On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators

Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers holds if the class has an envelope function that is μ-integrable, or if is bounded in L _p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of the class in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE) and to prove consistency for a class of simple M-estimators. This revised version was published online in June 2006 with corrections to the Cover Date.     

One-Dimensional Lattice Dynamics of the Diffusion-Limited Reaction A+A→A+S: Transient Behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A+AA+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynamics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.     

Novel polycyclic heterocycles. XIV. 1,2-Dihydro-4-(trifluoromethyl)-3H-8H-quino[1,8-ab][4,1]benzoxazepin-3-one and its derivatives

Procedures for the isolation of 1,2-dihydro-4-(trifluoromethyl)-3H,8H-quino[1,8-ab][4,1]-benzoxazepine, 3 , from reaction mixtures containing 3 as the minor component, and the isomer, 1,2-dihydro-11-(trifluoromethyl)-3H,7H-quino[8,1-cd][1,5]benzoxazepin-3-one, 2 , as the major component, are described. The reactivity of 3 toward hydroxylamine and aromatic aldehydes has been investigated and the preparation of derivatives with those reactants is described.     

Security of quantum bit string commitment depends on the information measure

Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum world. However, when committing to a string of n bits at once, how far can we stretch the quantum limits? In this Letter, we introduce a framework of quantum schemes where Alice commits a string of n bits to Bob, in such a way that she can only cheat on a bits and Bob can learn at most b bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: a + b is at least n. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where a = 4log2(n) + O(1) and b = 4, which is impossible classically. Our findings significantly extend known no-go results for quantum bit commitment.     

Impedance study of SrTi1−xFexO3−δ (x = 0.05 to 0.80) mixed ionic-electronic conducting model cathode

SrTi_1?xFe_xO_3?δ (STF) model cathodes, with compositions of x = 0.05 to 0.80 were deposited onto single crystal yttria stabilized zirconia by pulsed layer deposition as dense films with well defined area and thickness and studied by electrochemical impedance spectroscopy as a function of electrode geometry, temperature and pO₂. The STF cathode was observed to exhibit typical mixed ionic-electronic behavior with the electrode reaction occurring over the full electrode surface area rather than being limited to the triple phase boundary. The electrode impedance was observed to be independent of electrode thickness and to the introduction of CGO interlayers and inversely proportional to the square of the electrode diameter, pointing to surface exchange limited kinetics. Values for the surface exchange coefficient, k, were calculated and found to be comparable in magnitude to those exhibited by other popular mixed ionic-electronic conductors such as (La,Sr)(Co,Fe)O₃, thereby, confirming the suitability of STF as a model mixed conducting cathode material. The surface exchange coefficient, k, was also found to be insensitive to orders of magnitude change in both bulk electronic and ionic conductivities.     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Spectroscopy and electrochemistry of cytochrome P450 BM3-surfactant film assemblies

We report analyses of electrochemical and spectroscopic measurements on cytochrome P450 BM3 (BM3) in didodecyldimethylammonium bromide (DDAB) surfactant films. Electronic absorption spectra of BM3-DDAB films on silica slides reveal the characteristic low-spin FeIII heme absorption maximum at 418 nm. A prominent peak in the absorption spectrum of BM3 FeII-CO in a DDAB dispersion is at 448 nm; in spectra of aged samples, a shoulder at approximately 420 nm is present. Infrared absorption spectra of the BM3 FeII-CO complex in DDAB dispersions feature a time-dependent shift of the carbonyl stretching frequency from 1950 to 2080 cm(-1). Voltammetry of BM3-DDAB films on graphite electrodes gave the following results: FeIII/II E(1/2) at -260 mV (vs SCE), approximately 300 mV positive of the value measured in solution; DeltaS degrees (rc), DeltaS degrees , and DeltaH degrees values for water-ligated BM3 in DDAB are -98 J mol(-1) K(-1), -163 J mol(-1) K(-1), and -47 kJ mol(-1), respectively; values for the imidazole-ligated enzyme are -8 J mol(-1) K(-1), -73 J mol(-1) K(-1), and -21 kJ mol(-1). Taken together, the data suggest that BM3 adopts a compact conformation within DDAB that in turn strengthens hydrogen bonding interactions with the heme axial cysteine, producing a P420-like species with decreased electron density around the metal center.     

Crosslinked polydiacetylene and its two- and three-component interpenetrating polymer networks (IPNs)

The synthesis of crosslinked polydiacetylene [poly4ECMU (a polydiacetylene with ethoxy carbonyl methylene urethane substitution): where R = ? (CH₂)₄OCONHCH₂COOCH₂CH₃] was carried out utilizing its polar and flexible substituent groups. Polydiacetylene was crosslinked by the formation of allophanate linkages utilizing urethane groups in the substituent groups of the polydiacetylene. Two-component IPNs of polydiacetylene [poly4BCMU (a polydiacetylene with butoxy carbonyl methylene urethane substitution): where R = ? (CH₂)₄OCONHCH₂COO(CH₂)₃CH₃] and an epoxy resin (diglycidyl ether of Bisphenol A) were synthesized. Two-component IPNs of poly4ECMU with the above epoxy resin were also synthesized. For the first time, two-component stiff-backbone IPNs of two different kinds of polydiacetylene (poly4BCMU and polyECMU) and a three-component IPN of poly4BCMU, poly4ECMU, and the epoxy resin were synthesized. IPNs with fewer allophanate linkages were also made in order to examine morphological differences between them. The glass transition behavior of these networks was studied using differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) by means of a Rheovibron.