Problems and solutions for alkene polymerisation catalysts incorporating Schiff-bases; migratory insertion and radical mechanisms of catalyst deactivation

Steric blocking of an intramolecular 1,2-migratory insertion reaction of a zirconium salicylaldiminato complex leads to a long-lived catalyst for ethene polymerisation, but promotes a new radical catalyst decomposition mechanism in certain instances; kinetic and thermodynamic parameters for both pathways have been established.     

Recursive Structures and Ershov's Hierarchy

Ash and Nerode [2] gave natural definability conditions under which a relation is intrinsically r. e. Here we generalize this to arbitrary levels in Ershov's hierarchy of Δ sets, giving conditions under which a relation is intrinsically α-r. e. Mathematics Subject Classification: 03C57, 03D55.     

On Automorphic Tuples of Elements in Computable Models

A criterion is obtained for existence of two isomorphic but not hyperarithmetically isomorphic tuples in a hyperarithmetical model. This criterion is used to show that such a situation occurs in the models of well-known classes.Original Russian Text Copyright © 2005 Goncharov S. S., Harizanov V. S., Knight J. F., Morozov A. S., Romina A. V.The first four authors are supported by the Binational Grant NSF DMS-0075899; the first and fourth authors are partially supported by the Russian Foundation for Basic Research (Grant 02-01-00953) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.03.1).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 523–532, May–June, 2005.     

The computable embedding problem

Calvert calculated the complexity of the computable isomorphism problem for a number of familiar classes of structures. Rosendal suggested that it might be interesting to do the same for the computable embedding problem. By the computable isomorphism problem and (computable embedding problem) we mean the difficulty of determining whether there exists an isomorphism (embedding) between two members of a class of computable structures. For some classes, such as the class of \mathbbQ \mathbb{Q} -vector spaces and the class of linear orderings, it turns out that the two problems have the same complexity. Moreover, calculations are essentially the same. For other classes, there are differences. We present examples in which the embedding problem is trivial (within the class) and the computable isomorphism problem is more complicated. We also give an example in which the embedding problem is more complicated than the isomorphism problem.     

On the path of an inert object impinged on one side by a Brownian particle

A Brownian particle on R impinges at t = 0 on an inertial mass which is free to move but cannot be passed. We assume that for all t≥ 0 the total transfer of momentum by time t is a constant K times the local time that the two objects are in contact by time t. It is proved that, for each K > 0 and initial velocity V(0) of the inertial mass, there is, on the natural filtered probability space of a Brownian motion, a unique (in law) process describing the path of such a mass. If V(t) denotes its velocity, the law of V ^(-1)(t) is obtained explicitly for V(0) = 0, and its properties are examined. Received: 22 August 2000 / Revised version: 31 January 2001 / Published online: 9 October 2001     

A mathematical description of the acoustic coupling of the mass/spring model

This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results.