On Computation of Scattering Matrices and on Surface Waves for Diffraction Gratings

Summary.  A method for the numerical computation of the so-called augmented scattering matrices (ASM) is suggested for diffraction gratings. To construct such (unitary) matrices one has to take into account not only the oscillating modes but also those which exponentially grow (attenuate) in amplitude away from the grating. The method uses an optimization procedure to identify the coefficients in the asymptotics of such modes. A justification of the approach is given and its numerical implementation is discussed. Reliable numerical results allow us to study the occurrences of surface waves by means of a general existence criterion based on the properties of ASM. To illustrate the method we give some examples of surface waves in gratings. Received October 25, 2001 / Revised version received May 23, 2002 / Published online October 29, 2002 Mathematics Subject Classification (1991): 78M10, 78M50, 78A45     

Trace and Density Results on Regular Trees

Potential Analysis - The boundary of a regular tree can be viewed as a Cantor-type set. We equip our tree with a weighted distance and a weighted measure via the Euclidean arc-length and consider...     

Regularity theory and traces of -harmonic functions

In this paper we discuss two different topics concerning -
harmonic functions. These are weak solutions of the partial differential equation

where for some fixed , the function is bounded and for a.e. . First, we present a new approach to the regularity of -harmonic functions for . Secondly, we establish results on the existence of nontangential limits for -harmonic functions in the Sobolev space , for some , where is the unit ball in . Here is allowed to be different from .

     

Repeatable measurements in quantum theory: Their role and feasibility

Recent advantages in experimental quantum physics call for a careful reconsideration of the measurement process in quantum mechanics. In this paper we describe the structure of the ideal measurements and their status among the repeatable measurements. Then we provide an exhaustive account of the interrelations between repeatability and the apparently weaker notions of value reproducible or first- kind measurements. We demonstrate the close link between repeatable measurements and discrete observables and show how the ensuing measurement limitations for continuous observables can be lifted in a way that is in full accordance with actual experimental practice. We present examples of almost repeatable measurements of continuous observables and some realistic models of weakly disturbing measurements.Dedicated to Peter Mittelstaedt on the occasion of his 65th birthday.Leaving the Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany.     

Aggregation and protein binding of sodium maleate copolymers with varying hydrophobicities

Copolymers of sodium maleate with methyl methacrylate, styrene, or vinyl acetate have been synthesized and studied in aqueous NaCl solutions of various ionic strengths. The polymers are polyelectrolytes with varying hydrophobicities, and their solution properties have been studied using static and dynamic light scattering. Copolymers containing methyl methacrylate or styrene were shown to aggregate in water upon increasing salt concentration. Copolymers of sodium maleate and vinyl acetate do not associate with increasing ionic strength. The binding of bovine serum albumin and cytochrome C to the sodium maleate copolymers was also investigated by light scattering. It was observed that cytochrome C forms complexes with the copolymers containing methyl methacrylate or vinyl acetate whereas albumin does not bind to any of the copolymers studied. Copyright © 2004 John Wiley & Sons, Ltd.     

Why are hexavalent uranium cyanides rare while U–F and U–O bonds are common and short?

Relativistic small-core pseudopotential B3LYP and CCSD(T) calculations and frozen-core PW91–PW91 studies are reported for the series UF ₄X ₂ ( X=H, F, Cl, CN, NC, NCO, OCN, NCS and SCN). The bonding in UF ₆ is analyzed and found to have some multiple-bond character, approaching at a theoretical limit a bond order of 1.5. In addition to these s and p orbital interactions, the electrostatic attraction is important. Evidence for p bonding in the other systems studied was also found. The triatomic pseudohalides as well as fluorine and chlorine are in this sense better ligands than cyanide. The –CN group is a s donor and p acceptor, as uranium itself, and hence is unfit to bond to U(VI). The s-bonded UH ₆ is octahedral.     

New practical synthesis of prazosin

A new four step synthesis of prazosin, 2-[4-(2-furoyl)piperazin-l-yl]-4-amino-6,7-dimethoxyquinazoline, has been described. The method is also adaptable for the preparation of other substituted 4-aminoquinazolines. The yields are good in every step and the reactions are performed with ease. Prazosin hydrochloride of high purity is obtained directly in the last step.     

The elements of Flatland: Hartree-Fock atomic ground states in two dimensions for Z = 1–24

The Hartree–Fock problem in two dimensions (2D) has been solved for 1 ≤ Z ≤ 24 using a Gaussian basis and assuming r^?1 Coulomb interactions. The order of occupation of the one-electron states is like in the 3D case. The 1s shell is found to be particularly small and strongly bound, making the 2D hydrogen a “superhalogen” and the 2D He a “superinert gas.” In contrast to 3D, 4s¹3d² and 4s²3d³ configurations are preferred for the 2D “Sc” and “Cu,” respectively. The six first 2D atoms have stronger and the later ones weaker valence-bonding energies than do their 3D analogs. It is noted that the 2D Dirac energy expression for a hydrogenlike atom for m_j = l + 1/2 agrees with the 3D Klein–Gordon one.