[show abstract][hide abstract] ABSTRACT: In this paper is stablished a characterization of the solutions of the equation: zeta(z) = 0. Then such a characterization is used to give a proof for Riemann is Conjecture. Comment: 10 Pages, This is a proof of Riemann Conjecture
[show abstract][hide abstract] ABSTRACT: Fractional systems are associated with irrational transfer functions for which nonunique analytic continuations are available (from some right-half Laplace plane to a maximal domain). They involve continuous sets of singularities, namely cuts, which link fixed branching points with an arbitrary path. In this paper, an academic example of the 1D heat equation and a realistic model of an acoustic pipe on bounded domains are considered. Both involve a transfer function with a unique analytic continuation and singularities of pole type. The set of singularities degenerates into uniquely defined cuts when the length of the physical domain becomes infinite. From a mathematical point of view, both the convergence in Hardy spaces of some right-half complex plane and the pointwise convergence are studied and proved.
Physica Scripta 10/2009; 2009(T136):014023. · 1.03 Impact Factor
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