6,465 research outputs found
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
- …