Perspectivities of odd order and chevalley groups

LetP be a projective plane and X a finite group of Lie-type in Aut(P). Suppose Aut(P) is a perspectivity of odd prime order inducing a nontrivial automorphism on X. We show that in most cases X must contain involutory perspectivities.     

Bordismus verzweigter Überlagerungen von Niedrigdimensionalen Sphären

The concept of bordism between branched coverings is a generalization of the concept of regular homotopy between such maps as given in [3].The main result of this article states that for n=2,3 any two branched coverings of the n-sphere with a finite and equal number of sheets are bordant.

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Diese Arbeit entstand während eines Aufenthaltes des Autors am Sonderforschungsbereich Theoretische Mathematik der Universität Bonn.     

1H, 13C and 15N NMR spectral analysis of substituted 1,2,3,4‐tetrahydro‐pyrido[1,2‐a]pyrimidines

The NMR spectroscopic data of a series of thirty‐four 3‐acylpyrido[1,2‐a]pyrimidinium salts are analyzed, which were prepared as either perchlorates or chlorides. Methyl group substituted 3‐aroyltetrahydropyrido[1,2‐a]pyrimidines with the methyl substituent in positions 6, 8 and 9 as well as both in positions 6 and 8 were investigated bearing various aroyl substituents. Unequivocal assignment of all resonances was achieved via two‐dimensional ¹H,¹H‐COSY measurements, ¹H,¹³C and ¹H,¹⁵N HSQC as well as HMBC experiments, and important diagnostic CH and NH couplings in the heteroaromatic ring system are evaluated. The influence of the methyl substituents was analyzed on the proton, carbon and nitrogen shifts. A significant effect of the counter ion on some chemical shifts of the nuclei under discussion of the pyridopyrimidines is found, allowing the indirect detection of the anion, which is confirmed by direct measurement of the ³⁵Cl nucleus of the perchlorates. Copyright © 2013 John Wiley & Sons, Ltd.     

ÜBER EINIGE REAKTIONEN DER DIALKYLBENZYLPHOSPHINIMIDE

Abstract

Dialkylbenzylphosphine imides C₆H₅CH₂–PRR′[dbnd]N″ (R, R′ = CH₃, C₂H₅; R″ = H, CH₃, Si(CH₃)₃ react with aliphatic and aromatic aldehydes in benzene solution on heating to 80°C directly and in high yields according to a Horner-Wittig-reaction with formation of an olefine whereas ketones like benzophenone and acetophenone only perform an O/NR″ exchange (R″ = H).

Dialkylbenzylphosphinimide C₆H₅CH₂–PRR′[dbnd]N″ mit R, R′ = CH₃, C₂H₅ und R″ = H, CH₃, Si(CH₃)₃ reagieren mit aliphatischen und aromatischen Aldehyden in benzolischer Lösung beim Erwärmen auf 80°C direkt und mit hohen Ausbeuten im Sinne einer Horner-Wittig-Reaktion unter Olefinbildung, während sich mit Ketonen wie Benzophenon oder Acetophenon nur ein O/NR″-Austausch (R″ = H) vollzieht.     

Trace formulas for additive and non-additive perturbations

Trace formulas for pairs of self-adjoint, maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained. In particular, the existence of a complex-valued spectral shift function for a pair {H^′,H}$\{H^{\prime },H\}$ of maximal accumulative operators has been proved. We investigate also the existence of a real-valued spectral shift function. Moreover, we treat in detail the case of additive trace class perturbations. Assuming that H   and H^′=H+V$H^{\prime }=H+V$ are maximal accumulative and V is trace class, we prove the existence of a summable   complex-valued spectral shift function. We also obtain trace formulas for pairs {H,H^?}$\{H,H^{?}\}$assuming only that H and  H^?$H^{?}$are resolvent comparable. In this case the determinant of the characteristic function of H is involved in trace formulas.     

Molecular mobility and transport in polymer membranes and polyelectrolyte multilayers

Polyelectrolyte multilayers prepared by the layer-by-layer technique provide an efficient way to generate planar structures of tailored surface charge and hydrophobicity, which are used as membranes for pervaporation. The use of polyelectrolyte multilayers to form the membrane permits tailoring the surface charge of the membrane and, thus, selectivity; at the same time, it reduces fouling of the membrane by adsorption of organic matter. Pulsed field gradient (PFG) nuclear magnetic resonance has been used to investigate the diffusion of probe molecules into polymer systems. Evaluation of the apparent diffusion coefficient in porous poly(amide) results in a pore size of 4 microm, as found in electron micrographs. For the pore size obtained for polyelectrolyte multilayers, no equivalent pores could be found in microscopy. Propagators for the diffusion of propanol and propanol-water mixture into multilayers reveal that there might be selective interaction of probe molecules with the polyelectrolyte system.