Brauer groups,embedding problems,and nilpotent groups as Galois groups

Let ℚ _ab denote the maximal abelian extension of the rationals ℚ, and let ℚ_abnil denote the maximal nilpotent extension of ℚ _ab . We prove that for every primep, the free pro-p group on countably many generators is realizable as the Galois group of a regular extension of ℚ_abnil(t). We also prove that ℚ_abnil is not PAC (pseudo-algebraically closed). This paper was inspired by the author's participation in a special year on the arithmetic of fields at the Institute for Advanced Studies at the Hebrew University of Jerusalem. I would like to express my appreciation to the Institute for its hospitality, and to the organizers, especially Moshe Jarden. Partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund-Japan Technion Society Research Fund.     

In vivo proton magnetic resonance spectroscopy of alcohol in rhesus monkey brain

Brain alcohol was measured in rhesus monkeys (Macaca mulatta) by proton magnetic resonance spectroscopy (MRS) following acute nasogastric alcohol administration (0.8 g/kg). Monkeys were anesthetized with ketamine and xylazine. A 1.5 T whole body imager and a 3-inch surface coil were used to acquire TE 30 and 270 ms spectra from a 7.5 cc voxel localized with a stimulated echo (STEAM) sequence. Venous blood samples were collected during spectral acquisitions for gas chromatographic determination of temporally concordant blood alcohol levels (BALs). Acute alcohol administration did not alter the resonance areas of N-acetylaspartate/N-acetyl containing compounds (NAA), choline containing compounds, or total creatine. The NAA resonance was used as an internal standard to calculate approximate brain alcohol concentrations, which averaged 27 ± 3% and 27 ± 8% of temporally concordant BALs (T₂-corrected TE 30 and TE 270 ms spectra, respectively). In addition to reconfirming results from prior studies finding incomplete detection of brain alcohol with MRS, these results demonstrate the feasibility of measuring brain alcohol in anesthetized nonhuman primates to examine relationships between alcohol exposure history and MRS-visibility of brain alcohol.     

On the Methyl-Transfer Reaction in Crystalline Methyl 2-(Methylthio)benzenesulfonate: a Thermally Induced Non-Topochemical Solid-State Reaction

The rearrangement of methyl 2-(methylthio)benzenesulfonate ( 1 ) to the zwitterionic 2-(dimethyl-sulfonium)benzenesulfonate ( 2 ) is known to proceed in solution by intermolecular Me transfers. The same rearrangement has been observed to occur in crystalline 1 , but the crystal structure shows that the molecular packing is not conducive to intermolecular Me transfer. The reaction has been carried out with mixed crystals composed of 1 and deuteriomethylated (D₆)- l . By fast-atom-bombardment mass spectroscopy, it has been shown that the product consists of a 1:2:1 mixture of the non-, tri-, and hexadeuterated species, the mixture expected, if the solid-state reaction proceeds by intermolecular Me transfers. From this result, together with the slower rates of conversion in the single crystal compared with the melt, it can be concluded that the reaction must occur not topochemically but rather at defects such as microcavities, surfaces, and other irregularities in the ordered crystal arrangement.     

Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.     

A central cutting plane algorithm for the convex programming problem

An algorithm is developed for solving the convex programming problem which iteratively proceeds to the optimum by constructing a cutting plane through the center of a polyhedral approximation to the optimum. This generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem. Additionally, we present a simple, effective rule for dropping prior cuts, an easily calculated bound on the objective function, and a rate of convergence.