A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity

We establish the existence and local uniqueness of traveling wave solutions to the one-dimensional Euler equations with artificial viscosity. The equations are expressed as a fixed-point problem, which is solved by a computer-assisted method based on Yamamoto’s application of the Banach fixed-point theorem.     

Long-term preservation of voice improvement following surgical medialization and reinnervation for unilateral vocal fold paralysis

In June of 1996, we reported improved functional voice results when reinnervation was combined with surgical medialization for unilateral vocal fold paralysis. In addition, it was noted that further wasting of the reinnervated vocal fold was prevented in 96% of these patients beyond 2 years' follow-up. The study reported here compares the long-term preservation of voice improvement achieved by surgical medialization alone with that resulting from combined medialization and nerve-muscle pedicle reinnervation. Further significant wasting of the paralyzed vocal fold with voice deterioration from that achieved by surgical medialization alone was noted between 6 months and 2 years postoperatively in 28% of patients, while only 4% of those undergoing combined reinnervation demonstrated this finding at a minimum of 2 years' follow-up.     

Convergence in law of random sums with non-random centering

We extend results obtained in Kruglov,⁽⁷⁾ and Finkelstein and Tucker⁽³⁾ to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.⁽¹⁰⁾ Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692.     

Coloring graphs with stable cutsets

This paper proves that if a graph G has a stable cutset S such that no vertex of S lies on a hole, then G is k-colorable if and only if the G_iUS are k-colorable, where G_i are the components of G ? S and a hole is a chordless odd-length (≥5) circuit. This result shows that critical hole-free perfect graphs cannot contain stable cutsets.     

A general dispersion relation for spin-phonon excitations in paramagnets

The advantage of using standard basis operators in evaluating the semi-invariants occurring in the diagrammatic theory of spin-phonon modes is discussed. The dispersion relation of the coupled-mode excitations is derived for paramagnetic ions of arbitrary spin having a general static spin hamiltonian.     

Improved effective field treatment of the BEG model

A version of the effective field theory recently proposed by the author is applied to a study of the Blume-Emery-Griffiths model. The theory correctly accounts for all the single-kite kinematic relations and leads to results that are quite superior, and in some aspects crucially different, to those reported by other workers using a previous version of the formalism which was defective in its treatment of the kinematic relations. The critical temperature for the second-order phase transitions for a range of biquadratic exchange interactions and single-ion anisotropies is studied for the honeycomb, square and cubic lattices, and the tricritical points are also located. The magnetization curves are studied in depth for a range of interaction strengths, particularly in the vicinity where reentrant behaviour is predicted. The first-order transitions which can arise for a limited range of single-ion anisotropies are also studied, as well as the quadrupolar moment.     

Fermions without spinors

The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.