Spatial frequency range analysis for the nonlinear Schrödinger equation

An analysis of the spatial frequency ranges for the nonlinear Schrödinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.     

Suzuki–Miyaura reactions promoted by a PdCl2/sulfonate‐tagged phenanthroline precatalyst in water

This work reports Suzuki–Miyaura cross‐coupling reactions of arylboronic acid with aryl halide or aryl dibromide mediated by PdCl₂ (0.05 mol%) and sodium 4‐(1H‐imidazo[4,5‐f][1,10]phenanthrolin‐1‐yl)butane‐1‐sulfonate (0.05 mol%) at 100 °C in water. The corresponding cross‐coupling products were obtained in good to excellent yields. The catalytic system was recovered from the organic products by extraction with ether and the residual aqueous catalyst phase showed high activity after reuse of at least four cycles. Copyright © 2014 John Wiley & Sons, Ltd.     

Pointwise Efficiency in Multiobjective Stochastic Linear Programming

In most of the approaches to the Multiobjective Stochastic Linear Programming problem that have been proposed in the literature, the notion of quality of a solution is not adequately defined. We reconsider this problem from a decision point of view, in contexts where either the decision maker's preference structure cannot be described by a utility function, or where this structure is expressed by an unknown non-decreasing utility function and the probability distribution of the random parameters is unknown. We define a fundamental set of ‘pointwise admissible’ solutions, as well as several subsets of particular interest. We discuss the relevance of these various pointwise efficient sets, their interrelations, and their practical identification.     

Vibration and stability of rectangular strip-plates

The problem considered is that of free vibration and stability of a simply supported rectangular strip-plate subjected to constant in-plane forces. The relevant continuity conditions at the interface between the adjacent regions, which play a significant role in this type of problem, are derived. The eigenfrequencies and the buckling load are estimated by the method of the new quotient which is based on a variational statement proposed by Nemat-Nasser. The results are compared with those obtained by means of the usual Rayleigh quotient and the exact solution. The good accuracy obtained by the application of the method of the new quotient is demonstrated by means of numerical examples.     

On the usage of qualitative reasoning as an approach towards enterprise modelling

This paper analyzes the computational requirements of enterprise modelling, presents a reasoning framework, and reports about a prototype implementation. Enterprise modelling studies complex systems which are normally only partially known, and focuses on studying the qualitative properties of the underlying system, and thus differs from traditional quantitative approaches. Various modelling approaches from computer science and management science are discussed with respect to their suitability for enterprise modelling. Qualitative reasoning is identified as a promising basis to develop a computational framework for enterprise modelling. A rules-constraints-method of reasoning with imprecise knowledge, which is essentially an interval-based version of difference equations, is proposed as a powerful and versatile tool for enterprise modelling. As an illustrative example, a model of a business organization, derived from the concept of a financial statement, is developed and simulated.