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     

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.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.