. Comparison of simulation results based on this model for the bending tension of aluminum-alloy sheet-metal strips with corresponding experimental ones show good agreement.     

A Mild Method for the Esterification of Fatty Acids

In conjunction with a synthetic problem, we were in need of a method for the stoichiometric esterification of fatty acids, containing the aqueous acid labile tert-butyl dimethylsilyloxy group (OTBS), with a variety of alcohols. It has been reported² that fatty acids form acylureas in the presence of dicyclo-hexylcarbodiimide (DCC) and methanol³ without esterification.