The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H ₁. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.     

Endolaryngeal contact pressures

In this work, we present a new method for in vivo endolaryngeal contactpressure measurement with a miniature pressure transducer. Using this methodology, contact pressures can be measured during videoendoscopy at different locations between the artyenoids and also at various locations along the membranous vocal folds. Twenty adults with organic and functional voice disorders and two vocally healthy adults participated as subjects. Endolaryngeal contact pressure measures were made during a series of phonatory tasks varying pitch, loudness, and phonatory onset and offset. Measures were also made during nonphonatory tasks, including throat clearing, coughing, Valsalva maneuvres, and gagging. The most remarkable findings were: (1) interarytenoid contact pressures were considerably greater than intraglottal contact pressures; (2) interarytenoid contact pressures were greater for lower than higher pitches; (3) both interarytenoid and intraglottal contact pressures were remarkably large during hard glottal attack; and (4) overall, the largest endolaryngeal pressures were recorded between the arytenoids, during a thoracic fixation maneuver and during gag reflex.This work was supported in part by Deutsche Forschungsgemeinschaft (He 2869/1-1), by a grant from the “Verein zur Förderung hör-, sprach- und stimmgestörter Patienten an der FU Berlin e.V.” (nonprofit organization), Berlin, Germany, and by Grant No. K08 DC00139 from the National Institute on Deafness and Other Communication Disorders.     

On the average genus of a graph

Not all rational numbers are possibilities for the average genus of an individual graph. The smallest such numbers are determined, and varied examples are constructed to demonstrate that a single value of average genus can be shared by arbitrarily many different graphs. It is proved that the number 1 is a limit point of the set of possible values for average genus and that the complete graph K₄ is the only 3-connected graph whose average genus is less than 1.     

On the fragmentation of multiply charged sodium clusters

The fragmentation of multiply charged atomic sodium clusters of mass 200 is investigated using the Micro-canonical Metropolis Monte Carlo (MMMC) statistical technique for excitation energies up to 200 eV and for cluster charges up to +9e. In this work we present caloric curves and charged and uncharged fragment mass distributions for clusters with charges 0, 2, and 4. The caloric curves show a dip at the critical point implying a negative specific heat, as expected for finite systems, while the fragment mass distributions corroborate the picture of a phase transition from one dominant liquid-like cluster to complete vaporization. Received 7 November 2001 / Received in final form 4 April 2002 Published online 28 June 2002     

γ-ray spectroscopy of excited states in 61 30Zn31

The ⁶¹ ₃₀Zn₃₁ isotope has been produced at the Oak Ridge National Laboratory in the fusion-evaporation reaction ⁴⁰Ca(²⁴Mg, 2pn)⁶¹Zn at 104MeV. The experimental set-up allowed γ-rays to be detected in the CLARION Ge detector array in coincidence with the detection of recoiling nuclei in the focal plane at the end of the recoil mass spectrometer. This provides a unique identification of γ-rays belonging to ⁶¹Zn. The excited states have been explored by means of recoil- γγ coincidences, and the resulting decay scheme comprises almost 70 transitions. The data reveal numerous non-yrast states and suggest a revised spin and parity assignment for a previously observed superdeformed band. The resulting decay scheme is compared to predictions from different sets of large-scale shell model calculations.     

Cuprate-catalyzed Three-Component Couplings of Functionalized Organozinc Reagents

Organozinc reagents FG-(CH₂)_nZnX containing electrophilic centers (FG) upon conversion to their corresponding zincates (FG-(CH₂)_nZnMe₂Li) and in the presence of 5–8 mol % MeCu(CN)Li, undergo 1,4-additions to cyclic conjugated enones. The intermediate zinc enolates can be trapped with aldehydes to afford products of three-component couplings.     

Synthesis of novel annulated uracils via domino Knoevenagel-hetero-Diels-Alder reaction in aqueous media

An efficient synthesis of tetracyclic uracil derivatives (polycyclic pyrans) is achieved via domino Knoevenagel-hetero-Diels-Alder reactions of O-propargylated salicylaldehyde derivatives with 1,3-dimethylbarbituric acid in water as solvent in the presence of CuI. The products are formed in good yields.