Low-Temperature Polymerization of endo- and exo-2-Methyl-7-oxabicyclo-[2.2.1]-heptane

Abstract

Polymerization of the title compounds in methylene di-chloride with PF, catalyst have shown that the rate of polymer formation drops sharply with temperature and the polymerization ceases entirely around -60 to -70°C. Ex-periments carried out with the exo-2-Me isomer have shown that at -30°C a limiting conversion of approx 40% is attained and simultaneously the molecular weight and the molecular weight distribution level off. At -50°C the same limiting conversion level is reached; however, the molecular weight level is higher and a study of changes in molecular weight distribution with time indicates that at this tempera-ture a greater proportion of chains remain active throughout the polymerization. Even at -30°C, however, experiments with changing conditions, especially the temperature, during the runs have demonstrated that the systems are not “dead” after the limiting conversion has been reached. Polymeriza-tion of the endo-2-Me isomer at -50°C has shown that in the time interval studied the limiting viscosity number increases essentially linearly with time.     

Reply to the Comment by S. J. Kowalski,TIPM 40, 113, 2000

Transport in Porous Media -     

Decomposition in global optimization

The purpose of this article is to propose a simple framework for the various decomposition schemes in mathematical programming.Special instances are discussed. Particular attention is devoted to the general mathematical programming problem with two sets of variables. An economic interpretation in the context of hierarchical planning is done for the suggested decomposition procedure.The framework is based on general duality theory in mathematical programming and thus focussing on approaches leading to global optimality.     

Measurement of ultrasonic absorption in a gel by light diffraction and resonator methods

A new sample cell construction for a light diffraction method permits absolute measurements of the ultrasonic absorption coefficient for a strongly absorbing transparent gel. By means of this cell the absorption coefficient at 6.2 MHz has been measured as a function of the temperature in the gelling temperature range for a 25% (w/w) aqueous solution of the ABA polyoxyethylene-polyoxypropylene block copolymer PLURONIC^R F 127. The resonator method has been used under the same experimental conditions. The strongly absorbing gel causes overlapping of the resonance signals. A calibration based on resonance experiments compared with the absolute measurements yields a solution to that problem and thus makes the resonator method applicable to a strongly absorbing gel.     

Positive linear extension operators for spaces of affine functions

The following result is proved: letE be anF-space (that is, the space of all continuous affine functions defined on a compact universal cap van shing at zero) and letMχE be anM-ideal. Then, ifE/M is a π₁ with positive defining projections, then there is a positive linear operator ϱ:E/M→E of norm one such that ϱ lifts the canonical mapE→E/M. In the proof, which heavily depends on work of Ando, we study ensor products of certain convex cones with compact bases, and we calculate the norm of a positive linear operator defined on a finite dimensional space with range in aF-space. Various corollaries are deduced for split faces of compact convex sets and for morphisms ofC ^*-algebras.     

Blocking and antiblocking sets

The purpose of this paper is to study a generalization of the concept of blocking and antiblocking polyhedra that has been introduced by D.R. Fulkerson. The polyhedra studied by Fulkerson are restricted to the nonnegative orthant in R ^m . The present generalization considers sets restricted to a cone. This leads to two polarity correspondences, which are related to the Minkowski polarity for convex sets.