We consider further reduction of normal forms for nilpotent planar vector fields. We give a unique normal form for a special case of an open problem for the Takens–Bogdanov singularity.  2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Unicité des formes normales pour la singularité de Takens–Bogdanov dans un cas particulier Résumé. On étudie l’unicité des formes nor...

Let G be a connected, simple Lie group of rank n defined over the complex numbers. To a parabolic subgroup P in G of semisimple rank r, one can associate n−r positive integers coming from the theory of hyperplane arrangements (see P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), 167-189; Coxeter arrangements, in Proc. of Symposia in Pur...

This note is not intended to introduce schemes, but rather to accompany a presentation of their definition (such as [1, §II.1-2]) as an explanation of why they are defined the way they are. Compared to a classical notion such as that of a projective variety, schemes differ in several key aspects: • Schemes are constructed locally, using the machinery of sheaves. • Rather than the usual notion o...

— We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable tor...

[1] Fourier Analysis of Uniform Random Number Generators, with R. R. Coveyou, J. Assoc. Comp. Mach. 14 (1967), 100–119. [2] Singularities of Vector Bundle Maps, Proceedings of Liverpool Singularities Symposium I, Springer Lect. Notes in Math. (1971), 316–318. [3] Generic Vector Bundle Maps, Dynamical Systems, M. Peixoto, ed., Academic Press, 1973, 165–327. [4] Characteristic Classes for Singula...

| The Poisson boundary for a wide class of random walks on Gromov hyperbolic groups is shown to coincide with the hyperbolic boundary. muni de l'action de G tel que la formule de Poisson f(g) = h b f; gi est une isom etrie de l'espace L 1 (G;) et l'espace H 1 (G;) des fonctions-harmoniques born ees sur G. Trivialit e de la fronti ere de Poisson signiie que l'espace des fonctions-harmoniques bor...

Introduction: This paper treats the structure of those lattice-ordered rings which are subdirect sums of totally ordered rings—the f-rings of Birkhoff and Pierce [4]. Broadly, it splits into two parts, concerned respectively with identical equations and with ideal structure; but there is an important overlap at the beginning. D. G. Johnson has shown [9] that not every /-ring is unitable, i.e. e...

We give a geometric realization of the symmetric algebra of the tensor space C ⊗ C m together with the action of the dual pair (gln, glm) in terms of lagrangian cycles in the cotangent bundles of certain varieties. We establish geometrically the equivalence between the (gln, glm)-duality and Schur duality. We establish the connection between Springer’s construction of (representations of) Weyl ...

We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring. 2000 Mathematics Subject Classification. 16D70, 16U80. Throughout,...

If G is an omega-stable group with a normal definable subgroup H , then the Sylow-2-subgroups of G/H are the images of the Sylow-2-subgroups of G. Zusammenfassung. Sei G eine omega-stabile Gruppe und H ein definierbarer Normalteiler von G. Dann sind die Sylow-2-Untergruppen von G/H Bilder der Sylow-2-Untergruppen von G. Si H est un sous-groupe normal d’un groupe fini G, les p-sylows de G/H sont...