Nonlinear one-parametric bottleneck linear programming

We consider the one-parametric linear bottleneck problem min {c (x, t) ¦ x P (t)} where the bottleneck objectivec (x, t):=max {c_j (t) ¦ x_j>0} is minimized subject to linear constraints, i.e. P(t):={x ¦A (t) ·x=b (t), x0}. All coefficients are assumed to be continuous functions of one real parametert which varies in a real intervalS. A method is developed for constructing a partition ofS into subintervals on which either a basis stays optimal or the problem stays infeasible. Finiteness of the partition is due to certain finiteness assumptions on the zeroes of particular combinations of the coefficient functions. Using a lexicographic refinement of the objective function a characterization of the optimality interval of a fixed basis is derived which is independent on explicit information about other bases.

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Zusammenfassung Es werden einparametrische lineare Engpaßprobleme min {c (x, t) ¦x P (t)} betrachtet, wobei die Engpaßzielfunktionc (x, t):=max {c_j (t) ¦ x_j >0} unter linearen Nebenbedingungen, die durch P(t):={x ¦A (t) ·x=b (t), x0} gegeben sind, minimiert wird. Dabei wird angenommen, daß alle Koeffizienten stetige Funktionen eines reellen Parameterst aus einem IntervallS R sind. Es wird eine Methode entwickelt,S derart in Teilintervalle zu zerlegen, daß entweder eine Basis in solch einem Teilintervall optimal oder das Problem unzulässig bleibt. Die Endlichkeit dieser Partition vonS ergibt sich aus Endlichkeitsvoraussetzungen für die Nullstellen von Funktionen, die sich als gewisse Kombinationen der Koeffizientenfunktionen schreiben lassen. Durch eine lexikographische Verfeinerung der Zielfunktion gelingt es, das Intervall zu charakterisieren, in dem eine feste Basis optimal ist. Diese Charakterisierung ist unabhängig von expliziten Informationen über andere Basen.

     

Lösungsmitteleinfluß auf das Redoxverhalten von Bistriphenylphosphinquecksilber(II)-perchlorat

The influence of solvents on the redox behaviour of bistriphenylphosphinomercury perchlorate has been investigated by polarographic, voltammetric and potentiometric methods. The electrode process was found to be reversible in acetonitrile, propylene carbonate, N,N-dimethylformamide and dimethyl sulfoxide. An irreversible process was observed in nitromethane employing the dropping mercury electrode as well as in N,N-dimethylthioformamide and N-methyl-2-thiopyrrolidinone employing the rotating platinum electrode. Half wave potentials and diffusion coefficients have been measured. A linear relationship between theE _1/2 and the donor number (DN) of the solvent has been found for the reversible electrode reactions. Ligand replacement occurs in N,N-dimethylthioformamide and N-methyl-2-thiopyrrolidinone.

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Fast atom bombardment mass spectrometric analysis of the partial ozonolysis products of poly(isoprene) and poly(chloroprene)

The low molecular weight compounds formed by partial ozonolysis of poly(isoprene) and poly(chloroprene) were analyzed by fast atom bombardment mass spectrometry (FABMS). In the poly(chloroprene) case, the ozonized mixtures were treated with piperidine before the MS analysis to transform in amide end groups the reactive acyl chlorides formed by the cleavage of double bonds along the main chain. Only one family of compounds having carboxyl and ketone or carboxyl and amide end groups were obtained from the ozonolysis of poly(isoprene) and poly(chloroprene), respectively. The assigned structures were confirmed by FAB-MS analysis of the GPC separation fractions [poly(chloroprene)] or by FAB-MS of the KOH-doped ozonolysis mixtures [poly(isoprene)]. It has been also ascertained, by GPC experiments, that poly(chloroprene) decomposes more rapidly than poly(isoprene) and poly(butadiene).     

Phase Transition and Crystal Structure of the Monomeric Europium(II) Thiolate Eu(SC36H49)2

Single crystal X‐ray diffraction of Eu(SC₃₆H₄₉)₂ has revealed a first order phase transition at a temperature of 119 K, that involves a reduction of the specific volume by 1 %. The transition corresponds to a doubling of the unit cell, as it is the result from reorientations of isopropyl groups that appear at peripheral sites of the organic ligands. It is argued that a denser packing is achieved at the expense of a less favourable conformation of one of the two crystallographically‐independent complexes in the low‐temperature phase. The Bond‐Valence method is used to show that interactions of equal strengths are present between europium and both sulphur atoms and both coordinating phenyl rings.     

