Academic literature on the topic 'Henri Poincaré correspondence'

At the beginning of the twentieth century while Henri Poincaré (1854–1912) was already deeply involved in the developments of wireless telegraphy, he was invited, in 1908, to give a series of lectures at the École Supérieure des Postes et Télégraphes (today Sup'Télecom). In the last part of his presentation, he established that the necessary condition for the existence of a stable regime of maintained oscillations in a device of radio engineering completely analogous to the triode is the presence in the phase plane of stable limit cycle. The aim of this work is to prove that the correspondence highlighted by Andronov between the periodic solution of a nonlinear second-order differential equation and Poincaré's concept of limit cycle has been carried out by Poincaré himself, 20 years ago in some forgotten conferences of 1908.

Abstract We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven in Cunden et al. (Ann. Inst. Henri Poincaré D, to appear) that correlators have a topological expansion in terms of weakly or strictly monotone Hurwitz numbers that can be explicitly computed from our formulae. As a second result, we identify the Laguerre partition function with only positive couplings and a special value of the parameter $$\alpha =-1/2$$ α = - 1 / 2 with the modified GUE partition function, which has recently been introduced in Dubrovin et al. (Hodge-GUE correspondence and the discrete KdV equation. arXiv:1612.02333) as a generating function for Hodge integrals. This identification provides a direct and new link between monotone Hurwitz numbers and Hodge integrals.

The Henri Poincaré correspondence is a corpus of letters sent and received by this mathematician. The edition of this correspondence is a long-term project begun during the 1990s. Since 1999, a website is devoted to publish online this correspondence with digitized letters. In 2017, it has been decided to reforge this website using Omeka S. This content management system offers useful services but some user needs have led to the development of an RDFS infrastructure associated to it. Approximate and explained searches are managed thanks to SPARQL query transformations. A prototype for efficient RDF annotation of this corpus (and similar corpora) has been designed and implemented. This article deals with these three research issues and how they are addressed.

Motivated by Poincaré’s orbits going to infinity in the (restricted) three-body problem [see H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Vol. 3 (Gauthier-Villars, 1899) and A. Chenciner, Poincaré and the three-body problem, in Henri Poincaré, 1912–2012 (Birkhäuser, Basel, 2015), pp. 51–149], we investigate the generic existence of heteroclinic-like orbits in a neighborhood of the critical set of a [Formula: see text]-contact form. This is done by using a singular counterpart [R. Cardona, E. Miranda and D. Peralta-Salas, Euler flows and singular geometric structures, Philos. Trans. R. Soc. A 377(2158) (2019) 20190034] of Etnyre–Ghrist’s contact/Beltrami correspondence [J. Etnyre and R. Ghrist, Contact topology and hydrodynamics: I. Beltrami fields and the Seifert conjecture, Nonlinearity 13(2) (2000) 441–458], and genericity results concerning eigenfunctions of the Laplacian established by Uhlenbeck [Generic properties of eigenfunctions, Amer. J. Math. 98(4) (1976) 1059–1078]. Specifically, we analyze the [Formula: see text]-Beltrami vector fields on [Formula: see text]-manifolds of dimension [Formula: see text] and prove that for a generic asymptotically exact [Formula: see text]-metric they exhibit escape orbits. We also show that a generic asymptotically symmetric [Formula: see text]-Beltrami vector field on an asymptotically flat [Formula: see text]-manifold has a generalized singular periodic orbit and at least four escape orbits. Generalized singular periodic orbits are trajectories of the vector field whose [Formula: see text]- and [Formula: see text]-limit sets intersect the critical surface. These results are a first step towards proving the singular Weinstein conjecture.

