Modelling photonic crystal fibers with localized functions

In this paper we present an overview of of the standard methods used when modelling photonic crystal fibers with Hermite-Gaussian functions, as well as a new variant of this modelling scheme, based solely on Hermite-Gaussian expansion series, which introduces the possibility of directly modelling fibers with finite claddings. We investigate the challenges and advantages of such a model and compare it to a proven modelling tool, namely the plane wave method.     

Reliable Numerical Computation in Civil Engineering

Civil engineering is a field – as are many other engineering sciences – where most of the methods used for solving optimization problems are based on experience and experiments, and models using local information, but drawn from global models. The present work outlines an interesting class of problems from this field, and initiates some possible ways to solve those problems utilizing the wide tool capabilities of interval arithmetic for error handling and interval branch-and-bound algorithms to solve the original or modified industrial models automating civil engineers' work. The investigations are in the first state but are promising both in a theoretical and in a practical sense.     

Free channel fourier transform in the long-rangen-body problem

Research supported by NSF grant DMS-8807816.     

Photorefractive surface waves in a thin Bi12TiO20 crystal

A theoretical model considering total internal reflections of fanned beams from the side crystal surfaces and their coupling with the pump beam is proposed. The interaction of these beams results in the light intensity redistribution and in the generation of the photorefractive surface wave. An experimental observation of the light intensity self-concentration near the surface of a thin photorefractive Bi₁₂TiO₂₀ crystal is reported. It results in an acceleration of the photorefractive energy exchange process.     

Analogues of the antibiotic puromycin as potential prodrugs of 3′-amino-3′-deoxythymidine

Condensation of L- and D-3′-amino-2′,3′-dideoxynucleosides 2–5 with N-BOC-protected aminoacids 6 and 13 using dicyclohexylcarbodiimide and N-hydroxysuccinimide in DMF is reported to give the N-BOC-protected acylamino aminonucleosides 7– 9 and 14 in 51–81% yield. After deprotection using trifluoroacetic acid the corresponding unprotected new analogues of puromucin 10–12 and 15 were obtained in 43–56% yield. These compounds did not show any significant antiviral activity using HIV (stain HTLV-III B)-infected MT-4 cells as target system.     

On Tailoring of Nonlinear Spectral Properties of Nanocomposites Having Maxwell Garnett or Bruggeman Structure

Nonlinear spectral properties of two different types of conjugated polymers (polythiophene PT10 and polysilane PDHS) with nanoscale TiO₂ particles forming a Maxwell Garnett or a Bruggeman composite are studied. According to the present simulations, it is possible both to enhance and to tailor the magnitude and the spectral properties, respectively, of the effective degenerate third-order nonlinear susceptibility of the composite. This is done simply by tuning the volume fraction of TiO₂ inclusions and by changing the topology of the composite.     

Methods for rapid evaluation of electron repulsion integrals in large-scale LCGO calculations

A method is proposed for efficient use of molecular symmetry in the evaluation of two-electron integrals. This provides a means of avoiding the recalculation of symmetry-redundant integrals, and of symmetry-blocking matrices and supermatrices without the usual time-consuming transformation procedures. Various methods for speeding up the calculation of integrals are also discussed. Integral calculation times are given for some representative molecules.     

A smooth pseudoconvex domain without pseudoconvex exhaustion

A pseudoconvex demain with real —analytic smooth boundary on a complex manifold is constructed which cannot be exhausted by pseudoconvex domains.