Conformal Geometry of Gravitational Plane Waves

By Brinkmann’s theorem the only Ricci flat and nonflat 4-manifolds admitting non-homothetic conformal vector fields are certain pp-waves. It seems that the converse direction was never completely clarified Which metrics really do occur? It is well known that the conformal group of a nonconformally-flat spacetime is atmost seven-dimensional and that seven is attained for certain pp-waves. Here we explicitly determine all solutions with a seven-dimensional conformal group. In other words We determine all Ricci flat Lorentzian manifolds admitting a seven-dimensional conformal group. They come in three particular families of gravitational plane waves. All of them are exact analytic solutions in terms of elementary functions. Furthermore, it turns out that Ricci flat Lorentzian manifolds with a six-dimensional conformal group are not necessarily real analytic.     

Photoelektronenspektren und konformationsverhalten von hydroxylamin und methylhydroxylaminen

Gas-phase He(I) photoelectron spectra of hydroxylamine (1) and the methyl hydroxylamines (2–6) have been measured. From 1 a He(II) spectrum has also been obtained. To study the interactions of the n(N) and n(O) orbitals, MINDO/2 calculations have been performed for various conformations of 1–6. The findings are consistent with trans- forms being the most stable conformations of 1–6, but additional cis- conformers cannot be excluded.     

Transannular 1,5-hydride shift in 5-hydroxycyclooctanone: an experimental and theoretical investigation

1H NMR measurements have shown that eight out of twelve methylene hydrogen atoms of 5-hydroxycyclooctanone (1HK) are exchanged for deuterium atoms under acidic and basic conditions. For the reaction in 7.9 M DCl/D2O, an activation energy Ea = 19.2 +/- 0.4 kcal mol(-1) is found. In order to explain these findings, a degenerate transannular 1,5-hydride shift is essential, and this reaction has been analyzed by quantum chemical calculations. Hydride transfer takes place via a tight transition state with a six-membered ring. The activation barrier is lowest in the presence of base. The molecular conformation of the eight-membered ring in the transition state resembles that of the starting structure. It is unlikely that solvent molecules such as water participate in the formation of the transition state.     

Nickel-Based Metal-Organic Frameworks as Electrocatalysts for the Oxygen Evolution Reaction (OER)

The exploration of earth-abundant electrocatalysts with high performance for the oxygen evolution reaction (OER) is eminently desirable and remains a significant challenge. The composite of the metal-organic framework (MOF) Ni₁₀Co-BTC (BTC = 1,3,5-benzenetricarboxylate) and the highly conductive carbon material ketjenblack (KB) could be easily obtained from the MOF synthesis in the presence of KB in a one-step solvothermal reaction. The composite and the pristine MOF perform better than commercially available Ni/NiO nanoparticles under the same conditions for the OER. Activation of the nickel-cobalt clusters from the MOF can be seen under the applied anodic potential, which steadily boosts the OER performance. Ni₁₀Co-BTC and Ni₁₀Co-BTC/KB are used as sacrificial agents and undergo structural changes during electrochemical measurements, the stabilized materials show good OER performances.     

Synthesis,Spectroscopic, and X‐Ray Diffraction Studies of cis‐Dichlorobis(4‐propanoyl‐2,4‐dihydro‐5‐methyl‐2‐phenyl3 H‐pyrazol‐3‐onato) Tin(IV)

Reaction between an aqueous ethanol solution of tin(II) chloride and that of 4‐propanoyl‐2,4‐dihydro‐5‐methyl‐2‐phenyl‐3 H‐pyrazol‐3‐one in the presence of O₂ gave the compound cis‐dichlorobis(4‐propanoyl‐2,4‐dihydro‐5‐methyl‐2‐phenyl‐3 H‐pyrazol‐3‐onato) tin(IV) [(C₂₆H₂₆N₄O₄)SnCl₂]. The compound has a six‐coordinated Sn^IV centre in a distorted octahedral configuration with two chloro ligands in cis position. The tin atom is also at a pseudo two‐fold axis of inversion for both the ligand anions and the two cis‐chloro ligands. The orange compound crystallizes in the triclinic space group P 1 with unit cell dimensions, a = 8.741(3) Å, b = 12.325(7) Å, c = 13.922(7) Å; α = 71.59(4), β = 79.39(3), γ = 75.18(4); Z = 2 and D_x = 1.575 g cm^–3. The important bond distances in the chelate ring are Sn–O [2.041 to 2.103 Å], Sn–Cl [2.347 to 2.351 Å], C–O [1.261 to 1.289 Å] and C–C [1.401 Å] the bond angles are O–Sn–O 82.6 to 87.7° and Cl–Sn–Cl 97.59°. The UV, IR, ¹H NMR and ¹¹⁹Sn Mössbauer spectral data of the compound are reported and discussed.     

Über die asymptotische Verteilung gewisser konvergenzerzeugender Faktoren

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