Topologically nontrivial field configurations in noncommutative geometry

In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only a finite number of modes.Part of the Project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich.     

Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Resonances in low-energy rare-gas atom scattering

Precise values of energies and widths of low-lying resonances in some rare-gas atom systems (Ar-Ar, Ne-Kr, Ne-Xe) are reported.     

Global (and local) analyticity for second order operators constructed from rigid vector fields on products of tori

We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the Hörmander condition and where satisfies a ``maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is

(with analytic , naturally, but not identically zero). The results, because of the flexibility of the methods, generalize recent work of Cordaro and Himonas in [4] and Himonas in [8] which showed that certain operators known not to be locally analytic hypoelliptic (those of Baouendi and Goulaouic [1], Hanges and Himonas [6], and Christ [3]) were globally analytic hypoelliptic on products of tori.

     

Chemistry of 1-Alkoxy-1-glycosyl Radicals: The Manno- and Rhamnopyranosyl Series. Inversion of alpha- to beta-Pyranosides and the Fragmentation of Anomeric Radicals

The formation and stereoselective quenching of 1-mannopyranosyl radicals by a tributyltin hydride-mediated intramolecular 1,5-hydrogen abstraction sequence is described. A competing process is 1,4-hydrogen atom abstraction leading principally to glucopyran-2-ulosides. Fragmentation of the anomeric radical resulting in the formation of ring opened products is a problem in certain series. The chemistry is dictated to a considerable extent by the nature of the protecting groups employed with the 4,6-benzylidene series and, for rhamnose, the Ley 3,4-dispiroketal, being particularly susceptible to the 1,4-hydrogen atom abstraction but less to the fragmentation. Photochemical conditions are described, in which these side reactions are practically eliminated, and applied to the inversion of an alpha- to a beta-mannoside in a disaccharide.