Measure theoretical entropy of covers

In this paper we introduce three notions of measure theoretical entropy of a measurable cover in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We then prove that these three notions coincide, thus answering a question posed in [R], and recover a variational inequality (proved in [GW]) and a proof of the classical variational principle based on a comparison between the entropies of covers and partitions.     

Restricted unimodular chordal graphs

A chordal graph is called restricted unimodular if each cycle of its vertex‐clique incidence bipartite graph has length divisible by 4. We characterize these graphs within all chordal graphs by forbidden induced subgraphs, by minimal relative separators, and in other ways. We show how to construct them by starting from block graphs and multiplying vertices subject to a certain restriction, which leads to a linear‐time recognition algorithm. We show how they are related to other classes such as distance‐hereditary chordal graphs and strongly chordal graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 121–136, 1999     

Forces between mica surfaces, prepared in different ways, across aqueous and nonaqueous liquids confined to molecularly thin films

We have measured normal and lateral interactions across a range of different liquids between mica surfaces using a surface force balance (SFB). The mica surfaces were prepared either by melt cutting using Pt wire and standard procedures in our laboratories or by tearing sheets (that had not been exposed to Pt) off from a freshly cleaved sheet of mica. AFM micrographs revealed the substantial absence of Pt nanoparticles on the melt cut and torn-off mica surfaces. Normal-force versus surface-separation (D) profiles and shear force versus D measurements for purified water (no added salt), for concentrated aqueous NaCl solutions, and for cyclohexane revealed that in all cases the behavior of the highly confined liquids between melt-cut and between torn-off mica sheets was identical within experimental scatter. These results demonstrate directly that interactions measured between melt-cut mica surfaces as routinely prepared using established procedures in our laboratories and in other laboratories are free of the effect of any Pt contamination.     

Stable radicals formation in coals undergoing weathering: effect of coal rank

Once coal is excavated it comes into contact with atmospheric oxygen and begins to undergo low temperature oxidation. The mechanism by which the molecular oxygen interacts with the coal macromolecule is suggested to occur in several steps. These steps primarily involve O(2) diffusion to the surface where physical adsorption followed by chemical adsorption takes place. The chemical adsorption forms several types of oxides that can subsequently react to form several products, primarily CO(2). It has also been suggested that some of these oxidation mechanisms might involve radical reactions. As the previous studies were conducted under conditions where significant structural changes occur it is possible that in the low temperature range (T < 100 °C) the oxidation mechanism is different. Several different rank (lignite-subbituminous-bituminous) coals were isothermally heated at 95 °C in an air atmosphere for a period of up to 6 months and samples were collected at two week intervals. The radical concentration of each sample was measured by Continuous Wave Electron Paramagnetic Resonance (CW-EPR). It is apparent that there are distinct differences between the lower rank (lignite) and the higher rank (subbituminous, bituminous) coals. The lower rank coals exhibited only carbon centered radicals with an adjacent oxygen atom and the higher rank coals exhibited only carbon centered radicals. Interestingly, the lower rank coals exhibited no change in radical concentration due to the long term oxidation treatment while the higher rank coals showed a distinct increase in the radical concentration. These findings shed new light on the complex heterogeneous low temperature oxidation reactions occurring at the coal surface.     

RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism

Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using time-resolved small-angle X-ray scattering (TR-SAXS), we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly one-third complete within 35 ms, following a two-state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 10(9) M(-1) s(-1). The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.     

Preservation of Absolutely Continuous Spectrum of?Periodic Jacobi Operators Under Perturbations of?Square-Summable Variation

We study self-adjoint bounded Jacobi operators of the form:

More results in polychromatic Ramsey theory

We study polychromatic Ramsey theory with a focus on colourings of [ω ₂]². We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2 ^ω = ω ₂ and \(\omega _2 \to ^{poly} (\alpha )_{\aleph _0 - bdd}^2 \) for every α <ω ₂; (2) 2 ^ω = ω ₂ and \(\omega _2 \nrightarrow ^{poly} (\omega _1 )_{2 - bdd}^2 \).     

Incentive regulation and the change in productive efficiency in telecommunications in the United States

Incentive regulation has become an important regulatory tool in the telecommunications industry in the United States. The issue explored here is whether incentive regulation has resulted in an increase in productive efficiency. After providing an overview of the nature of incentive regulation, a methodology for measuring technical inefficiency and its change is introduced. This is a stochastic frontier production function approach reflecting technical inefficiency effects. The results of implementing this methodology suggest that in the production of interLATA billed access minutes for interstate calls, there was no change in technical efficiency, something that incentive regulation was specifically designed to enhance. Finally, an assessment of technical efficiency across individual LECs in the United States indicates considerable variability. Published in 2001 by John Wiley & Sons, Ltd.