Title of the Paper: A Note on Banach
Principle for JW-algebras
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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
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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
Green’s dyadic elds is superuous. In the absence of gravity our method reproduces (i) Jemenko’s equations and
(ii) an expression for the particular solution of the wave equation satised by the electromagnetic eld. Expression
(ii) is simpler than Jemenko’s 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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