On the transmission problem of the helmholtz equation for quadrants

The plane transmission problem of the Helmholtz equation for quadrants is characterized by a one-dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along the x-axis. It is derived by solving the transmission problem for the upper and the lower half-plane involving a Neumann condition at y = 0. This is done by a two-dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one to y = 0 then lead to the integral equation. Thereby the transmission conditions of the original problem at y = 0 have to be taken into account. The resulting integral equation is of generalized Wiener-Hopf-type. It is solved via the contraction theorem imposing restricting conditions on the wave numbers.     

Oxygen chemisorption on Cu(110): A combined study by second-harmonic spectroscopy and photoemission

We have studied the formation of the addedrow (2×1)O overlayer on Cu(110) using Second-Harmonic Generation (SHG). To characterize the electronic properties of the surface, simultaneous observations with LEED and angle-resolved photoemission were performed. We are able to interpret our results in terms of transitions between surface bands of Cu(110) and Cu(110)-(2×1)O, respectively.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May. 30 to June 1, 1994     

Isolation and identification of three urinary metabolites of retinoic acid in the rat.

After the intraperitoneal administration of high doses of ¹⁴C- and ³H-labelled retinoic acid ( 1 ) to rats three major urinary metabolites have been isolated in microgram amounts by use of column, thin-layer and high-pressure liquid chromatography. Their structures were elucidated by mass spectroscopy and Fourier transform ¹H-NMR. spectroscopy as 2 (5-methyl-5-[2-(2,6,6-trimethyl-3-oxo-1-cyclohexen-1-yl)vinyl]-2-tetrahydrofuranone), 3 (5-[2-(6-hydroxymethyl-2,6-dimethyl-3-oxo-1-cyclohexen-1-yl)vinyl]-5-methyl-2-tetrahydrofuranone) and 4 (6-(6-hydroxymethyl-2,6-dimethyl-3-oxo-1-cyclohexen-1-yl)-4-methyl-4-hexenoic acid). In these metabolites the tetraene side chain of 1 is shortened and the cyclohexene ring oxidized. The radioactivity of 2 and 3 accounted for about 10% (0.9% of the dose) each, metabolite 4 for about 6% (0.5% of the dose) of the total urinary radioactivity.     

Characterization of coalitionally ordered games

Summary In the sequel we will derive sufficient and necessary conditions for the existence of certain numeric representations of simple games. In § 2 the above mentioned representation is given by a so called, coalitionally ordered function, i.e. a numeric function representing the desirability of each coalition in the class of all coalitions. Simple games which possess a c.o.f are called coalitionally ordered games. Sufficient and necessary criteria are given for a simple game to be a c.o.g. Analogously weighted majority games are characterized in § 3. The criteria to be presented are linked by properties of the desirability relation of a simple game. The concept of a desirability relation was introduced by Peleg 1978.

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Zusammenfassung Im folgenden werden wir hinreichende und notwendige Bedingungen zur Existenz von gewissen numerischen Darstellungen einfacher Spiele (simple games) herleiten. Diese oben genannte Darstellung wird in § 2 durch eine sogenannte coalitionally ordered function, gegeben, wobei wir darunter eine numerische Funktion verstehen, die die Desirability, jeder Koalition innerhalb der Klasse aller Koalitionen beschreibt. Einfache Spiele, die eine c.o.f besitzen, werden coalitionally ordered games genannt. Es werden hinreichende und notwendige Bedingungen dafür genannt, daß ein einfaches Spiel ein c.o.g ist. Analog werden gewichtete Abstimmungsspiele (weighted majority games) in § 3 charakterisiert. Die angegebenen Kriterien werden mit Eigenschaften der sogenannten desirability relation eines einfachen Spieles in Verbindung gebracht. Das Konzept einer desirability relation wurde von Peleg 1978 verwendet.

     

Bestimmung der Hexabromidzahl, insbesondere des Lein?ls

Ohne Zusammenfassung     

Substituent increments for the 1H-NMR. Chemical shifts of the 18- and 19-methyl protons of steroids. Part I: 9beta, 10alpha(retro)-steroids

This paper reports 261 substituent increments for the ¹H? NMR. chemical shifts (solvent: CDCl₃) of the 18- and 19-methyl protons of 9β, 10α(retro)-steroids relative to 5β,9β,10α,-androstane. The increments were calculated by a least-squares procedure from 1334 spectra of 759 different steroids.     

A memory‐efficient finite volume method for advection‐diffusion‐reaction systems with nonsmooth sources

We present a parallel matrix‐free implicit finite volume scheme for the solution of unsteady three‐dimensional advection‐diffusion‐reaction equations with smooth and Dirac‐Delta source terms. The scheme is formally second order in space and a Newton–Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix‐vector product required is hardcoded without any approximations, obtaining a matrix‐free method that needs little storage and is well‐suited for parallel implementation. We describe the matrix‐free implementation of the method in detail and give numerical evidence of its second‐order convergence in the presence of smooth source terms. For nonsmooth source terms, the convergence order drops to one half. Furthermore, we demonstrate the method's applicability for the long‐time simulation of calcium flow in heart cells and show its parallel scaling. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 143–167, 2015