Since its publication in 1882, Rayleigh's work on electrically charged conducting drops has been widely quoted, but its rigorous derivation has not been given in the literature. By means of the domain perturbation technique, this work presents a rigorous derivation of Rayleigh's results, following his approach with Lagrange's equation. With the systematic procedure, it becomes explicit that the...

The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced representations of C *-algebras, in the light of L. Schwartz' theory of Hilbert sub-spaces. This turns out to account for the freedom in the induction proce...

In this paper, we are interested in the global existence result for a class of Klein–Gordon equations, particularly unified time decay concerning possibly vanishing mass parameter. We give first rigorous proof problem, which relies on both flat foliation and hyperboloidal Minkowski spacetime. To take advantage foliations, an iteration procedure is used.