Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Congruences between modular forms and lowering the level mod l^n

In this article we study the behavior of inertia groups for modularGalois mod l^n representations and in some cases we give a generalizationof Ribet s lowering the level result (cf. [Rib90]).

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

De l'évaluation de l'effet structurant d'un projet urbain à l'analyse des congruences entre stratégies d'acteurs : le réaménagement du Vieux-Port de Montréal

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Un modèle animal simple pour l'apprentissage des techniques de microanastomoses vasculaires de congruences diefférentes

BACKGROUND Since the pioneering work of Jacobson and Suarez, microsurgery has steadily progressed and is now used in all surgical specialities, particularly in plastic surgery. Before performing clinical procedures it is necessary to learn the basic techniques in the laboratory. OBJECTIVE To assess an animal model, thereby circumventing the following issues: ethical rules, cost, anesthesia and training time. METHODS Between July 2012 and September 2012, 182 earthworms were used for 150 microsurgical trainings to simulate discrepancy microanastomoses. Training was undertaken over 10 weekly periods. Each training session included 15 simulations of microanastomoses performed using the Harashina technique (earthworm diameters >1.5 mm [n=5], between 1.0 mm and 1.5 mm [n=5], and <1.0 mm [n=5]). The technique is presented and documented. A linear model with main variable as the number of the week (as a numeric covariate) and the size of the animal (as a factor) was used to determine the trend in time of anastomosis over subsequent weeks as well as differences between the different size groups. RESULTS The linear model showed a significant trend (P<0.001) in time of anastomosis in the course of the training, as well as significant differences (P<0.001) between the groups of animal of different sizes. For diameter >1.5 mm, mean anastomosis time decreased from 19.6±1.9 min to 12.6±0.7 min between the first and last week of training. For training involving smaller diameters, the results showed a reduction in execution time of 36.1% (P<0.01) (diameter between 1.0 mm and 1.5 mm) and 40.6% (P<0.01) (diameter <1.0 mm) between the first and last weeks. The study demonstrates an improvement in the dexterity and speed of nodes' execution. CONCLUSION The earthworm appears to be a reliable experimental model for microsurgical training of discrepancy microanastomoses. Its numerous advantages, as discussed in the present report, show that this model of training will significantly grow and develop in the near future.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Éléments de la théorie des nombres. Congruences. Formes quadratiques. Nombres incommensurables. Questions diverses;

Available on demand as hard copy or computer file from Cornell University Library.

Sur la théorie générale des congruences.

"Extrait des Mémoires publiés par la Classe des Sciences de l'Académie Royale de Belgique. Collection in-4⁰. 2. sér., tome 3, 1911."

Congruences in modular, Jacobi, Siegel, and mock modular forms with applications

We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the Fourier expansion. We have several applications. We describe the Ramanujan congruences in the counting functions for overparitions, overpartition pairs, crank differences, and Andrews' two-coloured generalized Frobenius partitions. We also study Ramanujan congruences in the Fourier coefficients of certain ratios of Eisenstein series. We also determine the exact number of holomorphic modular forms with Ramanujan congruences when the weight is large enough. In a chapter based on joint work with Olav Richter, we study Ramanujan congruences in the coefficients of Jacobi forms and Siegel modular forms of degree two. Finally, the last chapter contains a completely unrelated result about harmonic weak Maass forms.

Remarks on an algebraic semantics for paraconsistent Nelson's logic

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

Les effets du débat public dans la nouvelle ville de Montréal : regard sur le plan d'urbanisme et sa mise en oeuvre

Débat public, participation, délibération, autant de termes utilisés pour parler de normes et de dispositifs qui participeraient au nouvel « impératif délibératif » (Blondiaux et Sintomer 2002). Ce mémoire présente une analyse du débat public sur le plan d'urbanisme de Montréal avec un schéma d'analyse inspiré de celui de Simard et Fourniau (2007). Notre discussion du processus de débat porte non seulement sur la phase formelle des audiences publiques, mais aussi sur les étapes de concertation en amont et sur divers processus plus ou moins publicisés en aval. Ceci permet une réflexion d'ordre procédural plus riche qui considère la diversité des dispositifs dans une perspective de complémentarité. Pour chercher des effets du débat public sur le plan d'urbanisme, nous adoptons le parti de la congruence (Offner 1993), ce qui nous amène à une analyse de l'interaction entre des dynamiques contextuelles et des mobilisations des participants au débat. Certaines de ces congruences concordent avec des modifications au plan d'urbanisme. Notre étude propose aussi des implications du contexte particulier de la nouvelle ville de Montréal (avec la création des arrondissements) sur le contenu du débat public, sur certaines de ses manifestations procédurales ainsi que sur sa portée. Notre dernier chapitre montre que la dynamique du débat public en aval, dans la phase de mise en oeuvre du plan d'urbanisme, se déploie beaucoup plus dans les débats sur les grands projets que sur les mécanismes prévus à cette fin, qui comportent des embûches de par leur faible publicité et le caractère technique du processus réglementaire. Dans l'ensemble, notre étude met en lumière l'importance du contexte : autant le processus de débat que ses effets s'inscrivent dans des dynamiques contextuelles.

Exercise sheet 4 pdf

Exercises and solutions in PDF

Lecture notes pdf

Lecture notes in PDF