A molecular mechanics approach to mapping the conformational space of diaryl and triarylphosphines

A molecular mechanics force field has been developed which accurately reproduces experimental solid state structures and conformer interconversion barriers for a series of sterically congested diaryl and triaryl phosphines and some of their chalcogenide and Cr(CO)5 derivatives.     

An Efficient Stereoselective Synthesis of a Tricyclic Intermediate for the Synthesis of Derivatives of Abietic and Podocarpic Acids

For many years the synthesis of diterpene acids has attracted the attention of organic chemists. Kröniger and Wheeler¹ reported that the condensation of the dimethylate 1a with methyl malonate gave the cis compound 2a which on heating with palladised charcoal was converted into the trans isomer 3a. Compound 3a is a promising intermediate in the synthesis of derivatives of both abietic and podocarpic acids, while 2a could be a starting material for the synthesis of cis fused diterpene acids. However, the route to 2a and 3a was inefficient; 1a was only available as the minor component of a mixture with its epimer 1b; and the yield for the stage 2a + 3a was poor.     

Influence of nitroxide structure on the 2,5‐ and 2,6‐spirodicyclohexyl substituted cyclic nitroxide‐mediated free‐radical polymerization of styrene

The 2,6‐spirodicyclohexyl substituted nitroxide, cyclohexane‐1‐spiro‐2′‐(3′,5′‐dioxo‐4′‐benzylpiperazine‐1′‐oxyl)‐6′‐spiro‐1″‐cyclohexane (BODAZ), was investigated as a mediator for controlled/living free‐radical polymerization of styrene. The values of the number‐average molecular weight increased linearly with conversion, but the polydispersities were higher than for the corresponding 2,2,6,6‐tetramethylpiperidinyl‐1‐oxy (TEMPO) and 2,5‐bis(spirocyclohexyl)‐3‐benzylimidazolidin‐4‐one‐1‐oxyl (NO88Bn) mediated systems at approximately 2.2 and 1.6 at 100 and 120 °C, respectively. These results were reflected in the rate coefficients obtained by electron spin resonance spectroscopy; at 120 °C, the values of the rate coefficients for polystyrene‐BODAZ alkoxyamine dissociation (k_d), combination of BODAZ and propagating radicals (k_c), and the equilibrium constant (K) were 1.60 × 10^?5 s^?1, 5.19 × 10⁶ M^?1 s^?1, and 3.08 × 10^?12 M, respectively. The value of k_d was approximately one and two orders of magnitude lower, and that of K was approximately 20 and 7 times lower than for the NO88Bn and TEMPO adducts. These results are explained in terms of X‐ray crystal structures of BODAZ and NO88Bn; the six‐membered ring of BODAZ deviates significantly from planarity as compared to the planar five‐membered ring of NO88Bn and possesses a benzyl substituent oriented away from the nitroxyl group leading to a seemingly more exposed oxyl group, which resulted in a higher k_c and a lower k_d than NO88Bn. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3892–3900, 2003     

Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems

We generalise the current theory of optimal strong convergence rates for implicit Euler-based methods by allowing for Poisson-driven jumps in a stochastic differential equation (SDE). More precisely, we show that under one-sided Lipschitz and polynomial growth conditions on the drift coefficient and global Lipschitz conditions on the diffusion and jump coefficients, three variants of backward Euler converge with strong order of one half. The analysis exploits a relation between the backward and explicit Euler methods.     

An information-based computational technique for estimation of chromatographic peak purity

Assessment of the purity of chromatographic peaks is an important step in developing and validating purification procedures for complex mixtures. While curve-fitting techniques can be useful for determining the retention times and relative concentrations of the components of a chromatographic peak, their utility is limited by the lack of unambiguous criteria for determining the number of such components. In this work, we present a computational technique for analyzing chromatograms to estimate the number of components, their retention times, and their relative concentrations. In contrast to Fourier-transform-based techniques, the technique we present does not require manual peak identification. It is based on curve-fitting and uses the Akaike information criterion to estimate the number of components. Application of the technique to chromatograms obtained from size-exclusion and reverse-phase chromatography of test mixtures indicates that it is useful for the characterization of complex mixtures.     

The effect of uni-axial stretching on the roughness of microfiltration membranes

Atomic force microscopy (AFM) was used to characterize the surface morphology of uni-axially stretched and non-stretched microporous microfiltration (MF) membranes. The effect of stretching on the pore structure and bulk properties of MF membranes has been previously reported [J.A. Morehouse, L.S. Worrel, D.L. Taylor, D.R. Lloyd, B.D. Freeman, D.F. Lawler, The effect of uni-axial orientation on macroporous membrane structure, J. Porous Mater. 13 (2006) 63–75.]; this paper focuses solely on the use of AFM to characterize the surface of stretched and non-stretched MF membranes. A new way of representing surface roughness that may prove useful in relating roughness to performance in cross-flow applications is presented.     

Strengthened invex and perturbations

If the strengthened invex property holds for a constrained minimization problem, then a Karush-Kuhn-Tucker point is a strict minimum. The strict minimum property is preserved under small perturbations of the problem. This allows sufficient conditions to be given for a minimax, starting from Karush-Kuhn-Tucker conditions. They extend to vector-valued minimax and to nonsmooth (Lipschitz) problems. An example is provided to illustrate the strengthened invex property, also a discussion of quadratic-linear (nonconvex) programming implications.     

Spectral clustering and its use in bioinformatics

We formulate a discrete optimization problem that leads to a simple and informative derivation of a widely used class of spectral clustering algorithms. Regarding the algorithms as attempting to bi-partition a weighted graph with N vertices, our derivation indicates that they are inherently tuned to tolerate all partitions into two non-empty sets, independently of the cardinality of the two sets. This approach also helps to explain the difference in behaviour observed between methods based on the unnormalized and normalized graph Laplacian. We also give a direct explanation of why Laplacian eigenvectors beyond the Fiedler vector may contain fine-detail information of relevance to clustering. We show numerical results on synthetic data to support the analysis. Further, we provide examples where normalized and unnormalized spectral clustering is applied to microarray data—here the graph summarizes similarity of gene activity across different tissue samples, and accurate clustering of samples is a key task in bioinformatics.