WSEAS CONFERENCES. WSEAS, Unifying the Science

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October 2007, Nov. 2007, December 2007, 2008


Issue 10, Volume 6, October 2007
Print ISSN: 1109-2769
E-ISSN: 2224-2880








Title of the Paper:  A Note on Banach Principle for JW-algebras


Authors: Genady Ya. Grabarnik and Alexander A. Katz

Abstract: In the sequel we establish the Banach Principle for semifinite JW-algebras without direct summand of type I 2 , which extends the recent results of Chilin and Litvinov on the Banach Principle for semifinite von Neumann algebras to the case of JW-algebras.

Keywords: von Neumann algebras, Jordan operator algebras, JW-algebras, Banach Principle, *-algebra of τ -measurable operators affiliated to a semifinite von Neumann algebra, Jordan algebra of τ -measurable operators affiliated to a semifinite JW-algebra.

Title of the Paper:  The Electromagnetic Radiation Problem in an Arbitrary Gravitational Background Vacuum


Authors: Ghislain R. Franssens

Abstract: Electromagnetism in an arbitrary gravitational background vacuum is formulated in terms of Clifford analysis over a pseudo-Riemannian space with signature (1,3). The full electromagnetic radiation problem is solved for given smooth compact support electric and magnetic monopole charge-current density source elds. We show that it is possible to attack this problem by analytical means in four dimensional form and without invoking electromagnetic potentials. Our approach reveals that the solution for the full electromagnetic eld can be expressed in terms of a fundamental solution of the Laplace-de Rham scalar wave equation, so that calculating Greenís dyadic elds is superuous. In the absence of gravity our method reproduces (i) Jemenkoís equations and (ii) an expression for the particular solution of the wave equation satised by the electromagnetic eld. Expression (ii) is simpler than Jemenkoís result and has the additional advantage that its evaluation avoids integrating over singularities.

Keywords: Electromagnetism, Gravity, Clifford analysis, Exterior differential forms, Curved space-time.

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