Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Long-range order in a simple model of interacting fermions

We consider a model of spinless fermions on a lattice, interacting through a nearest neighbor repulsion. In the half-filled band case and for dimensionsd 2, we rigorously prove that there is long-range order in some domain of the parameters=(k _B T)^–1 andt/U, wheret is the hopping amplitude of the particles,U the strength of their repulsion, and the inverse temperature. Our technique is based on the usual Peierls argument of classical statistical mechanics but fails for the groundstate. We discuss the specific difficulties introduced by the Fermi statistics.Work supported in part by U.S. NSF grant PHY 90-19433-A02.     

Un théorème de convergence presque-sŭre pour des familles subordonnées à un semi groupe discret

LetP be a positive contraction ofL ¹, we say that a sequence (Q _n ) _n of positive operators is subordinated toP if $$Q_0 = Id, \forall n \in \mathbb{N} Q_n P \geqslant Q_{n + 1} .$$ Let (Q _n,k ) be a double sequence of operators such that for each integerk the sequence (Q _n,k ) _n is subordinated toP. We prove a result of almost everywhere convergence for the quotientsW ^k f/W _k g, whereW ^k f=∑ _n=0 ^∞ Q _n,k f.     

Shape-tunable polymer nodules grown from liposomes via ring-opening metathesis polymerization

A new inisurf (acting as surfactant and initiator) molecule for ring-opening metathesis polymerization (ROMP) was synthesized and used in aqueous solution in order to control the size and shape of polymer nodules grown from liposomes. Nodules were observed to grow in size with conversion of monomer, and depending on the monomer used, they adopted either a spherical or comet-like shape. Here, we investigate polymer production from a liposome surface. We use a hydrophobic derivative of the Grubbs catalyst positioned at the liposome surface to allow for ROMP of monomers dissolved in the aqueous outer phase. We obtain nodules of polymer that can grow up to tens of micrometers, unveiling new efficient possibilities of polymerization from a membrane in an aqueous solution.     

Zirconocene-mediated route to enantiopure 9-oxabicyclononanes functionalized on both carbon bridges

[reaction: see text] A zirconocene-mediated ring contraction of 4-vinylfuranosides generated either from d-arabinose or d-glucose is followed by sequential oxidation to the ketone and alkynyl Grignard addition. The resulting cis-cyclobutanediols are subjected in turn to thermal rearrangement and intramolecular oxymercuration-demercuration. The regiochemistry of the final ring closure is controlled by the nature of R.     

Giant vesicles formed by gentle hydration and electroformation: a comparison by fluorescence microscopy

Giant unilamellar vesicles (diameter of a few tens of micrometers) are commonly produced by hydration of a dried lipidic film. After addition of the aqueous solution, two major protocols are used: (i) the gentle hydration method where the vesicles spontaneously form and (ii) the electroformation method where an ac electric field is applied. Electroformation is known to improve the rate of unilamellarity of the vesicles though it imposes more restricting conditions for the lipidic composition of the vesicles. Here we further characterize these methods by using fluorescence microscopy. It enables not only a sensitive detection of the defects but also an evaluation of the quantity of lipids in these defects. A classification of the defects is proposed and statistics of their relative importance in regard to both methods and lipid composition are presented: it shows for example that 80% of the vesicles obtained by electroformation from 98% 1,2-dioleoyl-sn-glycero-3-phosphocholine are devoid of significant defects against only 40% of the vesicles with the gentle hydration method. It is also shown that the presence of too many negatively charged lipids does not favor the formation of unilamellar vesicles with both methods. For the gentle hydration, we checked if the negatively charged lipids were inserted in the vesicles membrane in the same proportion as that of the lipid mixture from which they are formed. The constant incorporation of a negatively charged labeled lipid despite an increasing presence of negatively charged 1,2-dioleoyl-sn-glycero-3-[phospho-l-serine] tends to confirm that the composition of vesicles is indeed close to that of the initial mixture.