Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Learn to Design Attractive Web Sites

A review of The Principles of Beautiful Web Design by Jason Beaird. The book aims to cover the demand to build Web sites by targeting designers who want to learn how to make Web sites look more attractive.     

Minimum boundary touching tilings of polyominoes

We study the problem of tiling a polyomino P with as few squares as possible such that every square in the tiling has a non‐empty intersection with the boundary of P . Our main result is an algorithm which given a simply connected polyomino P computes such a tiling of P . We indicate how one can improve the running time of this algorithm for the more restricted row‐column‐convex polyominoes. Finally we show that a related decision problem is in NP for rectangular polyominoes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic NMR study of the flexibility of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts

Dynamic NMR investigations of a number of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts were carried out. The barrier to rotation of the partial C, N double bond was determined and proved to be in the range of 62 to 63 kJ/mol. Quantum chemical calculations of bond orders and electron densities of the different atoms in the molecules show the distinct double bond character of the exocyclic C, N bond. This is in agreement with the relatively high barrier to rotation. By quantum chemical ab initio 3-21G calculations, the dynamic behaviour of this kind of compounds was simulated; two pairs (image and mirror image) of ground state conformations, in coincidence with the experiment, were obtained. Received: 10 May 1996 / Revised: 1 July 1996 / Accepted: 4 July 1996     

Metal Complexes with Macrocyclic Ligands. Part XXIX.. Structural and kinetic studies of two isomeric Cu2+ complexes with 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetradecane

The synthesis and complexation properties of 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetra-decane ( 2 ) are described. This ligand forms with Cu²⁺ two complexes, one of which has been characterized by X-ray structure analysis. The structural, spectral, and kinetic studies indicate that the two Cu²⁺ complexes are isomers with the macrocycle in the trans-III and trans-I configuration. The rate of the interconversion of the trans-I isomer to the thermodynamically more stable trans-III species is proportional to [OH^?]. A mechanism for this reaction is proposed.     

Synthesis and characterization of a semiflexible liquid crystalline polyester with a broad nematic region

In this paper, we report on the synthesis and detailed characterization of a new semiflexible nematic liquid crystalline polyester which could serve as a 'model' polyester for a variety of physical and physico-chemical investigations. The polymer is a nematic liquid over a wide temperature range-from the glass transition temperature at ∼95°C to the isotropic transition at ∼240°C. We expect this polyester to be particularly useful for studying the effect of flow on the orientation of liquid crystalline polymers, as well as the production and removal of disclinations.     

Synthesis and blending behavior of an oligoarylenevinylene. Design towards processable materials for LED applications

A bisstyrenebenzene with improved solubility can be obtained by a lateral phenyl substituent on the phenylene ring. The phenyl substituted bisstyrenebenzene (PBSB) was synthesized by Pd-catalyzed coupling of 2,5-dibromobiphenyl and styrene. PBSB exhibits blue fluorescence in solution. Blends of PBSB and polystyrene or polycarbonate are homogeneous over a wide concentration range of PBSB, based on differential scanning calorimetry (DSC) and scanning electron microscopy (SEM). The results were compared with the blending behavior of unsubstituted bisstyrenebenzene.