A mapping of spinors with j=p/2 onto polynomial algebras has been recently proposed (M. Chaichian and A. P. Demichev, Phys. Lett. A 222, 14 (1996).). These algebras are proved to be parafermionic algebras of order p (or generalized parafermionic algebras (D. Bonatsos, P. Kolokotronis and C. Daskaloyannis, Mod. Phys. Lett. A 10, 2197 (1995).) of order p). The diagonal number operator of the parafermionic algebras is proved to be able to be written as a combination of monomials of the ladder operators.
[J13.02] Representation Theory and Applications of the Deformed U(su) and U(osp(1,2)) Algebras and the Parafermionic Oscillators
C. Daskaloyannis (U. Thessaloniki, Greece), D. Bonatsos (N.C.S.R. Demokritos, Aghia Paraskevi, Greece)
A large number of algebras with three generators can be studied in a unified framework using Verma modules, which are quotient modules of the algebra. The representation theory and the applications of associative algebras, which are usually referred to as nonlinear deformed extensions (or polynomial variations) of the U(su), U(su(1,1)), U(osp(1,2)) or U(sl(2)) algebras are reviewed here. Realizations of these algebras can be obtained by using the deformed parafermionic oscillators. The applications of the parafermionic algebras to the discrete phase space problems and the spectra of the deformed nuclei will be discussed.
[J13.03] Nonlinear Deformed su Algebras Involving Two Deforming Functions
P. Kolokotronis, D. Bonatsos (N.C.S.R. Demokritos, Aghia Paraskevi, Greece), C. Daskaloyannis (U. Thessaloniki, Greece), A. Ludu (U. Bucharest, Romania), C. Quesne (U. Libre de Bruxelles, Belgium)
The most common nonlinear deformations of the su Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present work, less common nonlinear deformations of su(2), introduced by Delbecq and Quesne and involving two deforming functions of J_0, are reviewed. Such algebras include Witten's quadratic deformation of su(2) as a special case. Contrary to the former deformations, for which the spectrum of J_0 is linear as for su(2), the latter give rise to exponential spectra, a property that has aroused much interest in connection with some physical problems. Another interesting algebra of this type, denoted by \cal A^+_q(1), has two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2,~\ldots. To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed. The resulting algebraic structure, referred to as a two-colour quasitriangular Hopf algebra, is described.
[J13.04] Certainty Law
R.B. Cunningham (P.O. Box 190 Murphys, CA 95247)
This abstract was not submitted electronically.
[J13.05] Magnetic Reynolds Stress Tensor Closely Estimated,...PartII
K.L. McDonald (P.O. Box 2433, Salt Lake City, UT)
This abstract was not submitted electronically.
[J13.06] Magnetic Reynolds Stress Tensor Closely Est. Thru Multiplying Reynolds Stress Tensor by \beta [B_m \bullet (\hatøminus \hatøminus + \hatøminus \hatøminus]^2, \beta= constant, B_m Being Ensemble Meaned Magnetic Induction
Keith L. McDonald (P.O. Box 2433, Salt Lake City, UT)
This abstract was not submitted electronically.
[J13.07] On the Physics of Alonso De La Veracruz
Armando Barranon Cedillo (Universidad Autonoma Metropolitana)
Some aspects regarding the natural philosophy at the virreinal period in the XVI century Mexico are discused. Mainly on the social impact of the Lectures of this scholar at the first University of Mexico and his inquisitorial process. The structure and significance of his course on aristotelic physics is explained in regard to the Logic perspectives. (FR. ALONSO DE LA VERACRUZ. Dialectica Resolutio. Mexico: U:N:A:M.)