Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.Comment: 46 pages, no figure; LaTeX2e, amssymb, latexsym; typos correcte

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Continuous dependence estimates for nonlinear fractional convection-diffusion equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.Comment: In this version we have corrected Example 3.4 explaining the link with the results in [51,59

Photonic crystal fiber with a hybrid honeycomb cladding

We consider an air-silica honeycomb lattice and demonstrate a new approach to the formation of a core defect. Typically, a high or low-index core is formed by adding a high-index region or an additional air-hole (or other low-index material) to the lattice, but here we discuss how a core defect can be formed by manipulating the cladding region rather than the core region itself. Germanium-doping of the honeycomb lattice has recently been suggested for the formation of a photonic band-gap guiding silica-core and here we experimentally demonstrate how an index-guiding silica-core can be formed by fluorine-doping of the honeycomb lattice.Comment: 5 pages including 3 figures. Accepted for Optics Expres

Frequency Dependent Specific Heat from Thermal Effusion in Spherical Geometry

We present a novel method of measuring the frequency dependent specific heat at the glass transition applied to 5-polyphenyl-4-ether. The method employs thermal waves effusing radially out from the surface of a spherical thermistor that acts as both a heat generator and thermometer. It is a merit of the method compared to planar effusion methods that the influence of the mechanical boundary conditions are analytically known. This implies that it is the longitudinal rather than the isobaric specific heat that is measured. As another merit the thermal conductivity and specific heat can be found independently. The method has highest sensitivity at a frequency where the thermal diffusion length is comparable to the radius of the heat generator. This limits in practise the frequency range to 2-3 decades. An account of the 3omega-technique used including higher order terms in the temperature dependency of the thermistor and in the power generated is furthermore given.Comment: 17 pages, 15 figures, Substantially revised versio

Harmonizing Software Standards with a Semantic Model

The application of standards in the software development process supports interoperability between systems. Maintenance of standards must be guaranteed on the organisational and technical level. The use of semantic technologies can contribute to the standard maintenance process by providing a harmonizing bridge between standards of different knowledge domains and languages and by providing a single point of administration for standard domain concepts. This paper describes a case study of the creation of a semantic layer between software standards for water management systems in The Netherland