A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables.     

Application of polymer-supported triphenyl phosphine in the palladium-catalyzed cyanation reaction under microwave conditions

A variety of aryl nitriles were prepared in excellent yields from the palladium acetate catalyzed coupling of aryl halides with Zn(CN)₂ using polymer-supported triphenyl phosphine as the ligand and dimethylformamide as solvent under microwave irradiation conditions.     

Bringing the balance function into focus

Charge balance functions provide important insight concerning hadronization and charge transport in heavy ion collisions at RHIC. Unfortunately, this observable is clouded by several effects. One of these effects is resonance production. Here, we present a simple thermal model where resonance production is included via a Monte Carlo technique based on the canonical ensemble. Resonance production is not found to have a large effect on the width.     

Identifying assembly maps in K- and L-theory

In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K- and L-theory, and C^*-theory.Partially supported by NSERC grant A4000 and NSF grant DMS 9104026. The authors also wish to thank the SFB für Geometrie und Analysis, Münster, and the Max Planck Institut für Mathematik, Bonn, for their hospitality and support.Received: 7 May 2001     

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

Improving Construction for Connected Dominating Set with Steiner Tree in Wireless Sensor Networks

The connected dominating set plays an important role in ad hoc wireless networking. Many constructions for approximating the minimum connected dominating set have been proposed in the literature. In this paper, we propose a new one with Steiner tree, which produces approximation solution within a factor of 6.8 from optimal. This approximation algorithm can also be implemented distributedly.     

Ferrocenyl-substituted fluorescent anthracenes and anthraquinones

The synthesis of a range of ferrocene-substituted ethynylanthracenes and 1,1^′-(bis-(2-ethenylanthraquinoyl)ferrocene has been achieved. The synthesis relies on the production of ferrocenylanthraquinones as key precursors. The products were obtained in the reactions of ferrocenylanthraquinones with phenylethynyllithium or trimethylsilylethynyllithium followed by reduction with tin chloride. The key products such as 1- and 2-ferrocenyl(9,10-bis-phenylethynyl)anthracenes have been characterised by X-ray single crystal diffraction.