Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

Can mass dissociation patterns of transition-metal complexes be predicted from electrochemical data?

The Cooks kinetic method has been very convenient to correlate the relative dissociation rates obtained by collision-induced fragmentation experiments with the energies of two related bonds in molecules and complexes in the gas phase. Reliable bond energy data are, however, not always available, particularly for polynuclear transition-metal complexes, such as the triruthenium acetate clusters of the general formula [Ru(3) (mu(3)-O)(mu-CH(3)COO)(6)(py)(2)(L)](+), where L = ring substituted N-heterocyclic ligands. Accordingly, their gas-phase collision-induced tandem mass spectrometry (CID MS/MS) dissociation patterns have been analyzed pursuing a relationship with the more easily accessible redox potentials (E(1/2)) and Lever`s E(L) parameters. In fact, excellent linear correlations of In(1/2A(L)/A(py)), where A(py) and A(L) are the abundance of the fragments retaining the pyridine (py) and L ligand, respectively, with E(1/2) and E(L) were found. This result shows that those electrochemical parameters are correlated with bond energies and can be used in the analysis of the dissociation data. Such modified Cooks method can be used, for example, to determine the electronic effects of substituents on the metal-ligand bonds for a series of transition-metal complexes. Copyright (C) 2008 John Wiley & Sons, Ltd.

Modeling Information Diffusion in University Libraries: Assessing Peer Interaction Patterns as a Complex Dynamic System

This presentation was offered as part of the CUNY Library Assessment Conference, Reinventing Libraries: Reinventing Assessment, held at the City University of New York in June 2014.