Given a static Schwarzschild spacetime of ADM mass M , it is wellknown that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time. In the present paper we show that in gravitational collapse of Vlasov matter this behaviour can be very different. We construct initial data for which a black hole forms and all matter crosses...

By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS , such that RP is a finitely generated projective generator in R-Mod and S = EndR(P ). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPS . Here we start from the o...

Assume 〈א0,א1〉 → 〈λ, λ +〉. Assume M is a model of a first order theory T of cardinality at most λ+ in a vocabulary L(T ) of cardinality ≤ λ. Let N be a model with the same vocabulary. Let ∆ be a set of first order formulas in L(T ) and let D be a regular filter on λ. Then M is ∆-embeddable into the reduced power N /D, provided that every ∆-existential formula true in M is true also in N . We ob...

Mayo Clinic Electrophysiology Manual is a concise book on cardiac electrophysiology from the Mayo Clinic Scientific Press, published by the Oxford University Press. Preface from the Editor-in-Chief Prof. Samuel J Asirvatham ends with a very interesting note: “If there is one regret in choosing a career in cardiac electrophysiology, it is that I can never again experience the unparalleled wonder...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...

In this paper, we consider fractional reaction-diffusion equations with linear and nonlinear fractional reaction terms in a semi-infinite domain. Using q-Homotopy Analysis Method, solutions to these equations are obtained in the form of general recurrence relations. Closed form solutions in the form of the Mittag-Leffler function are perfectly obtained in the case with linear fractional reactio...

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of ge...

In this paper, we study the asymptotic stability of three fractional scalar systems by using the method of universal adaptive stabilization: (I) Fractional dynamics with integer-order control strategy, (II) Fractional dynamics with fractional control strategy, and (III) Application of fractional viscoelastic and electromagnetic theories in universal adaptive stabilization. It is shown that the ...

Assume 〈א0,א1〉 → 〈λ, λ +〉. Assume M is a model of a first order theory T of cardinality at most λ+ in a vocabulary L(T ) of cardinality ≤ λ. Let N be a model with the same vocabulary. Let ∆ be a set of first order formulas in L(T ) and let D be a regular filter on λ. Then M is ∆-embeddable into the reduced power N/D, provided that every ∆-existential formula true in M is true also in N . We obt...

Let X be a complex manifold and γ a simple closed curve inX . We address the question: What conditions on γ insure the existence of a 1-dimension complex variety Σ with boundary γ in X . When X = C, an answer to this question involves the polynomial hull of gamma. When X = P, complex projective space, the projective hull γ̂ of γ, a generalization of polynomial hull, comes into play. One always h...