Asymmetric synthesis of 1-substituted-1-(pyridin-2-yl)methylamines by diastereoselective reduction of enantiopure N-p-toluenesulfinyl ketimines

Reduction of enantiopure N-p-toluenesulfinyl ketimines derived from 2-pyridyl ketones affords N-p-toluenesulfinyl amines with good yields and diastereoselectivities.     

Thin‐Film Infrared Spectroscopy of Acetonitrile

Acetonitrile and [D₃]acetonitrile in the vicinal region of a planar AgX fiber contain linear dipole–dipole linked oligomers as shown by 1) comparison of infrared band intensity ratios in the gaseous and condensed phases and 2) remarkable plots of absorbance (C? N stretch) versus time during evaporation from an AgX planar fiber element. The plots (CH₃CN 2252 cm^?1, CD₃CN 2262 cm^?1) reveal the presence of octamers, hexamers, tetramers, and dimers along with some heptamer, trimer, and monomer structures. A novel isotope effect arises from the somewhat smaller size of the CD₃CN resulting in an increase in the CN band intensity. The organized oligomers may be termed pseudocrystals and are the main components responsible for absorption intensity in the infrared spectrum of acetonitrile, on the AgX planar fiber or in an IR cell.     

Modellbetrachtungen zum Verständnis unerwarteter Eigenschaften der metalloiden Clusterverbindung [Ga84(N(SiMe3)2)20][Li6Br2(THF)20]·2Toluol

Towards the Understanding of the Unexpected Properties of the Metalloid Cluster Compound [Ga₈₄(N(SiMe₃)₂)₂₀][Li₆Br₂(THF)₂₀]·2Toluol In several short communications we have recently reported on the electrical and superconducting properties of the crystalline title compound 1 which contains anionic Ga₈₄R₂₀‐moieties. Here we present a collection of these results, complemented and interpreted by using DFT‐calculations on model clusters (Ga₈₄(NH₂)₂₀^?). These calculations allow a) a first insight into the dynamics of the Ga₈₄‐moieties (e.g. a rotation of the central Ga₂‐dumbbell) and thus an explanation of the temperature‐dependent Ga‐NMR‐spectra described recently, and b) estimations on the lattice energy of 1 and its resulting unexpected energetic stabilization compared to metallic gallium. A possible contribution of the cations in the electrical conduction mechanism of 1 can also be made feasible with model calculations. The basis for all the results presented is to be found in the “perfect” arrangement of nanoscopic Ga₈₄‐clusters in the crystal. This theoretically predicted condition for superconductivity in a “chain” of identical metal cluster molecules is a requirement which can hardly be realized by means of physical fabrication methods. Therefore, on the one hand the results presented here make for some disillusionment in the field of nanoscience, but on the other hand, especially in the field of synthetic chemistry, they present rewarding challenges for fundamental work in the future.     

A guest-induced assembly of a molecular box from methylcobaloxime and 1, 4-phenylenebisboronic acid

The guest-induced synthesis of a molecular box from methylaquacobaloxime and 1,4-phenylenebisboronic acid, with pyrazine (pz) as guest, is described. The resulting supramolecular species was characterized by X-ray structural analysis, 1H and 13C NMR spectroscopy, and low-resolution electrospray ionization (ES) mass spectrometry. The assembly was monitored by a time dependent 1H NMR experiment, which showed that the guest thermodynamically drives the assembly of the host. The effectiveness of pyrazine in this role arises from its having both the correct geometry and a sufficiently low pKa value. Several other ditopic ligands were tested, but none led to formation of an analogous product. However, a second supramolecular species was formed in the case of ethylenediamine (en). X-ray structural analysis and 1H and 13C spectroscopy revealed that this is closely related to the first, with a phenyl side removed and the pz bridge substituted by the en bridge.     

Über einige neue Bispirane

We have obtained four new bispirane systems in which both spiroatoms are vicinal atoms in cyclopropane or cyclobutane rings and in which the heterocyclic component has the basic structure of 1,4-dioxep-2-ene. We have shown that from two possibilities (bispiran, propellan) the general reaction leads only to a bispiran system. To the bispiran2 exhibiting the highest hyperchromism we ascribed the bispirocoplanar conformation (Fig. 1).

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