Characterizations of the Kerr metric

For stationary, asymptotically flat solutions of Einstein's equations, covariant functionals of the metric variables are defined which characterize the Kerr metric uniquely. For instance, we obtain a generalization of the Bach tensor to stationary metrics, which vanishes if and only if the solution is Kerr. We also give a new interpretation of the Schwarzschild-to-Kerr-transformation. Our results might be applicable to simplify the proof of the uniqueness theorem for stationary black holes.     

The Henicosaphosphide Iodides of Potassium and Rubidium,K4P21I and Rb4P21I

The novel ternary polyphosphides M₄P₂₁I (M = K, Rb) have been synthesized from the elements in single crystalline form, representing further examples for the formation of mixed crystals between simple salts and binary phosphides. They form as ruby‐red platelets and dark‐red prisms, respectively, and are only slightly sensitive to moisture and oxygen. The compounds are isotypic (Ccmm (no 63); Z = 4; oP104; K₄P₂₁I: a = 12.853Å; b = 21.795Å; c = 9.748Å; 1168 hkl, R = 0.033; Rb₄P₂₁I: a = 13.281Å; b = 21.868Å; c = 9.771Å; 777 hkl, R = 0.053) and feature corrugated 2D networks formed from two different types of polymerized P₇ units. The networks form large cavities filled by M⁺ and I^‐ ions. Zigzag chains of condensed trigonal M₆ prisms, centered by the I^‐ anions, separate the polyphosphide nets. The mean homoatomic P‐P bond length (d = 2.216Å) corresponds to a P‐P single bond. However, the individual P‐P distances vary with position and function (2.126 ‐ 2.247Å) and these are compared with those of the isolated P₂₁^‐3 anion.     

Äthinierungsreaktionen, 24. Mitt.: Äthinierung von 2-Alkyl-pyrazolanthronen

Zusammenfassung In 2-Stellung aliphatisch substituierte Pyrazolanthrone sind-im Gegensatz zu aromatisch substituierten Pyrazolanthronenleicht zu äthinieren.

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Pyrazolanthrones with aliphatic substituents at position 2 readily undergo ethynation in contrast to those with aromatic substituents.

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Die Stellungsbezeichnung folgt dem Ringindex (RRI 4453) wonach das Grundsystem der Pyrazolanthrone als Anthra [1,9-cd] pyrazol bezeichnet wird.

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23. Mitt.:W. Ried undSt. Piesch, Chem. Ber.99, 233 (1965).

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Teil der Dissertat.St. Piesch, Univ. Frankfurt/M., 1965.     

Transient absorption spectral evidence for phenyl nitrene as the chain propagator in the photo-initiated autocatalytic chain decomposition of phenyl azide and phenyl isocyanate

Transient absorption spectra were recorded 15 ns to 6 μs following a 266 nm laser pulse for phenyl azide and for phenyl isocyanate in aerated acetonitrile and 3-methylpentane solutions. Transient spectra which are independent of concentration and of delay time, are essentially identical for phenyl azide and for phenyl isocyanate, except at higher energies where phenyl azide absorbs, and are assigned as that of triplet phenyl nitrene. Since there is no spectral evidence for a second species, phenyl nitrene is thought the chain propagator in the autocatalytic chain decomposition that occurs for phenyl azide and for phenyl isocyanate.     

Partitioning behavior of erythrocytes in aqueous two-phase systems containing hydroxypropyl starch and polyethylene glycol

The partitioning behavior of erythrocytes in Reppal PES 200 (a hydroxypropyl starch produced by Reppe Glykos AB, V?xj?, Sweden)-polyethylene glycol (PEG) and in dextran (Dx)-PEG aqueous phase systems made isotonic with phosphate is similar in a number of ways: (i) There is a correlation between the relative electrophoretic mobilities and partition ratios, P, of red blood cells from different species; (ii) The cell P is reduced when, at constant polymer concentrations, phosphate is systematically replaced by sodium chloride (with the total concentration isotonic); (iii) The cell P is increased with reduced polymer concentrations (decreased interfacial tensions); (iv) Treatment of erythrocytes with neuraminidase results in a reduced P value; (v) Rat red cells of different ages can be fractionated by counter-current distribution; and (vi) Differences between red blood cells from genetically distinct rats or between humans can be detected. Aquaphase (a hydroxypropyl starch marketed by Perstorp AB, Lund, Sweden) has been tested as in ii-iv above with analogous results. The partitioning behavior of erythrocytes in PES-PEG and Dx-PEG aqueous phase systems containing sodium chloride differs in a number of ways: (vii) The correlation, apparent in Dx-PEG systems, between the P value of red blood cells from different species and the ratio of their membrane poly- to monounsaturated fatty acids is absent in PES-PEG systems. It is replaced by a correlation as in i; (viii) The increase in P value in Dx-PEG observed from red blood cells after treatment with neuraminidase is replaced by a decrease in P value in PES-PEG or Aquaphase-PEG systems. We conclude that PES (and Aquaphase) can be substitutes for dextran in cell partitioning studies when charge-sensitive phases are used (e.g., those containing phosphate) while separations based on properties reflected by Dx-PEG systems containing sodium chloride are not duplicated by PES-PEG (and probably not by Aquaphase-PEG). The hydroxypropyl starch-PEG systems containing sodium chloride, unlike the analogous Dx-PEG systems, have a significant electrostatic potential difference between the phases.     

