In this paper an algorithm that provides an equivalent, but of reduced order, representation for multivariate polynomial matrices is given. It combines ideas from computational symbolic algebra and from established techniques in graph representation and polynomial/matrix algebraic manipulations. The algorithm is applied to the problem of finding minimal linear fractional transformation models. ...

We consider a cointegrated system generated by processes that may be fractionally integrated, and by additive polynomial or generalized polynomial trends. In view of the consequent competition between stochastic and deterministic trends, we consider various estimates of the cointegrating vector and develop relevant asymptotic theory, including the situation where fractional orders of integratio...

The goal of this paper is to propose observer-based controllers, either in state-space form or in polynomial representation, for fractional diierential systems. As for linear diierential systems of integer order, polynomial representation will allow us to take advantage of the Youla parametrization in order to asymptotically reject some perturbations. This will be illustrated on a worked-out ex...

Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for th...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a r...

We revisit the pairwise kidney exchange problem established by Roth Sonmez and Unver [23]. Our goal, explained in terms of graph theory, is to find a maximum fractional matching on an undirected graph, that Lorenz-dominates any other fractional matching. The Lorenz-dominant fractional matching, which can be implemented as a lottery of integral matchings, is in some sense the fairest allocation ...