A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics

A ``hybrid method'', dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions--this, even in the case when the unit circle is a natural boundary. A prime application is to coefficients of several types of infinite product generating functions, for which full asymptotic expansions (involving periodic fluctuations at higher orders) can be derived. Examples relative to permutations, trees, and polynomials over finite fields are treated in this way.Comment: 31 page

Algorithmique du theoreme fondamental de l'algebre

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Largest Component in Random Combinatorial Structures

Résumé disponible dans le fichier PD

Une introduction à Maple

Nous présentons le logiciel de calcul formel {\sc Maple} sans en supposer aucune connaissance et décrivons ses fonctionnalités essentielles dans le but de rendre le lecteur autonome. La structure des objets et l'écriture des programmes sont illustrées d'exemples détaillés

Random Polynomials and Polynomial Factorization

We give a precise average-case analysis of a complete polynomial factorization chain over finite fields by methods based on generating functions and singularity analysis

Sur une famille de polynomes issus de l'analyse numerique

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Development of sustainable energy systems: a new challenge for process systems engineering education

This paper presents the main features of the master-level programme in “EcoEnergy” offered as a full-time one year course at “Institut National Polytechnique of Toulouse” in order to provide engineers with a state-of-the-art education in the area of advanced energy technologies and systems. It is based on an original and equilibrated combination of process systems engineering and electrical engineering disciplines, with an interdisciplinary problem-solving approach necessary for identifying sustainable solutions in the energy sector. More precisely, the students learn how to design, develop and implement energy systems and technologies in various industrial sectors for which efficient management of energy issues is vital to remain competitive

Controlled Activation of Substrate Templating in Molecular Self-Assembly by Deprotonation

Kittelmann M, Nimmrich M, Neff JL, et al. Controlled Activation of Substrate Templating in Molecular Self-Assembly by Deprotonation. Journal of Physical Chemistry C. 2013;117(45):23868-23874.Templated assembly of organic molecules constitutes a promising approach for fabricating functional nanostructures at surfaces with molecular-scale control. Using the substrate template for steering the adsorbate growth enables creating a rich variety of molecular structures by tuning the subtle balance of intermolecular and molecule-surface interactions. On insulating surfaces, however, surface templating is largely absent due to the comparatively weak molecule-surface interactions compared to metallic substrates. Here, we demonstrate the activation of substrate templating in molecular self-assembly on a bulk insulator by controlled deprotonation of the adsorbed molecules upon annealing. Upon deposition of 4-iodobenzoic acid onto the natural cleavage plane of calcite held at room temperature, high molecular mobility is observed, indicating a small diffusion barrier. Molecular islands only nucleate at step edges. These islands show no commensurability with the underlying substrate, clearly indicating the absence of surface templating. Upon annealing the substrate, the molecules undergo a transition from the protonated to the deprotonated state. In the deprotonated state, the molecules adopt a well-defined adsorption position, resulting in a distinctly different, substrate-templated molecular structure that is stable at room temperature. Our work, thus, demonstrates the controlled activation of substrate templating by changing the molecule-surface interaction upon annealing