Continuous weak approximation for stochastic differential equations

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations (SDEs) by general one-step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge–Kutta methods containing the continuous extension of the second order stochastic Runge–Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Itô SDEs with respect to a multi–dimensional Wiener process are presented.     

Synthesis and characterization of a series of diverse poly(2‐oxazoline)s

This article describes the synthesis and characterization of a variety of new poly(2‐oxazoline)s. With regard to functional polymers, 2‐oxazolines represent an interesting class of monomers because of the easy variation of the substituent in 2‐position. Starting from the corresponding nitriles, different 2‐oxazolines were obtained containing a diverse set of 2‐substituents, including thioether bonds ( M11 ), trifluoromethyl groups ( M8 , M10 ), and alkyl‐ or aryl groups ( M1 – M7 ). The subsequent polymerization of the majority of these monomers proceeded in a living manner, which was demonstrated by linear first‐order kinetics, a linear increase of molar mass with conversion, and relatively narrow molar mass distributions. In addition, selected thermal and surface properties of the polymers were studied utilizing DSC and contact‐angle measurements to determine the effects of different 2‐substituents on the macroscopic properties. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3829–3838, 2009     

Republication of: Observations in cosmology

This is a reprinting of a paper by Jerome Kristian and Rainer K. Sachs, first published in 1966, in which they proposed a power-series scheme for reading out various parameters of the Universe directly from observations in a model-independent way. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis and by a brief biography of J. Kristian, compiled by A. Krasiński from internet sources.     

A general solution to the Schrödinger–Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation.     

Classification of certain subgraphs of the 3‐dimensional grid

We prove by “trial‐ and‐error” that up to isometry, there are exactly four different non‐empty cubic induced subgraphs of the 3‐dimensional grid with girth ≥ 10. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 34–60, 2003     

Sampling and interpolation of entire functions and exponential systems in convex domains

Research supported by the Norwegian Research Council for Science and Humanities (NAVF).