Lifting endomorphisms to automorphisms

Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some detail, and apply those results to complete the identification of asymptotic lifts of unital completely positive linear maps on von Neumann algebras in terms of their minimal dilations to endomorphisms.

     

A Facile synthesis of 3-alkylthio-(or arylthio-)pyridines and 3,5-bis(alkylthio)pyridines

3-Alkylthio- (or 3-arylthio-)pyridines and 3,5-bis(alkylthio)pyridine can be conveniently prepared by the reaction of 3-thiocyanato- or 3,5-bis(thiocyanato)pyridines with tri-n-butylphosphine in the presence of alcohol.     

Random quantum states

This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems.     

Co‐oxidation of ammonia and ethanol in supercritical water,part 2: Modeling demonstrates the importance of H2NNOx

A co‐oxidation model was constructed from available submechanisms for ammonia and ethanol oxidation. The ammonia submechanism validated for combustion at atmospheric pressure conditions was modified for the higher densities and lower temperatures (655–700°C) of supercritical water. The ethanol submechanism had previously been tested and validated at supercritical water conditions. The initial model poorly reproduced experimental ammonia conversion data and was not able to consistently match nitrous oxide production as a function of temperature over a range from 655–700°C at 246 bar. To improve model predictions, the low‐pressure NH₂ + NO_x submechanism was replaced with a submechanism that included the H₂NNO_x adduct species that are expected to be stabilized in the high‐pressure supercritical water environment. Thermochemical and kinetic parameters for the adduct species were estimated with quantum chemical calculations using Gaussian 98 with the CBS‐Q method. The explicit treatment of the H₂NNO_x adducts resulted in nitrous oxide yield predictions that correctly reproduced experimental trends. This work represents a vital first step in improving the understanding of ammonia oxidation in supercritical water. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 653–662, 2008     

The origin of the residual conductivity of GaN films on ferroelectric materials

In this paper, the origin of the conductivity of GaN films grown on ferroelectric materials was investigated using XPS, AES, and XRD analysis tools. Depth profiles confirmed the existence of impurities in the GaN film originating from the substrates. Bonding energy analysis from XPS and AES verified that oxygen impurities from the substrates were the dominant origin of the conductivity of the GaN film. Furthermore, Ga-rich GaN films have a greater chance of enhancing diffusion of lithium oxide from the substrates, resulting in more substrate phase separation and a wider inter-mixed region confirmed by XRD. Therefore, the direct GaN film growth on ferroelectric materials causes impurity diffusion from the substrates, resulting in highly conductive GaN films. Future work needs to develop non-conductive buffer layers for impurity suppression in order to obtain highly resistive GaN films.     

Analytic solutions for optimal statistical arbitrage trading

In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein-Uhlenbeck process. By framing the problem in terms of the first-passage time of the process, we derive expressions for the mean and variance of the trade length and the return. We examine the problem of choosing an optimal strategy under two different objective functions: the expected return, and the Sharpe ratio. An exact analytic solution is obtained for the case of maximising the expected return.