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.     

Untersuchung pharmazeutischer Pr?parate

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Zur Bestimmung des Schwefels im Eisen

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Zur Schwefelbestimmung nach der Methode

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Nachweis von Obstwein

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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.