Stereoselective Synthesis of cis,cis‐Configured Perhydroquinoxaline‐5‐Carbonitrile from Cyclohex‐2‐en‐1‐ol

cis,cis‐Configured perhydroquinoxaline‐5‐carbonitrile 10 was synthesized stereoselectively by ditosylation of trans,cis‐2,3‐dihydroxycyclohexane‐1‐carbonitrile 4 and subsequent reaction with ethylenediamine. The diol precursor 4 was stereoselectively obtained by regioselective opening of the epoxide 3 with KCN in water avoiding hazardous Et₂AlCN.     

The scaling limit of Poisson-driven order statistics with applications in geometric probability

Let _ηt${\eta }_t$ be a Poisson point process of intensity t≥1$t\ge 1$ on some state space Y$\mathbb{Y}$ and let f$f$ be a non-negative symmetric function on Y^k${\mathbb{Y}}^k$ for some k≥1$k\ge 1$. Applying f$f$ to all k$k$-tuples of distinct points of _ηt${\eta }_t$ generates a point process _ξt${\xi }_t$ on the positive real half-axis. The scaling limit of _ξt${\xi }_t$ as t$t$ tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the m$m$-th smallest point of _ξt${\xi }_t$ is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as k$k$-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry.     

A Linear Model for the Interpretation of Optical Emission Spectroscopy Measurements in Low Pressure DC Magnetron Sputtering

For a balanced dc magnetron discharge a linear model for the formation of excited and ionized species is presented. The consideration is based on collisional kinetic theory and a correlation of discharge current with ionization rates, and leads to normalized rate coefficients. The electron energy distribution changes according to the determining external parameters, but needs neither to be known in detail nor to be of Maxwellian type. The model calculations are consistent with measurements done by optical emission spectroscopy (OES) on the magnetron sputtering of aluminium in argon discharges. The dependences of optical emission intensities on discharge current and on argon pressure show that both, excited argon atoms as well as excited argon ions, are generated from neutral argon by direct, fast electron impact. It is additionally shown that at least for low argon pressure the excitation of aluminium atoms is also caused by direct electron impact.     

Regular Polytopes in Ordinary Space

The three aims of this paper are to obtain the proof by Dress of the completeness of the enumeration of the Grünbaum—Dress polyhedra (that is, the regular apeirohedra, or apeirotopes of rank 3) in ordinary space E ³ in a quicker and more perspicuous way, to give presentations of those of their symmetry groups which are affinely irreducible, and to describe all the discrete regular apeirotopes of rank 4 in E ³ . The paper gives a complete classification of the discrete regular polytopes in ordinary space. Received June 6, 1996, and in revised form October 28, 1996.     

Microwave electric field induced spin transitions of AlAs 2D electrons

We present the first direct electron spin resonance (ESR) on a 2D electron gas in a III–V semiconductor. ESR on a high mobility 2D electron gas in a single AlAs quantum well reveals an electronic g-factor of 1.991 at 9.35 GHz and 1.989 at 34 GHz with a minimal linewidth of 7 Gauss. Both the signal amplitude and its dependence on the position and orientation of the sample in the cavity unambiguously demonstrate that the spin transitions in our experiment are caused by the microwave electric field. We present a model that ascribes the spin transitions to the effective magnetic field acting on the electron spins that arises from (Bychkov–Rashba) spin-orbit interaction and the modulation of the electron wavevector around k_F induced by the microwave electric field.     

Nitroxide‐mediated living free‐radical polymerization of styrene: A systematic study of the variation of the alkoxyamine concentration

The effect of the variation of the alkoxyamine concentration on the conversion and polydispersity of the nitroxide‐mediated living free‐radical polymerization of styrene is discussed. Four different alkoxyamines ( 1 – 4 ) have been used for these studies. For an alkoxyamine with a small equilibrium rate constant (K), such as styryl–TEMPO 2 , the conversion is governed by the autopolymerization of styrene. For efficient alkoxyamines 1 , 3 , and 4 , the conversion at high alkoxyamine concentrations is higher than the conversion obtained by autopolymerization. At high alkoxyamine concentrations, the conversions vary to a small extent for all the alkoxyamines studied. As long as the conversion remains high, the polydispersity index is small. In addition, simulations of polymerizations with a program for modeling nonlinear dynamics are discussed. Polymerizations with efficient alkoxyamines at high alkoxyamine concentrations are well described by the kinetic scheme applied. K for alkoxyamines 1 and 4 has been estimated with the simulations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3342–3351, 2004     

Dissociation of small metal particles induced by surface plasmon excitation with laser light

This paper reports the dissociation of supported metal clusters after illumination with low intensity visible laser light. The process is non-thermal and exhibits a resonant dependence on the laser frequency. This indicates that a surface plasmon excitation preceeds the dissociation.     

Manifold structures on abstract regular polytopes

Summary Abstract regular polytopes are complexes which generalize the classical regular polytopes. This paper discusses the topology of abstract regular polytopes whose vertex-figures are spherical and whose facets are topologically distinct from balls. The case of toroidal facets is particularly interesting and was studied earlier by Coxeter, Shephard and Grünbaum. Ann-dimensional manifold is associated with many abstract (n + 1)-polytopes. This is decomposed inton-dimensional manifolds-with-boundary (such as solid tori). For some polytopes with few faces the topological type or certain topological invariants of these manifolds are determined. For 4-polytopes with toroidal facets the manifolds include the 3-sphereS ³, connected sums of handlesS ¹ × S ² , euclidean and spherical space forms, and other examples with non-trivial fundamental group.     

Anomalous small‐angle X‐ray scattering characterization of composites based on sulfonated poly(ether ether ketone), zirconium phosphates,and zirconium oxide

The morphology and distribution of zirconium oxide and zirconium phosphates in a matrix of sulfonated poly(ether ether ketone) (SPEEK) were investigated with anomalous small‐angle X‐ray scattering (ASAXS) and electron microscopy. ASAXS revealed that ZrO₂ was distributed in the SPEEK matrix in the form of nanoparticles smaller than 13 Å. A decrease in the conductivity suggested that the sulfonic groups were bound to the zirconium oxo species at the particle surface. Furthermore, two kinds of membranes containing zirconium phosphate were investigated. In one case, the phosphate was directly dispersed in the polymer solution for the casting of the membrane. In the other case, the phosphate was previously treated with n‐propyl ammonium and polybenzimidazole. From ASAXS data, the fractal dimension could be estimated. Mass‐fractal behavior was confirmed for the SPEEK membrane containing previously exfoliated zirconium phosphate, with aggregates of 6.3–165 Å. Surface‐fractal behavior was detected for membranes with untreated phosphates, with aggregates of 6.4–185 Å. The untreated phosphates caused an increase in the permeability, without changing the proton conductivity much. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 567–575, 2004