Dissimulation des opinions politiques sous contrôle: Le cas d’Ibn Ḥazm à Séville

This article tackles a difficult problem involving the biography of Ibn Ḥazm, namely the classical Arab historians have alluded to the fact that al-Mu‛taḍid, king of Seville, had persecuted Ibn Ḥazm and decreed that his books must be burnt. The same historians give no explicit nor accurate details on the political circumstances that led to this tragedy. We have studied and reconstructed the historical context of the events while taking greater advantage of some new facts discovered from our recent study on the textual history of Kitāb al-Faṣl.[fr] Les historiens arabes classiques ont fait allusion au fait qu’al-Mutaḍid, roi de Séville, avait persécuté Ibn Ḥazm et aurait condamné ses livres au feu. Ces mêmes historiens ne disaient rien d’explicite qui pourra nous renseigner avec exactitude et détails sur les circonstances politiques qui ont donné lieu à ce drame. Nous avons étudié et reconstruit le contexte historique des événements tout en tirant un plus grand profit de quelques faits nouveaux qu’avait révélés notre récente étude consacrée à l’histoire du texte de Kitāb al-Faṣl

Identificación de un manuscrito andalusí anónimo de una obra contra Ibn Ḥazm al-Qurṭubī (m. 456/1064)

This article presents an unpublished fragment of an Andalusí manuscript of a text criticizing Ibn Ḥazm. Identifications are offered of the title of the work and its author, as well as suggestions as to where it was composed. The text also provides valuable information about Ibn Ḥazm, his writings, his opponents and those who protected him as well as about the author of the text itself. The historical value of the manuscript is great, but the manuscript is incomplete. It is to be hoped that this article will make it possible to discover another manuscript whose contents complement and perhaps complete those of this manuscript, in poor condition, preserved in Fez and, in microfilm, in the Bibliothèque Genèrale de Rabat.En este artículo se aborda el estudio de un fragmento manuscrito andalusí que contiene una crítica dirigida a la doctrina ẓāhirí de Ibn Ḥazm. En primer lugar, se intenta determinar el título de la obra y la identidad del autor. Posteriormente, se ofrece una estimación aproximada de la fecha y el lugar de composición del libro. Por último, se proporciona información relevante en tomo a la figura de Ibn Ḥazm, sus obras, sus adversarios, sus protectores, al igual que sobre el autor del fragmento. El valor histórico del manuscrito es realmente considerable, por lo que aprovecho estas líneas para expresar mi deseo de que en el futuro otros investigadores puedan localizar otro ejemplar de este fragmento que, de algún modo, permita completar la información proporcionada por el deteriorado manuscrito, actualmente preservado en la Biblioteca de al-Qarawiyyīn de Fez, y cuyo microfilm se halla en la Biblioteca General de Rabat

The Fourier Singular Complement Method for the Poisson problem. Part II: axisymmetric domains

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was introduced and analysed, in prismatic domains. In this second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges or vertices of the domain, nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used

The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains

This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed, in prismatic domains. In the second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges of the domain nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used

Identificación de «al-Qurṭubī», autor de al-I‛lām bimā fī dīn al-naṣārà min al-fasād wa-l-awhām

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Calcul de champs électromagnétiques et de répartition de charges surfaciques dans des domaines quasi-singulier.

First, we focus on solving numerically the Poisson problem with homogenous Dirichlet conditions in a three dimensional prismatic or axisymmetric domain, with a reentrant edge at the boundary. We present the Fourier Singular Complement Method based on a Fourier expansion in the direction parallel to the reentrant edge and the Singular Complement Method for solving the 2D problems in the Fourier modes. The analysis shows that we recover the optimal rate of convergence O(h) when using P 1 Lagrange finite elements for the discretization. No refinement near the reentrant edge is required in the computations. Second, we are interested in computing the charge density and the electricfield at the rounded tip of an electrode of small curvature radius. Our model problem is the electrostatic problem. For this problem, Peek's empirical formulas describe the relation between the electric field at the surface of the electrode and its curvature radius. However, they apply only to thin electrodes with either a purely cylindrical, or a purely spherical, geometrical shape. Our aim is to justify rigorously these formulas, and to extend them to more general, either two dimensional or three dimensional axisymmetric, geometries. With the help of multiscaled asymptotic expansions, we establish rigorously an explicit formula for the electric potential in geometries that coincide with a cone at infinity. We also prove a formula for the surface charge density, which is very simple to compute with the FE Method. In particular, the meshsize can be chosen independently of the curvature radius. We illustrate our mathematical results by numerical experiments.La première partie de ce mémoire est consacrée à la résolution numérique du problème de Poisson avec conditions aux limites de Dirichlet dans un domaine prismatique ou axisymétrique, possédant une arête rentrante sur sa frontière. Nous présentons la Méthode de Fourier et du Complément Singulier consistant à combiner un développement en série (de Fourier) dans la direction parallèle à l'arête et la Méthode du Complément Singulier pour les problèmes bidimensionnels associés aux modes (de Fourier). L'analyse de la MFCS conduit à une vitesse de convergence optimale en O(h) lorsqu'on utilise les éléments finis de Lagrange P1 pour la discrétisation. La méthode ne requiert aucun raffinement de maillage au voisinage de la singularité. Nous nous intéressons ensuite au calcul de la densité de charge à la pointe d'une électrode lorsque celle-ci présente un faible rayon de courbureque nous abordons par la résolution du problème électrostatique. La relation entre le rayon de courbure et le champ électrique à la surface de la pointe est décrit par la loi empirique de Peek. Toutefois, celle-ci n'est valable que pour des électrodes minces à géométrie cylindriques ou sphériques. On justifie mathématiquement cette loi et on l'étend à d'autres géométries. A l'aide des développements asymptotiques multi-échelles, on établit explicitement le comportement de la densité de charge pour des géométries coincidant avec un cône à l'infini. Enfin, nous illustrons ce comportement asymptotique par des expériences numériques réalisées en dimension deux, et en dimension trois, pour des domaines axisymétriques. Les résultats sont comparés à ceux obtenue par une méthode intégrale

Multiscaled asymptotic expansions for the electric potential: Surface charge densities and electric fields at rounded corners

International audienceWe are interested in computing the charge density and the electric field at the rounded tip of an electrode of small curvature. As a model, we focus on solving the electrostatic problem for the electric potential. For this problem, Peek's empirical formulas describe the relation between the electric field at the surface of the electrode and its curvature radius. However, it can be used only for electrodes with either a purely cylindrical, or a purely spherical, geometrical shape. Our aim is to justify rigorously these formulas, and to extend it to more general, two-dimensional, or three-dimensional axisymmetric, geometries. With the help of multiscaled asymptotic expansions, we establish an explicit formula for the electric potential in geometries that coincide with a cone at infinity. We also prove a formula for the surface charge density, which is very simple to compute with the Finite Element Method. In particular, the meshsize can be chosen independently of the curvature radius. We illustrate our mathematical results by numerical experiments. © World Scientific Publishing Company