Quasi-classical trajectories study of the chemisorption of H2 on the Pt(111) surface: effect of surface motion

The effect of energy exchange on the dynamics of the chemisorption of H₂ on Pt (111) is studied within a LEPS potential quasi-classical trajectories treatment. The Einstein model is assumed for the solid. The rigidity of the surfaces is shown to be an acceptable approximation.     

Reaction of N,N'-dialkyldithiodianilines with β-ketoesters. A new synthesis of N-alkyl-2-acyl-3-oxo-3,4-dihydro-1,4-benzothiazines

The title compounds 3a-j together with the N-alkylacylketene S,N-acetals 12a-j were obtained by reaction of N,N'-dialkyldithiodianilines with β-ketoesters compounds. A possible reaction pathway is suggested.     

A multivariate extension of Sarhan and Balakrishnan’s bivariate distribution and its ageing and dependence properties

A new class of bivariate distributions (NBD) was recently introduced by Sarhan and Balakrishnan [A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, J. Multivariate Anal. 98 (2007) 1508-1527]. In this note, we give the joint survival function of a multivariate extension of the NBD, which is not an absolutely continuous multivariate distribution, and its marginal and extreme order statistics distributions are also derived. The multivariate ageing and dependence properties of the proposed n-dimensional distribution are also discussed, and then we analyze the stochastic ageing of its marginals and its minimum and maximum order statistics.     

Facilitated modelling in operational research

The traditional way of employing operational research in organisational interventions has been the expert mode. In this mode, the problem situation faced by the client is given to the operational research consultant, who then builds a model of the situation, solves the model to arrive at an optimal (or quasi-optimal) solution, and then provides a recommendation to the client based on the obtained solution. An alternative mode of engagement is to conduct the whole intervention together with the client: from structuring and defining the nature of the problem situation of interest, to supporting the evaluation of priorities and development of plans for subsequent implementation. In this latter mode, the operational researcher works throughout the intervention not only as an analyst, but also as a facilitator to the client. This paper discusses this latter mode of engagement with clients, with particular emphasis on the use of facilitated modelling as the intervention tool. Drawing on research scattered across a range of publications and domains, the review presented here provides a formal definition of facilitated modelling, together with a general framework that allows the conceptualisation of a wide variety of facilitated modelling approaches to organisational intervention. Design issues in facilitated modelling and their practical implication are discussed, and directions for future research identified.     

On the direct solution of Riccati equations arising in boundary control theory

Two classes of Riccati equations arising in the boundary control of parabolic systems are studied by direct methods. The new feature with respect to previous works on this subject is the low regularity of the final data. The classes considered here generalize those of [7]and [5]on one side, and of [14]on the other one. Completely new methods are used to obtain the solution of the Riccati equations, in both cases. The central theme is the dependence of the solutions on a «symmetric» norm of the final data, yielding these new results as well as a new proof of existence for the related algebraic Riccati equation under more general assumptions. The synthesis of the associated linear-quadratic-regulator problems is easily solved using these results.     

Pathwise global attractors for stationary random dynamical systems

Summary The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA() is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A() attracts bounded sets, is measurable with respect to the -algebra of invariant sets, and is independent of when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.     

Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.