Kohlenwasserstoffe

Ohne Zusammenfassung     

On Teichmüller’s theorem on the quasi-invariance of cross ratios

Teichmüller’s theorem gives necessary and sufficient conditions for mapping one ordered quadruple by aK-quasiconformal map onto a second ordered quadruple. We give a simple non-computational proof of the necessity part. We then characterize such extremal mappings, and obtain as a consequence a new formula for the modular function, with leads to a very simple derivation of the known expression for the Poincaré metric on the thrice-punctured sphere. Research partially supported by NSF grant MCS 76-04969A01.     

How Not to Schedule a Stitching Room

This is a case study of a project to introduce computer-aided scheduling into the stitching room of a shoe factory, which led instead to an automated microcomputer-controlled work-handling system. The outcome has been an increase in productivity and wages earned, together with a large reduction in throughput time and work-in-progress.     

On the use of loss functions in the changepoint problem

Summary We consider a sequence of independent random variables whose densities depend on a parameter which is subject to a change at an unknown time point. A Bayesian decision-theoretic approach is used to obtain an optimal choice of changepoint. The exponential and multivariate normal models are analyzed, and some numerical examples are given.     

The use of SO2Cl2 in organometallic chemistry. Convenient high yield syntheses of [Fe(η-C5H5)(CO)3] [FeCl4] and [M(CO5Cl] (M = Mn or Re)

Depending on the substrate and the reaction conditions, SO₂Cl₂ is a useful reagent which brings about either chlorination or the formation of cationic species on reaction with transition metal carbonyl complexes.     

Sensitivity analysis and model optimization for reaction-diffusion systems

This paper presents a computational framework for the optimization and sensitivity analysis of a process whose state depends upon several parameter functions. Assuming that the process is described by a system of quasilinear, parabolic, partial differential equations, we show how determining the problem parameters so as to improve an associated objective functional is directly related to knowing the state function sensitivities. An expression for the gradient of the objective functional in terms of the solutions of an adjoint system enables one to bypass the calculation of state function sensitivities. These concepts are illustrated for a simple model of cooperative processes in chemical kinetics. Since sensitivity analysis and model optimization are important tools for investigating parameter dependence and validating mathematical models, research developments in such diverse fields as optimal design theory, chemical kinetics, and parameter identification are important motivations for this paper.This author would like to gratefully acknowledge Dr. M. Delle Donne, EGG, for several helpful discussions.This author was partially supported by NSF Grant No. CMS-80-05677.     

Orientational sampling and rigid-body minimization in molecular docking revisited: On-the-fly optimization and degeneracy removal

Summary Strategies for computational association of molecular components entail a compromise between configurational exploration and accurate evaluation. Following the work of Meng et al. [Proteins, 17 (1993) 266], we investigate issues related to sampling and optimization in molecular docking within the context of the DOCK program. An extensive analysis of diverse sampling conditions for six receptor-ligand complexes has enabled us to evaluate the tractability and utility of on-the-fly force-field score minimization, as well as the method for configurational exploration. We find that the sampling scheme in DOCK is extremely robust in its ability to produce configurations near to those experimentally observed. Furthermore, despite the heavy resource demands of refinement, the incorporation of a rigid-body, grid-based simplex minimizer directly into the docking process results in a docking strategy that is more efficient at retrieving experimentally observed configurations than docking in the absence of optimization. We investigate the capacity for further performance enhancement by implementing a degeneracy checking protocol aimed at circumventing redundant optimizations of geometrically similar orientations. Finally, we present methods that assist in the selection of sampling levels appropriate to desired result quality and available computational resources.