Two-dimensional state-space discrete models for hyperbolic partial differential equations

It is shown that the finite difference technique can be used to transform some important linear distributed processes described by partial differential equations into so-called Roesser discrete state-space models. Two illustrative examples of numerical solutions are given and compared with exact solutions.     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

An efficient algorithm for a job shop problem

We study the problem of minimizing makespan in a two-machine job shop with unit processing time operations. An efficient algorithm with respect to a succinct encoding of the problem instances is proposed. The algorithm is an improvement of earlier algorithms proposed for the problem by Brucker [1,2], Hefetz and Adiri [7], and Timkovskiy [15]. The idea behind the algorithm has the potential of extension to job shops with parallel machines.This research is supported in part by NSERC Grants A4619, OGP0105675, OGP0104900, General Motors of Canada, and the Manufacturing Research Corporation of Ontario.     

Synthesis and 1H NMR characterization of substituted 1-amino-9-imino-4-nitro-9,10-dihydr oacridines as potential antitumor agents

A convenient method for the synthesis of unsubstituted and substituted 1-amino-9-imino-4-nitro-9,10-dihydroacridines, 9 and 10 , respectively, is reported. Their ¹H nmr data are reported and discussed in order to confirm the imino tautomeric structure.     

Observation of nonlinear self-trapping in triangular photonic lattices

We experimentally study light self-trapping in triangular photonic lattices induced optically in nonlinear photorefractive crystals. We observe the formation of two-dimensional discrete and gap spatial solitons originating from the first and second bands of the linear transmission spectrum.     

On σ-commutativity in Menger algebras of n-place functions

We present an abstract characterization of various types of Menger algebras of n-place functions allowing certain permutations of variables.     

Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

Willem J. Blok 1947–2003

Dedication

Willem J. Blok 1947–2003     

Interaction between rhodanine and silver species on a nanocolloidal surface and in the solid state

This paper discusses and compares molecular interactions of rhodanine (Rd), the heterocyclic compound containing N, S, and O atoms, with two forms of silver species, i.e. Ag(I) ions and silver nanocolloidal particles. Vibrational spectroscopic and powder crystallography studies on coordination of Ag(I) ions in the solid state, supported by density functional theory, clearly indicate complexation through the nitrogen (the deprotonated imino group) and exocyclic sulfur atoms. Molecules of the complex are arranged in a one‐dimensional infinite polymeric chain structure that intertwines to give a helix motif. On the other hand, adsorption geometry of Rd on the silver surface was determined by using surface‐enhancement Raman scattering (SERS) spectroscopy. Observed differences between the SERS and the normal Raman spectra of Rd suggest that Rd adsorbs on the silver species after the rearrangement of the keto‐thione form into the enol‐thiol tautomer in acidic and neutral solutions. This leads to adsorption on this silver species through the thiolate ion. On the other hand, the alkaline pH forces first N‐deprotonation of Rd, and, in consequence, the obtained anion of the keto‐thione form interacts with the silver surface as a result of the presence of lone pairs of nitrogen and sulfur atoms, similar to the case discussed for the solid state. Copyright © 2009 John Wiley & Sons, Ltd.