Equivariant mappings: a new approach in stochastic simulations

Stochastic simulations on manifolds usually are traced back to ⁿ via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry.     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Novel antibiotics: second generation macrocyclic peptides designed to trap Holliday junctions

Described are the syntheses of 15 macrocyclic peptides designed to trap Holliday junctions (HJs) in bacteria during site-specific and homologous recombination. This leads to inhibiting bacterial growth. These second generation macrocycles were based on the C-2 symmetrical HJ. They were synthesized using a strategy that permits elucidation of the amino acid role in binding HJs. The syntheses of these macrocycles are an important step in the development of a new class of antibiotics.     

Recent advances of group 14 dimetallenes and dimetallynes in bond activation and catalysis

Since the first heavy alkene analogues of germanium and tin were isolated in 1976, followed by West''s disilene in 1981, the chemistry of stable group 14 dimetallenes and dimetallynes has advanced immensely. Recent developments in this field veered the focus from the isolation of novel bonding motifs to mimicking transition metals in their ability to activate small molecules and perform catalysis. The potential of these homonuclear multiply bonded compounds has been demonstrated numerous times in the activation of H₂, NH₃, CO₂ and other small molecules. Hereby, the strong relationship between structure and reactivity warrants close attention towards rational ligand design. This minireview provides an overview on recent developments in regard to bond activation with group 14 dimetallenes and dimetallynes with the perspective of potential catalytic applications of these compounds.

This minireview highlights the recent advances in small molecule activation and catalytic applications of homonuclear dimetallenes, dimetallynes and interconnected bismetallylenes of heavier group 14 elements.     

Reactions of the ionized enol tautomer of acetanilide: elimination of HNCO via a novel rearrangement

The reactions of ionised acetanilide, C(6)H(5)NH(=O)CH(3)(.+), and its enol, C(6)H(5)NH(OH)=CH(2)(.+), have been studied by a combination of tandem mass spectrometric and computational methods. These two isomeric radical cations have distinct chemistries at low internal energies. The keto tautomer eliminates exclusively CH(2)=C=O to give ionised aniline. In contrast, the enol tautomer loses H-N=C=O, via an unusual skeletal rearrangement, to form predominantly ionised methylene cyclohexadiene. Hydrogen atom loss also occurs from the enol tautomer, with the formation of protonated oxindole. The mechanisms for H-N=C=O and hydrogen atom loss both involve cyclisation; the former proceeds via a spiro transition state formed by attachment of the methylene group to the ipso position, whereas the latter entails the formation of a five-membered ring by attachment to the ortho position. The behaviour of labelled analogues reveals that these two processes have different site selectivities. Hydrogen atom loss involves a reverse critical energy and is subject to an isotope effect. Surprisingly, attempts to promote the enolisation of ionised acetanilide by proton-transport catalysis were unsuccessful. In a reversal of the usual situation for ionised carbonyl compounds, ionised acetanilide is actually more stable than its enol tautomer. The enol tautomer was resistant to proton-transport catalysed ketonisation to ionised acetanilide, possibly because the favoured geometry of the encounter complex with the base molecule is inappropriate for facilitating tautomerisation.     

Inelastic electron tunneling spectroscopy

Inelastic electron tunneling spectroscopy (IETS) is a relatively new form of vibrational spectroscopy which is able to address problems previously unsolved by either IR or Raman. It is particularly useful for surface analysis.     

Die Acidität von Silanolgruppen. Vorläufige Mitteillung

The intrinsic acidity constant K_int. of surface silanol groups has been determined by coulometric titration of silicagel at 25° in solutions of the constant ionic strength 0,1M consisting primarily of sodium perchlorate. The experimental data are consistent with