On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

Velocity inversion: A case study in infinite-dimensional optimization

The goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict, in a least-error sense, seismic waveforms measured at its surface. We present velocity inversion as a case study in the various infinite-dimensional pathologies which may afflict practically important problems of distributed parameter identification, treated as optimization problems in function spaces. These features differentiate various problem formulations far beyond the degree one would expect for finite- (small-) dimensional problems. We illustrate this differentiation by comparing the characteristics of three different least-squares formulations of velocity inversion.