The Centroaffine Volume of Generalized Geodesic Balls Under Inversion at the Sphere

On an analytic Riemannian manifold (M,g), several authors have studied the Taylor expansion for the volume of geodesic balls under the exponential mapping. In the foregoing paper [1] we studied a more general structure (M,D,g), where D is a torsion-free and Ricci-symmetric connection. We calculated the Taylor expansion up to order (n+4) for the volume of what we called a generalized geodesic ball under the exponential mapping in case that all metric notions are Riemannian, while the exponential mapping is induced from the connection D. For the structure $(M,D,{\cal G})$ the coefficients of the Taylor expansion are much more complicated than in the Riemannian case. It is one of the main objectives of the present paper to study centroaffine hypersurfaces in Euclidean space, their geometric invariants which appear in the very complicated coefficient of order (n+4), and their behaviour under polarization (inversion at the unit sphere). Our results complement applications in the foregoing paper [1], where mainly the coefficients up to order (n+2) and geometric consequences have been studied.     

Ultrasonic Broadband Spectrometry of Liquids A Research Tool in Pure and Applied Chemistry and Chemical Physics

This review is a survey of the many scientific applications of ultrasonic broadbandspectrometry (absorption and velocity measurements with coherent sound waves)in liquids and liquid systems, covering, at present, a frequency range from nearly10 kHz to 10 GHz. Ultrasonic spectrometry has proved to be an almost universalresearch tool in many laboratories, one that is useful for investigation of variouschemical, biochemical, and physicochemical systems. Sound waves traversingliquids induce periodic perturbations in pressure and temperature, which can shiftequilibria, resulting in characteristic sound absorption and velocity dispersionspectra. An analysis of such spectra yields valuable information about thermodynamic and kinetic parameters of the particular system that is often difficult toobtain by other methods. Since such periodic perturbations imposed on the systemare incremental in nearly all cases, the system can be studied under equilibriumconditions. All nonlinear effects (heating, nonconstant fluid compressibility, andothers) are negligible, permitting, for instance, the application of linearized rateequations. In this review, various examples of measured broadband spectra arepresented. Related elementary processes are discussed. Among these are ionicand molecular reactions, including mechanisms of association and complexation,proton transfer, solvation, isomerization, interconversion, side-group rotation,hydrogen-bonding, as well as stacking processes and micelle formation. Specialattention will be given to the extensive research on chemical relaxation.Fundamental early and recent publications are cited and discussed. Many referencesare included with particular emphasis on less well known research and publicationsfrom countries of the former USSR. This review aims at a demonstration of thewidespread applications of modern ultrasonic techniques in many fields ofliquid-state research.     

Bragg-grating-enhanced polarization instabilities

Experiments demonstrate a dramatic decrease in polarization-instability threshold as an optical pulse is tuned near the short-wavelength edge of the photonic bandgap formed by a fiber Bragg grating. These enhanced nonlinear interactions and birefringent effects are modeled with coupled-mode numerical simulations. Nonlinearities are shown to increase much more rapidly than the effective birefringence as the pulse wavelength approaches the bandgap edge.     

Experimental results on neutrino-electron scattering

A determination of sin² θ _w based on measurements of elastic scattering of muon-neutrinos and muon-anti-neutrinos on atomic electrons is described. These purely leptonic processes were studied using the CHARM calorimeter exposed to neutrino and antineutrino wide-band beams at the CERN super proton synchrotron. A total of 83±16 neutrino-electron and 112±21 antineutrino-electron events have been detected. From the measurement of the ratio of muon-neutrino and muon-antineutrino cross-sections a value of sin² θ _w =0.211±0.037 was obtained.     

[Ni(NHC)2] as a Scaffold for Structurally Characterized trans [H−Ni−PR2] and trans [R2P−Ni−PR2] Complexes

The addition of PPh₂H, PPhMeH, PPhH₂, P(para-Tol)H₂, PMesH₂ and PH₃ to the two-coordinate Ni⁰ N-heterocyclic carbene species [Ni(NHC)₂] (NHC=IiPr₂, IMe₄, IEt₂Me₂) affords a series of mononuclear, terminal phosphido nickel complexes. Structural characterisation of nine of these compounds shows that they have unusual trans [H−Ni−PR₂] or novel trans [R₂P−Ni−PR₂] geometries. The bis-phosphido complexes are more accessible when smaller NHCs (IMe₄>IEt₂Me₂>IiPr₂) and phosphines are employed. P−P activation of the diphosphines R₂P−PR₂ (R₂=Ph₂, PhMe) provides an alternative route to some of the [Ni(NHC)₂(PR₂)₂] complexes. DFT calculations capture these trends with P−H bond activation proceeding from unconventional phosphine adducts in which the H substituent bridges the Ni−P bond. P−P bond activation from [Ni(NHC)₂(Ph₂P−PPh₂)] adducts proceeds with computed barriers below 10 kcal mol⁻¹. The ability of the [Ni(NHC)₂] moiety to afford isolable terminal phosphido products reflects the stability of the Ni−NHC bond that prevents ligand dissociation and onward reaction.     

Zur Konstitution des Cytisins

Ohne Zusammenfassung