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.     

The signal/noise of an HMBC spectrum can depend dramatically upon the choice of acquisition and processing parameters

The effect of various acquisition and processing parameters on the sensitivity of HMBC spectra for typical organic molecules has been systematically investigated. For molecules in the 200–600 molecular weight range, an acquisition time of 0.2 to 0.4 s, a recycle time of no more than 1.0 s, optimization for ⁿJ_CH = 8 Hz and 512 time increments (with two‐ to fourfold linear prediction) are recommended. Some form of sine bell weighting along f₂ and either Gaussian or sine bell weighting along f₁ is suggested. The use of a 0.1‐s acquisition time and/or Gaussian or exponential weighting along f₂ can result in dramatic sensitivity loss, particularly for correlation peaks involving protons with complex splitting patterns, and should be avoided. Copyright © 2009 John Wiley & Sons, Ltd.     

Random homogeneous sodium sulfonate polysulfone ionomers: Preparation,characterization, and blend studies

The sodium salts of randomly sulfonated polysulfone (Na-SPSF), derived from 1,1′-sulfonylbis-[4-chlorobenzene] with 4,4′-(1-methylethylidene)-bis-[phenol], were prepared over the composition range of 3–30 mol% sodium sulfonate, using improved procedures in which the sulfonating complex was introduced into an intensely agitated polymer solution. In contrast to earlier work, T_g was found to increase nonlinearly with sodium sulfonate content. A SAXS study provided no evidence of ionic clustering in these polymers. Binary blends of Na-SPSFs differing only in composition were prepared by casting films from solution, and their phase behavior was studied by dynamic mechanical analysis after annealing at 250°C. It was found that the blends were miscible up to a composition difference of about 9–10 mol% sodium sulfonate. Using this fact it was possible to calculate a value for χ_ABn of 200–250, where χ_AB represents the segmental interaction parameter between unmodified and modified repeat units, and n is the degree of polymerization. Uncertainty in the degree of ionic association places a degree of uncertainty on the effective value of n and therefore on χ_AB. The product, however, is independent of any assumptions regarding molecular associations.     

Cutting-plane proofs in polynomial space

Following Chvátal, cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution. We show that such proofs may be carried out in polynomial workspace.Research supported by Sonderforschungsbereich 303 (DFG), Institut für Operations Research, Universität Bonn, FR Germany and by NSF grant ECS-8611841.     

An improved detailed chemical kinetic model for C3-C4 linear and iso-alcohols and their blends with gasoline at engine-relevant conditions

Propanol and butanol isomers have received significant research attention as promising fuel additives or neat biofuels. Robust chemical kinetic models are needed that can provide accurate and efficient predictions of combustion performance across a wide range of engine relevant conditions. This study seeks to improve the understanding of ignition and combustion behavior of pure C3-C4 linear and iso-alcohols, and their blends with gasoline at engine-relevant conditions. In this work, a kinetic model with improved thermochemistry and reaction kinetics was developed based on recent theoretical calculations of H-atom abstraction and peroxy radical reaction rates. Kinetic model validations are reported, and the current model reproduces the ignition delay times of the C3 and C4 alcohols well. Variations in reactivity over a wide range of temperatures and other operating conditions are also well predicted by the current model. Recent ignition delay time measurements from a rapid compression machine of neat iso-propanol and iso-butanol [Cheng et al., Proc. Combust Inst. (2020)] and blends with a research grade gasoline [Goldsborough et al., Proc. Combust Inst. (2020)] at elevated pressure (20–40 bar) and intermediate temperatures (780–950 K) were used to demonstrate the accuracy of the current kinetic model at conditions relevant to boosted spark-ignition engines. The effects of alcohol blending with gasoline on the autoignition behavior are discussed. The current model captures the suppression of reactivity in the low-temperature and negative-temperature-coefficient (NTC) region when either isopropanol and isobutanol are added to a research grade gasoline. Sensitivity and reaction flux analysis were performed to provide insights into the relevant fuel chemistry of the C3-C4 alcohols.