Influence of catalyst depletion or deactivation on polymerization kinetics. III. Solution polymerization of acrylonitrile in N,N-dimethylformamide at −30°C.

The experimental results on homogeneous polymerization of acrylonitrile initiated with the sodium triethylthioisopropoxyaluminate, NaAlEt₃S(i-Pr), catalyst in DMF at ?30°C. are compared with the prediction of equations based on a postulated mechanism. The agreement between the calculated and observed number-average molecular weight combined with the kinetic data and the relationship between the conversion and the initial catalyst concentration provides a rigorous test concerning the validity of the equations and the mechanism of the polymerization. A plausible mechanism is postulated as follows: The initiation must be relatively fast in accordance with the rate equations and the growing polymer undergoes propagation, transfer (to monomer), and deactivation simultaneously. The infrared spectrum of the low molecular weight polymer prepared at a high catalyst concentration showed strong absorption at 2337, 2205, and 1620 cm.^?1 but no absorption at 900 cm.^?1, indicating that there are two nitriles in the polymer, one of which is conjugated. The possibility of having ? CH?CH₂ groups in the polymer is ruled out by the absence of the band at 900 cm.^?1. In view of these facts, it is concluded that the polymer has a ? CH?CHCN endgroup resulting from the transfer reaction.     

Instability criteria for steady flows of a perfect fluid

An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.     

Generic eigenvalue multiplicities for two-parameter families of operators

A theorem about two-parameter families of Schrödinger operators in proved; the potential is parameter dependent.     

Hölder Continuity of Solutions to the Kinematic Dynamo Equations

We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with respect to the natural scaling of the equations.     

Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Equality Constraints: Corrigendum and Addendum

In this paper we give corrections to our paper on an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints.     

Volume Contents

Volume Contents

Volume Contents