Collapsing irreducible 3-manifolds with nontrivial fundamental group

Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman’s proof of Thurston’s Geometrisation Conjecture.     

Scindements de Heegaard et groupe des homéotopies des petites variétés de Seifert

Sans résuméOblatum 12-XI-1990     

An exactly solvable Ogston model of gel electrophoresis. VI. Towards a theory for macromolecules

In this article, we present a generalized version of our lattice model of low-field gel electrophoresis that allows us to treat the case of macromolecules such as short linear or circular oligomers and semi-flexible rods. We show that free-solution electrophoresis problems can be seen as random walks in the conformational space of the analyte. For sufficiently small molecules, our mathematical approach provides exact mobilities. In a quenched gel-like environment, however, both conformational and positional degrees of freedom must be used, but exact solutions can also be obtained. As an example, we then investigate several two-dimensional model gels, as well as a simple channel system where we see evidence of entropic effects that cannot be captured by the traditional Ogston concept of free volume.     

Chemical models of the hydrophobic interaction: Apparent molal volumes and heat capacities of three symmetrical bolaform electrolytes and their homologous monomers in aqueous solution at 25°C

The densities and volumetric specific heats of aqueous solutions of Bu₃NHBr, Pent₃NHCl, and three diazonium salts, HN?Oct₃?NHBr₂, HN?Dec₃?NHCl₂, and Bu₃N?Oct?NBu₃Br₂, have been measured at 25°C. From these data, the apparent molal volumes φ _v and apparent molal heat capacities φ _c have been calculated and are reported here. In the series of compounds chosen, the diazonium (higher homologs) can be regarded as dimers of the alkyl-substituted ammonium ions (lower homologs), and these systems are examined as chemical models for the hydrophobic interaction. With the three homologous pairs studied here, the chemical model predicts that the strong interaction (limitingly, chemical binding) of two hydrocarbon chains in water leads to a major decrease in both φ _v and φ _c of the interacting solutes, ca.?22 cm³-mole^?1 and ?200 J-^oK^?1-mole^?1. These predictions constitute limiting behavior — useful, but not sufficient, to explain the observed concentration dependence of φ _v and φ _c in aqueous solutions of the lower homologs Bu₃NHBr, Pent₃NHCl, and Bu₄NBr. An explanation for the concentration dependence of φ _c is suggested with reference to ultrasonic relaxation data.     

New fluorinated polysiloxanes containing an ester function in the spacer. I. Synthesis and characterization

Unsaturated perfluoroalkyl esters derived from undecylenic acid: CH₂?CH? (CH₂)₈? COO? CH₂? CH₂? R_F (with R_F?C₆F₁₃, 2a and R_F?C₈F₁₇, 2b ) and C₈F₁₇? (CH₂)₁₀? COO? CH₂? CH?CH₂, 2c were prepared with excellent yields. Their hydrosilylation by methylhydrodimethylsiloxane copolymers of various Si? H contents gives new fluorinated polysiloxanes which were examined by ¹H- and ¹³C-NMR, GPC, differential scanning calorimetry, and optical polarizing microscopy. Polymers derived from compounds 2a and 2b exhibit mesomorphic structures. © 1994 John Wiley & Sons, Inc.     

Synthesis of polymers containing tertiary phosphine oxides using complex bases

Tertiary phosphine oxides have been prepared in excellent yield from primary alkyl halides or aromatic halides and activated sodium phosphinates obtained by reaction of dialkyl phosphine oxides with complex bases (NaNH₂/tBuONa). This reaction has been successfully applied to soluble and cross-linked bromopolystyrenes and to macroporous polystyrenes with bromooctyl substituents giving polymers which contain pendant phosphine oxide groups.