Landau singularities and singularities of holonomic integrals of the Ising class

We consider families of multiple and simple integrals of the ``Ising class'' and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of the head polynomial of these linear ODE's and the subset of singularities occurring in the integrals, with the singularities obtained from the Landau conditions. For these Ising class integrals, we show that the Landau conditions can be worked out, either to give the singularities of the corresponding linear differential equation or the singularities occurring in the integral. The singular behavior of these integrals is obtained in the self-dual variable $w= s/2/(1+s^2)$, with $s= \sinh(2K)$, where $K=J/kT$ is the usual Ising model coupling constant. Switching to the variable $s$, we show that the singularities of the analytic continuation of series expansions of these integrals actually break the Kramers-Wannier duality. We revisit the singular behavior (J. Phys. A {\bf 38} (2005) 9439-9474) of the third contribution to the magnetic susceptibility of Ising model $\chi^{(3)}$ at the points $1+3w+4w^2= 0$ and show that $\chi^{(3)}(s)$ is not singular at the corresponding points inside the unit circle $| s |=1$, while its analytical continuation in the variable $s$ is actually singular at the corresponding points $2+s+s^2=0$ oustside the unit circle ($| s | > 1$).Comment: 34 pages, 1 figur

Role of Nlrp6 and Nlrp12 in the maintenance of intestinal homeostasis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102624/1/eji2871.pd

Complexity spectrum of some discrete dynamical systems

We first study birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of $3 \times 3$ matrices. We introduce a semi-numerical analysis which enables to compute the Arnold complexities for all the $9!$ possible birational transformations. These complexities correspond to a spectrum of eighteen algebraic values. We then drastically generalize these results, replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters. Again it is shown that the associated birational, or even rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil

Renormalization, isogenies and rational symmetries of differential equations

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization group.Comment: 36 page

Globally nilpotent differential operators and the square Ising model

We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their lambda-extensions. These integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations. These differential operators are very selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing on the factorised parts of all these operators, we find out that the global nilpotence of the factors corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, and even a remarkable weight-1 modular form emerging in the three-particle contribution $\chi^{(3)}$ of the magnetic susceptibility of the square Ising model. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or $\infty$) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new structures associated with simple deformations of the nilpotent property.Comment: 55 page

Le texte littéraire, passeur culturel et interculturel ? Discours d'enseignants et pratiques de classe dans une université algérienne.

Le présent article s\u27intéresse aux dynamiques interculturelles qui se manifestent dans les interactions "autour" d\u27un texte littéraire  (un extrait du Figuier enchanté de Marco Micone), lors d\u27un cours de littérature dans une université algérienne. Trois aspects retiennent plus particulièrement notre attention : - quel est la place de cette dimension interculturelle dans la lecture du texte menée par l\u27enseignante ; - quelles sont les modalités du dialogue entre soi et l’autre (les autres) qui se tisse dans cette lecture ; - quels sont les tensions et les conflits nés de cette dynamique ? L’étude de cette séquence met en évidence les dynamiques (inter) culturelles à l’œuvre lors de la lecture d’un texte littéraire, témoigne des potentialités de  cette  approche ; elle est aussi révélatrice des difficultés à mener  à bien de  manière  pertinente  cette démarche (inter) culturelle et de la  concilier avec une lecture attentive du texte.

Poésie et musique : propositions pour la classe de langue

Cet article est consacré à à la poésie mise en musique, à la place et au rôle qu’il est possible de lui attribuer dans l’enseignement du français langue étrangère. Après avoir rappelé brièvement quand et comment, dans l’histoire littéraire, la poésie a pu être accompagnée de musique et / ou mise en voix , nous nous plaçons sur le terrain de la pratique : quels poèmes en musique travailler dans la classe de FLE ? quelles activités mettre en œuvre ? à quelles fins