We construct bivariate polynomial approximations of the Lerch function, which for certain specialisations of the variables and parameters turn out to be HermitePadé approximants either of the polylogarithms or of Hurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prévost. Finally, we make ...

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrence...

RÉSUMÉ. Nous présentons une méthode pour calculer un score d’un élément quelconque d’un document structuré qui prend en compte la proximité des termes de la requête dans le texte du document. Plus précisément nous définissons autour de chaque occurrence d’un terme de la requête une fonction d’influence. Pour une occurrence qui apparaît dans le texte proprement dit, cette fonction d’influence dé...

To optimize the quality of service through a telecommunication network, we propose an algorithm based on Lagrangian relaxation. The bundle-type dual algorithm is adapted to the present situation, where the dual function is the sum of a polyhedral function (coming from shortest paths problems) and of a smooth function (coming from the congestion). Key-words: Convex optimization, routing, multico...