A note on adapting methods for continuous global optimization to the discrete case

In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported.     

线性离散事件动态系统的可达性

可达性是动态系统的重要性质之一。本文讨论离散事件动态系统的可达性,给出了系统完全可达的充要条件,得到了利用系统的特征矩阵判断系统可达性的判据,证明了系统可按可达性进行分解、状态反馈不影响系统可达性等结论,还进一步讨论了一类流水线生产加工系统的可达性,本文的结果对于这类系统的分析和控制是有意义的。     

Permanence for the Michaelis-Menten type discrete three-species ratio-dependent food chain model with delay

A discrete three trophic level food chain model with ratio-dependent Michaelis-Menten type functional response is investigated. It is shown that under some appropriate conditions the system is permanent. The results indicate that, to make the species coexist in the long run, it is a surefire strategy to keep the death rate of the predator and top predator rather small and the intrinsic growth rate of the prey relatively large.     

A dynamical strategy for approximation methodsUne stratégie dynamique pour les méthodes d'approximation

The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one. To cite this article: F. Jézéquel, C. R. Mecanique 334 (2006).     

How well do discrete element granular flow models capture the essentials of mixing processes?

Flowing granular materials, undergoing both mixing and segregation, play important roles in industries ranging from minerals and food to pharmaceuticals and ceramics. Sometimes it is desirable to enhance the mixing and inhibit segregation and in other cases it is desirable to minimise the mixing and enhance the segregation. The fundamentals of these processes are poorly understood. Computational modelling of such granular flows offers a good opportunity to study these fundamentals. But how well do these discrete element based modelling techniques capture the essential features of mixing processes? The capabilities of our discrete element modelling package are described. Two different methods for measuring the rates of mixing are presented and three different configurations are studied. Qualitatively reasonable flows are obtained. A detailed study of the mixing demonstrates that the amount and nature of the mixing is quite sensitive to a range of physical parameters.     

Monge properties,discrete convexity and applications

Starting from Monge’s mass transportation problem we review the role Monge properties play in optimization. In particular we discuss transportation problems whose cost functions fulfill a Monge property, Monge sequences, algebraic Monge properties, the recognition of permuted Monge arrays and multidimensional Monge arrays and the connections between Monge properties and discrete convexity. Finally we discuss Prékopa’s recent approach using Monge arrays in bounding multivariate probability distribution functions.     

A bound-improving approach to discrete programming problems

This note deals with the extension of the bound-improving sequence idea to general discrete programming problems.Corresponding author.     

Discrete-event dynamic systems: The strictly convex case

Given the observed outputg _j of a discrete-event system, a classical problem is to find a matrix realisationg _j =cA ^jb withA of least possible dimension. When the sequenceg _j is convex and ultimately 1-periodic, a linear-time algorithm suffices to construct such a realisation over the algebra (R, max, +). When the transient is strictly convex, this realisation is minimal-dimensional.     

New integrable cases of a Cremona transformation: a finite-order orbits analysis

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters ( and ), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations, namely taking the inverse of q × q matrices and permuting some of the entries of these matrices. It has been seen to yield weak chaos and integrability. We have found new integrable cases of this Cremona transformation, corresponding to the values of = 0 when , besides the already known values = 0 and = −1, and also arbitrary when = 0. For these cases, one has a foliation of the parameter space in elliptic curves. We give the equations of these elliptic curves. Based on this very example we show how one can find these integrability cases of the Cremona transformation and actually integrate it using a method based on the systematic study of the finite-order conditions of the Cremona transformation. The method is shown to be efficient and straightforward. The various integrability cases are revisited using many different representations of this very mapping (birational transformations, recursion in one variable, …).