A composite methodology for multistage degradation of polymers

Five different analytical schemes for examining isothermal and nonisothermal degradation of polymers were reviewed and found inadequate for describing multistage decomposition. The different schemes were experimentally tested using thermogravimetric analysis data for an ethylene-vinyl acetate (EVA) copolymer, which exhibited a well-behaved two-step decomposition process in a nitrogen environment. Based on these experimental and analytical findings, a generalized methodology was developed capable of describing the exhibited complex decomposition behavior of polymers by combining two or more kinetic mechanisms in a series or parallel arrangement. This composite of combinational methodology thus extends established analytical schemes for describing complex decomposition of polymers in a rational manner, incorporating both experimental and theoretical considerations.     

The 1-type of a Waldhausen K-theory spectrum

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Oscillations and concentrations in weak solutions of the incompressible fluid equations

The authors introduce a new concept of measure-valued solution for the 3-D incompressible Euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations. One application of the concepts developed here is the following important result: a sequence of Leray-Hopf weak solutions of the Navier-Stokes equations converges in the high Reynolds number limit to a measure-valued solution of 3-D Euler defined for all positive times. The authors present several explicit examples of solution sequences for 3-D incompressible Euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations. An extensions of the concept of Young measure is developed to incorporate these complex phenomena in the measure-valued solutions constructed here.Partially supported by N.S.F. GrantPartially supported by N.S.F. Grant 84-0223 and 86-11110     

Current methods for site-directed structure generation

Summary There has been a rapid growth of interest in techniques for site-directed drug design, fuelled by the increasing availability of structural models of proteins of therapeutic importance, and by studies reported in the literature showing that potent chemical leads can be obtained by these techniques. Structure generation programs offer the prospect of discovering highly original lead structures from novel chemical families. Due to the fact that this technique is more-or-less still in its infancy, there are no case studies available that demonstrate the use of structure generation programs for site-directed drug design. Such programs were first proposed in 1986, and became commercially available in early 1992. They have shown their ability to reproduce, or suggest reasonable alternatives for, ligands in well-defined binding sites. This brief review will discuss the recent advances that have been made in the field of site-directed structure generation.     

Consistency of a myopic Bayesian algorithm for one-dimensional global optimization

A sequential Bayesian method for finding the maximum of a function based on myopically minimizing the expected dispersion of conditional probabilities is described. It is shown by example that an algorithm that generates a dense set of observations need not converge to the correct answer for some priors on continuous functions on the unit interval. For the Brownian motion prior the myopic algorithm is consistent; for any continuous function, the conditional probabilities converge weakly to a point mass at the true maximum.