Exceptionally long-range self-assembly of hexa-peri-hexabenzocoronene with dove-tailed alkyl substituents

The substitution of a hexa-peri-hexabenzocoronene by bulky, space-demanding, 2-decyltetradecyl side chains proved to be an effective procedure to influence the thermal and self-aggregation behavior. The extremely large steric requirement of the introduced side chains modulated the aggregation and resulted in a dramatic lowering of the isotropization temperature and a higher solubility. As an additional consequence of the exceptional, long-range self-aggregation of the discotic molecule, spherulite formation was observed during crystallization by polarized light microscopy. Macroscopic self-assembly was induced by zone crystallization of the material, leading to aligned columnar superstructures as revealed by 2D-WAXS experiments. These extraordinary properties have not yet been reported for a discotic columnar material, making this compound very promising for application in electronic devices.     

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.     

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.