A G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z -actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoid. We show that a G-solenoid can be seen as a projective limit of branched manifo...

of Mini-course On the concentration properties of mean field particle models (based on a series of 4 joint works with : D.A. Dawson, A. Guionnet, E. Rio, S.L. Hu and L.M. Wu) Pierre Del Moral Centre de Recherche Bordeaux Sud-Ouest & Institut de Mathématique de Bordeaux INRIA, France Abstract This lecture is concerned with the exponential concentration properties of a general class of mean field...

For a large class of tilings of R, including the Penrose tiling in two dimension as well as the icosahedral ones in 3 dimension, the continuous hull ΩT of such a tiling T inherits a minimal R -lamination structure with flat leaves and a transversal ΓT which is a Cantor set. In this case, we show that the continuous hull can be seen as the projective limit of a suitable sequence of branched, ori...

(1) find colim-acyclic objects in Ab. Here, Ab denote the category of abelian groups and Ab denote the (abelian) functor category for the small category C. The functor colim : Ab → Ab is the direct limit functor and F ∈ Ab is colim-acyclic if colimi F = 0 for i ≥ 1 (see [16] and [5], and the classical books of Cartan and Eilenberg [2] and of MacLane [13]). It is clear that if F is projective th...

Giry and Lawvere’s categorical treatment of probabilities, based on the probabilistic monad G, offer an elegant and hitherto unexploited treatment of higher-order probabilities. The goal of this paper is to follow this formulation to reconstruct a family of higher-order probabilities known as the Dirichlet process. This family is widely used in non-parametric Bayesian learning. Given a Polish s...

let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

This paper considers a machine as a pair (G5M) where G is a group or a semi group and where M is a state space. The first part of the paper called reversible-state machines considers the case where G is a locally compact group and M is any locally compact group and M is any locally compact space. The essential requirement is that (x,p)~>x(p) be continuous where XGG, peM and x(p)eM; i.e., we req...

Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts: first, that work characterizes a process rather than an instantaneous state of a system and, second, that quantum systems are sensitive to the interactions with a measurement apparatus. We compare different measurement scenarios o...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...