De nombreux travaux historiques s'intéressent à la vie et à l'œuvre d'Henri Poincaré (1854-1912), notamment par l'étude et la publication du corpus de sa correspondance, qui se compose d'environ 2000 lettres et qui comprend des échanges relevant du cadre académique, privé ou scientifique. Depuis plusieurs années, des travaux numériques se sont développés pour stocker, publier et exploiter les données de ce corpus par la mise en œuvre de standards et de technologies du Web sémantique, en particulier RDF RDFS et SPARQL. Lors de l'interrogation d'un graphe RDF plusieurs situations peuvent mener à une volonté de formuler des interrogations flexibles. Ce terme caractérise des méthodes de recherche allant au-delà des systèmes de recherche classiques, qui se cantonnent aux interrogations exactes et qui ne permettent pas ou peu d'exprimer des préférences utilisateurs. La contribution principale de ce travail de recherche s'intéresse à la formalisation, à l'étude et aux applications d'un mécanisme d'interrogation flexible s'appuyant sur l'utilisation de règles de transformation de requêtes SPARQL. Ce système permet, à partir d'une requête initiale, d'un graphe RDF et d'un ensemble de règles, de générer des requêtes SPARQL afin d'offrir des résultats alternatifs à ceux initialement retournés suite à l'interrogation d'un corpus. Les règles de transformation peuvent être génériques, et donc facilement transposables à d'autres graphes, ou être dépendantes d'un domaine d'application. Plusieurs outils s'appuyant sur ce mécanisme ont été développés pour assister l'exploitation numérique du corpus de la correspondance d'Henri Poincaré. Un outil d'aide à l'édition manuelle de données RDF a été implémenté pour assister cette tâche parfois longue et fastidieuse et comportant un risque d'erreurs significatif. Celui-ci s'appuie sur les connaissances du domaine et sur l'utilisation du raisonnement à partir de cas pour fournir une liste ordonnée de suggestions lors de l'édition d'un triplet RDF. Le système d'interrogation flexible défini a également été intégré à un outil de navigation, qui propose une interface pour l'exploration visuelle de graphes RDF, et qui exploite les similarités entre les ressources d'un graphe pour générer des filtres de recherche. Ces outils exploitent les connaissances associées au corpus de la correspondance qui sont intégrées à diverses règles de transformation. Au travers de l'utilisation de ce mécanisme, ces travaux s'interrogent également sur l'évolution des pratiques de recherche en histoire, et tendent à illustrer comment un tel système d'interrogation flexible peut contribuer à la méthode heuristique. Les méthodes et les outils proposés peuvent être appliqués pour d'autres corpus, en particulier dans le cadre de projets d'humanités numériques
Numerous historical works are devoted to the life and works of Henri Poincaré (1854-1912), in particular through the study and the publication of his correspondence, which consists of about 2000 letters and includes academic, private and scientific exchanges. For several years, digital projects have been carried out to store, publish and exploit corpus data by implementing standards and technologies of the Semantic Web, including RDF, RDFS and SPARQL. When browsing an RDF graph, several situations may lead to a desire of flexible querying. This term describes search methods that go beyond conventional search systems, which are restricted to exact queries and allow limited or no expression of user preferences. The main contribution of this research work is the formalization, study and applications of a flexible query mechanism based on the use of SPARQL query transformation rules. This system allows, from an initial query, an RDF graph and a set of rules, to generate SPARQL queries which can provide alternative results to those initially returned. Some rules are generic, and therefore easily transposable to other graphs, and other rules are domain-dependent. Several tools based on this mechanism have been developed to assist the digital exploitation of the Henri Poincaré correspondence. A system has been implemented to assist the manual editing of RDF data, a task which can sometimes be tedious. This system relies on domain knowledge and the use of case-based reasoning to provide an ordered list of suggestions when editing an RDF triple. The proposed flexible querying system has also been integrated into a navigation tool, which provides an interface for visual exploration of RDF graphs, and which exploits similarities between resources in a graph to generate search filters. These tools exploit knowledge associated with the correspondence corpus which is represented through various transformation rules. Through the use of this mechanism, this work also considers the evolution of research practices in history, and tends to show how such a flexible querying system can contribute to the heuristic method. The methods and tools proposed can be applied to other corpora, in particular in the context of digital humanities projects