Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

Definite integrals and operational methods

An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results encompassing various aspects of the special function theory.Comment: 9 pages; minor changes to match published versio

A localized version of the basic triangle theorem

In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic functions for instance

Le support de l'algebre de lie libre

AbstractWe characterize the words appearing as monomials in Lie polynomials

Combinatorial Physics, Normal Order and Model Feynman Graphs

The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. Finally we show that a graphical representation of these combinatorial numbers leads to sets of model field theories, for which the graphs may be interpreted as Feynman diagrams corresponding to the bosons of the theory. The generating functions are the generators of the classes of Feynman diagrams.Comment: 9 pages, 4 figures. 12 references. Presented at the Symposium 'Symmetries in Science XIII', Bregenz, Austria, 200