Spectroscopic imaging display and analysis.

A system for display of magnetic resonance (MR) spectroscopic imaging (SI) data is described which provides for efficient review and analysis of the multidimensional spectroscopic and spatial data format of this technique. Features include the rapid display of spectra from selected image voxels, formation of spectroscopic images, spectral and image data processing operations, methods for correlating spectroscopic image data with high resolution 1H MR images, and hardcopy facilities. Examples are shown for 31P and 1H spectroscopic imaging studies obtained in human and rat brain.     

Spin Axioms in Different Geometries of Relativistic Continuum Physics

The 24 components of the relativistic spin tensor consist of 3 + 3 basic spin fields and 9 + 9 constitutive fields. Empirically only three basic spin fields and nine constitutive fields are known. This empirem can be expressed by two spin axioms, one of them denying purely relativistic spin fields, and the other one relating the three additional basic fields and the nine additional constitutive fields to the known (and measurable) ones. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from six to three basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.     

Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1

Summary For the numerical solution of non-stiff semi-explicit differentialalgebraic equations (DAEs) of index 1 half-explicit Runge-Kutta methods (HERK) are considered that combine an explicit Runge-Kutta method for the differential part with a simplified Newton method for the (approximate) solution of the algebraic part of the DAE. Two principles for the choice of the initial guesses and the number of Newton steps at each stage are given that allow to construct HERK of the same order as the underlying explicit Runge-Kutta method. Numerical tests illustrate the efficiency of these methods.     

Electron and oxygen transfer in polyoxometalate, H(5)PV(2)Mo(10)O(40), catalyzed oxidation of aromatic and alkyl aromatic compounds: evidence for aerobic Mars-van Krevelen-type reactions in the liquid homogeneous phase

The mechanism of aerobic oxidation of aromatic and alkyl aromatic compounds using anthracene and xanthene, respectively, as a model compound was investigated using a phosphovanadomolybdate polyoxometalate, H(5)PV(2)Mo(10)O(40), as catalyst under mild, liquid-phase conditions. The polyoxometalate is a soluble analogue of insoluble mixed-metal oxides often used for high-temperature gas-phase heterogeneous oxidation which proceed by a Mars-van Krevelen mechanism. The general purpose of the present investigation was to prove that a Mars-van Krevelen mechanism is possible also in liquid-phase, homogeneous oxidation reactions. First, the oxygen transfer from H(5)PV(2)Mo(10)O(40) to the hydrocarbons was studied using various techniques to show that commonly observed liquid-phase oxidation mechanisms, autoxidation, and oxidative nucleophilic substitution were not occurring in this case. Techniques used included (a) use of (18)O-labeled molecular oxygen, polyoxometalate, and water; (b) carrying out reactions under anaerobic conditions; (c) performing the reaction with an alternative nucleophile (acetate) or under anhydrous conditions; and (d) determination of the reaction stoichiometry. All of the experiments pointed against autoxidation and oxidative nucleophilic substitution and toward a Mars-van Krevelen mechanism. Second, the mode of activation of the hydrocarbon was determined to be by electron transfer, as opposed to hydrogen atom transfer from the hydrocarbon to the polyoxometalate. Kinetic studies showed that an outer-sphere electron transfer was probable with formation of a donor-acceptor complex. Further studies enabled the isolation and observation of intermediates by ESR and NMR spectroscopy. For anthracene, the immediate result of electron transfer, that is formation of an anthracene radical cation and reduced polyoxometalate, was observed by ESR spectroscopy. The ESR spectrum, together with kinetics experiments, including kinetic isotope experiments and (1)H NMR, support a Mars-van Krevelen mechanism in which the rate-determining step is the oxygen-transfer reaction between the polyoxometalate and the intermediate radical cation. Anthraquinone is the only observable reaction product. For xanthene, the radical cation could not be observed. Instead, the initial radical cation undergoes fast additional proton and electron transfer (or hydrogen atom transfer) to yield a stable benzylic cation observable by (1)H NMR. Again, kinetics experiments support the notion of an oxygen-transfer rate-determining step between the xanthenyl cation and the polyoxometalate, with formation of xanthen-9-one as the only product. Schemes summarizing the proposed reaction mechanisms are presented.     

Synthese und Strukturuntersuchungen von Ba2H[α-FeO4W12O36] · 26 H2O

Synthesis and Structure Studies of Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O The heteropolyanion compound Ba₂H[α-FeO₄W₁₂O₃₆] · 26 H₂O (I) crystallizes in the tetragonal space group P4 n2 with the lattice parameters a = 12.398(6), c = 18.721(6) Å; Z = 2; D_x = 4.128 g · cm^?3. The structure was solved on a twinned crystal from 1029 observed reflections and refined to an index R of 7.6%. The calculations were done by means of a modified ORFLS-programme by Eitel and Bärnighausen. The heteropolyanion [α-FeO₄W₁₂O₃₆]^5? has the well known α-Keggin structure. The average distance of the four central oxygen atoms to the Fe^III position (0, 0, 0) is 1.84 Å. The angles ? O? Fe? O are 112.3° (4X) and 103.9 (2X), respectively, which leads to an disphenoidal distortion of the FeO₄ tetrahedron. The powder and single crystal ESR spectra of I show the anisotropy of the Fe^III fine structure transition 1/2 ? ?1/2. The Mößbauer spectra confirm the tetragonal distortion of the central FeO₄ tetrahedron (quadrupole splitting Δ ≈ 0.50 mm · s^?1).