Bromine catalyzed conversion of S-tert-butyl groups into versatile and, for self-assembly processes accessible, acetyl-protected thiols

The facile and efficient conversion of a tert-butyl protecting group to an acetyl protecting group for thiols by catalytic amounts of bromine in acetyl chloride and the presence of acetic acid has been developed. The fairly mild reaction conditions are of particular interest for new protecting group strategies for sulfur functionalised target structures.     

Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations

Summary. We prove that a standard second order finite difference uniform space discretization of the semilinear wave equation with periodic boundary conditions, analytic nonlinearity, and analytic initial data conserves momentum up to an error which is exponentially small in the stepsize. Our estimates are valid for as long as the trajectories of the full semilinear wave equation remain real analytic. The method of proof is that of backward error analysis, whereby we construct a modified equation which is itself Lagrangian and translation invariant, and therefore also conserves momentum. This modified equation interpolates the semidiscrete system for all time, and we prove that it remains exponentially close to the trigonometric interpolation of the semidiscrete system. These properties directly imply approximate momentum conservation for the semidiscrete system. We also consider discretizations that are not variational as well as discretizations on non-uniform grids. Through numerical example as well as arguments from geometric mechanics and perturbation theory we show that such methods generically do not approximately preserve momentum.Mathematics Subject Classification (2000): 65M20, 58J70, 70H33     

Measuring skill in games: several approaches discussed

An aspect of casino games that in general leads to discussions among both participants and spectators, is the relative extent to which a player can positively influence his results by making appropriate strategic choices. This question is closely related to the issue of how to distinguish between games of skill and games of chance. This is an issue that is interesting from a juridical point of view too, since in many countries the legitimacy of exploiting a specific game depends on the category to which it belongs. This paper summarizes recent developments concerning the measurement of skill in games. It points out the elements in the definitions that need closer attention, it illustrates the analysis with examples and it discusses further possibilities.     

Active site structure and redox processes of cytochrome c oxidase immobilised in a novel biomimetic lipid membrane on an electrode

Membrane-bound cytochrome c oxidase was attached to an electrode via a His-tag linker and studied by surface enhanced resonance Raman spectroscopy, demonstrating intact redox site structures and electron transfer between the electrode and the immobilized enzyme.     

Classical Projections of Quantum Mechanics and the Limit ħ → 0

The convergence of the dynamics of classical projection to the dynamics of the classical limit is investigated for 0. A mistake from a previous paper is pointed out, and the correct version of the result is given. A new, similar result is presented if the function generating the Hamiltonian of both the classical projection and the classical limit is a polynomial.     

Diode-Laser Jet Spectra and Analysis of the nu(1) and nu(4) Fundamentals of CCl(3)F

High-resolution infrared spectra have been measured for mixtures of CCl(3)F in Ne, expanded in a supersonic planar jet. We present the first analysis for the nu(4) fundamental and a complete analysis for the nu(1) band. Accurate spectroscopic constants have been obtained for both the nu(1) fundamental of the most abundant isotopic species, C(35)Cl(3)F, C(35)Cl(2)(37)ClF, and C(35)Cl(37)Cl(2)F. With respect to an earlier work [M. Snels, A. Beil, H. Hollenstein, M. Quack, U. Schmidt, and F. D'Amato, J. Chem. Phys. 103, 8846-8853 (1995)], the observation of Q branches of the three most abundant isotopomers allowed for an unambiguous determination of the nu(1) band origins. The nu(4) fundamental has not been the subject of a high-resolution analysis up to now. The observation of high-resolution spectra of the central part of the band permitted the determination of band origin, rotational constants, and Coriolis constant for the symmetric-top species, C(35)Cl(3)F. Copyright 2001 Academic Press.     

Tables of curves with many points

These tables record results on curves with many points over finite fields. For relatively small genus () and a small power of or we give in two tables the best presently known bounds for , the maximum number of rational points on a smooth absolutely irreducible projective curve of genus over a field of cardinality . In additional tables we list for a given pair the type of construction of the best curve so far, and we give a reference to the literature where such a curve can be found.

     

Demand dispersion and logistics costs in one-to-many distribution systems

When an organization decides on which groups of consumers it should target, the locations of these target consumers often play a role. Methods from the field of market segmentation are able to identify target groups with high benefit levels, but the expected costs of supplying products to the target groups are less well understood. These costs can play a large role if the locations of the customers, the demand locations, are geographically widely dispersed. This paper focuses on one-to-many distribution systems in which a central facility serves all demand points. We derive accurate logistics cost estimates from the dispersion of demand points for such systems, enabling a comparison of the expected logistics costs of different candidate target groups. The most accurate measure combines the average distance from the demand locations to a central location and the mutual distances between neighboring demand locations. The average of the distances between all pairs of locations forms a good alternative measure.