A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes

We consider a convection–diffusion problem with Dirichlet boundary conditions posed on a unit square. The problem is discretized using a combination of the standard Galerkin FEM and an h–version of the nonsymmetric discontinuous Galerkin FEM with interior penalties on a layer–adapted mesh with linear/bilinear elements. With specially chosen penalty parameters for edges from the coarse part of the mesh, we prove uniform convergence (in the perturbation parameter) in an associated norm. In the same norm we also establish a supercloseness result. Numerical tests support our theoretical estimates.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

On Quasi-Hopf Smash Products and Twisted Tensor Products of Quasialgebras

We analyze some relations between quasi-Hopf smash products and certain twisted tensor products of quasialgebras. Along the way we obtain also some results of independent interest, such as a duality theorem for finite dimensional quasi-Hopf algebras and a universal property for generalized diagonal crossed products.     

On the Hellmann–Feynman theorem and the corrections to the energy in the Rayleigh–Schrödinger perturbation theory

In this work we present an alternative method, based on the Hellmann–Feynman theorem, to generate energy corrections within the standard Rayleigh–Schrödinger perturbation theory. As a result, compact expressions for the corrections to the energy at different orders are obtained. We also review a method that allows us to calculate the corrections to the wave function needed in the energy calculations. Finally, our results are compared with those obtained by other authors by a different technique.     

Vortex dynamics on a domain with holes

We explore the relationship between the hydrodynamic Green’s function and the Dirichlet Green’s function in a bounded domain with holes. This relationship is expressed using the harmonic measures on the domain, following the work of Flucher and Gustafsson (Vortex motion in two-dimensional hydrodynamics, energy renormalization and stability of vortex pairs, TRITA preprint series, 1997). The explicit form of this relation expresses velocity in terms of vorticity in a way which turns out to be very convenient, especially for analysis. We explain the advantages and describe some applications.     

Self-cleaning effect of sealing caps for infrared hollow fiber delivering pulsed Er:YAG laser light

A sealing cap had been proposed as an output device for hollow optical fibers in delivering laser light underwater. Properties of sealing cap were experimentally discussed when used in ablation on soft tissue for Er:YAG laser. A self-cleaning effect of the sealing cap was observed when various targets were used for different laser light power. Debris from pork fat formed a uniform oil layer on the output surface of the cap, and the oil layer is relatively transparent in Er:YAG laser light wavelength band. When the target was pork muscle, almost no debris could attach on the surface of the cap. The self-cleaning effect was more obvious when ablation was conducted underwater because of the protection of the water film between the target and the cap's surface.     

A management system for decompositions in stochastic programming

This paper presents two contributions: A set of routines that manipulate instances of stochastic programming problems in order to make them more amenable for different solution approaches; and a development environment where these routines can be accessed and in which the modeler can examine aspects of the problem structure. The goal of the research is to reduce the amount of work, time, and cost involved in experimenting with different solution methods.