Embedding the Vasicek model into the Cox–Ingersoll–Ross model

The Cox–Ingersoll–Ross (CIR) model and the Vasicek model are two well‐known single factor models of the interest spot rate. In this paper, we construct a mapping by means of which the price of a zero‐coupon bond in the CIR model may be obtained from a corresponding price in the Vasicek model. We use symmetry analysis to construct this mapping and verify it by transforming three arbitrary solutions of the pricing equation in the Vasicek model into solutions of the corresponding equation in the CIR model. Copyright © 2010 John Wiley & Sons, Ltd.     

Symmetry analysis of a model of stochastic volatility with time-dependent parameters

We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the determination of the Lie point symmetries of the governing 1+1 evolution partial differential equation. This is not the situation in the latter case, but we are able to infer the essential structure of the required nonlocal symmetry from that of the autonomous problem and hence can present the solution to the nonautonomous problem. As in the case of the standard Black-Scholes problem the presence of time-dependent parameters is not a hindrance to the demonstration of a solution.     

High-precision half-life measurement for the superallowed β+ emitter ²⁶Al(m)

A high-precision half-life measurement for the superallowed β+ emitter 26Al(m) was performed at the TRIUMF-ISAC radioactive ion beam facility yielding T 1/2 6346.54 ± 0.46(stat) ± 0.60 (syst) ms, consistent with, but 2.5 times more precise than, the previous world average. The 26Al(m) half-life and ft value, 3037.53(61) s, are now the most precisely determined for any superallowed β decay. Combined with recent theoretical corrections for isospin-symmetry-breaking and radiative effects, the corrected Ft value for (26)Al(m), 3073.0(12) s, sets a new benchmark for the high-precision superallowed Fermi β-decay studies used to test the conserved vector current hypothesis and determine the V(ud) element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix.     

The Large‐Time Solution of Burgers' Equation with Time‐Dependent Coefficients. I. The Coefficients Are Exponential Functions

In this paper, we consider an initial‐value problem for Burgers' equation with variable coefficients where x and t represent dimensionless distance and time, respectively, and , are given functions of t. In particular, we consider the case when the initial data have algebraic decay as , with as and as . The constant states and are problem parameters. Two specific initial‐value problems are considered. In initial‐value problem 1 we consider the case when and , while in initial‐value problem 2 we consider the case when and . The method of matched asymptotic coordinate expansions is used to obtain the large‐t asymptotic structure of the solution to both initial‐value problems over all parameter values.     

Do Glycosyl Sulfonium Ions Engage in Neighbouring‐Group Participation? A Study of Oxathiane Glycosyl Donors and the Basis for their Stereoselectivity

Neighbouring‐group participation has long been used to control the synthesis of 1,2‐trans‐glycosides. More recently there has been a growing interest in the development of similar strategies for the synthesis of 1,2‐cis‐glycosides, in particular the use of auxiliary groups that generate sulfonium ion intermediates. However, there has been some debate over the role of sulfonium ion intermediates in these reactions: do sulfonium ions actually engage in neighbouring‐group participation, or are they a resting state of the system prior to reaction through an oxacarbenium ion intermediate? Herein, we describe the reactivities and stereoselectivities of a family of bicyclic thioglycosides in which an oxathiane ring is fused to the sugar to form a trans‐decalin‐like structure. A methyl sulfonium ion derived from one such glycosyl donor is so stable that it can be crystallised from ethanol, yet it reacts with complete stereoselectivity at high temperature. The importance of a ketal group in the oxathiane ring for maintaining this high stereoselectivity is investigated using a combination of experiment and ab initio calculations. The data are discussed in terms of S_N1 and S_N2 type mechanisms. Trends in stereoselectivity across a series of compounds are more consistent with selective addition to oxacarbenium ions rather than a shift between S_N1 and S_N2 mechanisms.     

Optical second-harmonic generation study of exfoliated MoS2-malachite green inclusion materials

We have examined the properties of exfoliated and restacked MoS(2)-malachite green (MG) inclusion compounds to provide insight into the MG-MoS(2) interactions that characterize these materials. The results of X-ray diffraction experiments indicate that MG included into the restacked structure adopts a flat orientation approximately parallel to the MoS(2) sheets. Second-harmonic generation experiments conducted on the exfoliated and restacked materials provide information regarding the averaged orientation of the MG. At low MG coverage, our results support the X-ray diffraction findings, and yield large averaged orientation angles, consistent with a flat orientation of MG between the MoS(2) layers. However, as the MG coverage is increased, the SHG results indicate averaged MG orientations that are much more upright, consistent with the expulsion of excess MG from the layers to the outside of the restacked crystallites. Together with X-ray diffraction and adsorption isotherm data, our SHG results provide a model for the exfoliation, adsorption, and subsequent restacking of these MG-based inclusion materials and demonstrate the utility of nonlinear optical techniques as probes of these interesting layered structures.     

Reproducibility estimates from single-laboratory ruggedness tests compared with those derived from collaborative trials of six microbiological measurement methods

This work investigated the feasibility of single-laboratory ruggedness experiments to estimate between-laboratory reproducibility. Six microbiological measurement methods that had already been subject to multi-laboratory validation were studied. Ruggedness experiments were designed and executed to determine sensitivity coefficients for factors judged likely to vary between laboratories. These were combined with estimates of factor variation to give reproducibility estimates. The single-laboratory estimates of reproducibility were generally not similar to those generated from multi-laboratory work. The experimental plans were difficult to design and execute, and were only partially successful in producing useful sensitivity coefficients. The authors conclude that ruggedness tests do not offer a single-laboratory alternative to multi-laboratory method validation or a practical approach to the evaluation of measurement uncertainty for microbiological methods. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. Campden BRI was previously known as the Campden and Chorleywood Food Research Association.