Bestimmung des Enantiomerenüberschusses von chiralen Ammonium-Ionen mit Hilfe von Flüssigmembranelektroden

Determination of the Enantiomeric Excess of Chiral Ammonium long Using Liquid Membrane Electrodes A cell assembly with two membranes each containing one enantiomer of a chiral ionophore is described. It is suitable for the direct potentiometric determination of the enantiomeric excess of ions. The method is used to determine the enantiomeric excess of ephedronium ions in aqueous solutions.     

Determination of manganese and zinc in powdered chocolate samples by slurry sampling using sequential multi-element flame atomic absorption spectrometry

In the present work, a slurry sampling flame atomic absorption spectrometric method to determine directly manganese and zinc in powdered chocolate samples is proposed. The optimization step was performed using univariate methodology involving the following factors: nature and concentration of the acid solution, sonication time, and particle size. The established conditions led to the use of a sample mass of 150 mg, 2.0 mol L^− 1 nitric acid solution, sonication time of 15 min, and a slurry volume of 50 mL. This method allows the determination of manganese and zinc with detection limit of 52 and 61 ng g^− 1, respectively, and a precision expressed as relative standard deviation (RSD) of 2.6% and 3.2% (both, n = 10) for contents of manganese and zinc of 52.4 and 100.0 μg g^− 1, respectively. The proposed method was applied for determination of manganese and zinc in five powdered chocolate samples. In these, the manganese content varied from 42.8 to 52.7 and from 88.6 to 102.4 μg g^− 1 of zinc. The analytical results were compared with the results obtained by analysis of these samples after digestion using open vessel and acid bomb digestion procedures and determination using FS-FAAS. The statistical comparison by t-test (95% confidence level) showed no significant difference between these results.     

Affinity interactions between phenylboronic acid-carrying self-assembled monolayers and flavin adenine dinucleotide or horseradish peroxidase

A method is provided for the recognition of glycated molecules based on their binding affinities to boronate-carrying monolayers. The affinity interaction of flavin adenine dinucleotide (FAD) and horseradish peroxidase (HRP) with phenylboronic acid monolayers on gold was investigated by using voltammetric and microgravimetric methods. Conjugates of 3-aminophenylboronic acid and 3,3'-dithiodipropionic acid di(N-hydroxysuccinimide ester) or 11-mercaptoundecanoic acid were prepared and self-assembled on gold surfaces to generate monolayers. FAD is bound to this modified surface and recognized by a pair of redox peaks with a formal potential of -0.433 V in a 0.1 M phosphate buffer solution, pH 6.5. Upon addition of a sugar to the buffer, the bound FAD could be replaced, indicating that the binding is reversible. Voltammetric, mass measurements, and photometric activity assays show that the HRP can also be bound to the interface. This binding is reversible, and HRP can be replaced by sorbitol or removed in acidic solution. The effects of pH, incubation time, and concentration of H(2)O(2) were studied by comparing the catalytic reduction of H(2)O(2) in the presence of the electron-donor thionine. The catalytic current of the HRP-loaded electrode was proportional to HRP concentrations in the incubation solution in the range between 5 microg mL(-1) and 0.1 mg mL(-1) with a linear slope of 3.34 microA mL mg(-1) and a correlation coefficient of 0.9945.     

Mechanism of the oxidation of L-ascorbic acid by the bis(pyridine-2,6-dicarboxylate)cobaltate(III) ion in aqueous solution

A detailed investigation of the oxidation of L-ascorbic acid (H₂A) by the title complex has been carried out using conventional spectrophotometry at 510 nm, over the ranges: 0.010 [ascorbate] _T 0.045 mol dm^–3, 3.62 pH 5.34, and 12.0 30.0 °C, 0.50 I 1.00 mol dm^–3, and at ionic strength 0.60 mol dm^–3 (NaClO₄). The main reaction products are the bis(pyridine-2,6-dicarboxylate)cobaltate(II) ion and l-dehydroascorbic acid. The reaction rate is dependent on pH and the total ascorbate concentration in a complex manner, i.e., k _obs = (k ₁ K ₁)[ascorbate] _T /(K ₁ + [H⁺]). The second order rate constant, k ₁ [rate constant for the reaction of the cobalt(III) complex and HA^–] at 25.0 °C is 2.31 ± 0.13 mol^–1 dm³ s^–1. H = 30 ± 4 kJ mol^–1 and S = –138 ± 13 J mol^–1 K^–1. K ₁, the dissociation constant for H₂A, was determined as 1.58 × 10^–4 mol dm^–3 at an ionic strength of 0.60 mol dm^–3, while the self exchange rate constant, k ₁₁ for the title complex, was determined as 1.28 × 10^–5 dm³ mol^–1 s^–1. An outer-sphere electron transfer mechanism has been proposed.     

Crystal field parameters and crystal field linewidths in the (REY)Pd3 and (REY)Al2 alloys

The LLW-parametersx andW of dilute rare earth impurities (RE=Pr, Nd, Tb, Dy, Ho, Er, Tm;c0.05), in the cubic matrices YPd₃ and YAl₂ could be determined unequivocally in the crystal field scheme of Lea, Leask and Wolf by inelastic neutron scattering. The crystal field parameters derived fromx andW are not consistent with the point charge model. The ratio of N(E _F)J_ex for the (REY)Pd₃ and (REY)Al₂ extracted from the RE-linewidths correlates with the corresponding ratio extracted from their magnetic ordering temperatures.Supported by Sonderforschungsbereich 125, Deutsche Forschungsgemeinschaft