Une fantaisie récurrente de plusieurs mathématiciens ([22], [14], [19], [11], . . .) est l’existence d’un “corps à un élément”, noté F1, et d’une géométrie algébrique sur ce corps. On pense par exemple que le groupe des points de SLN dans F1 est le groupe symétrique des permutations de N lettres, et que ces N lettres sont les points dans F1 de l’espace projectif P N . Et l’on s’est aperçu depui...

We prove that the group of left self-distributivity, a cousin of Thompson’s group F and of Artin’s braid group B∞ that describes the geometry of the identity x(yz) = (xy)(xz), admits a bi-invariant linear ordering. To this end, we define a partial action of this group on finite binary trees that preserves a convenient linear ordering.

In this paper we characterize all Darboux polynomials and rational first integrals of the generalized Lorenz systems: ẋ = a(y − x), ẏ = bx + cy − xz, ż= dz+ xy. Our results include the corresponding ones for the Lorenz systems, the Chen systems and the Lü systems as special cases. © 2011 Elsevier Masson SAS. All rights reserved. MSC: 34A34; 34C20; 34C41; 37G05

The bis-(1,1-dimethylethylisocyanide) (tert-butylisocyanide) complexes of three iron porphyrinates (2,3,7,8,12,13,17,18-octaethyl-5,10,15,20-tetraphenylporphyrin, OETPP; 2,3,7,8,12,13,17,18-octamethyl-5,10,15,20-tetraphenylporphyrin, OMTPP; and 2,3,7,8,12,13,17,18-tetra-beta,beta'-tetramethylene-5,10,15,20-tetraphenylporphyrin, TC(6)TPP) have been prepared and studied by EPR and (1)H NMR spectr...

We show that arithmetic subgroups of semisimple groups of relative Q-type An, Bn, Cn, Dn, E6, or E7 have an exponential lower bound to their isoperimetric inequality in the dimension that is 1 less than the real rank of the semisimple group. Let G be a connected, semisimple, Q-group that is almost simple over Q. Let X be the symmetric space of noncompact type associated with G(R) and let XZ be ...

We describe weak BCC-algebras (also called BZ-algebras) in which the condition (xy)z = (xz)y is satisfied only in the case when elements x, y belong to the same branch. We also characterize branchwise commutative and branchwise implicative weak BCC-algebras satisfying this condition. We also describe connections between various types of implicative weak BCC-algebras.