We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.
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A persistence theorem for attracting invariant tori for systems subjected to rapidly oscillating perturbations is proved. The singular nature of these perturbations prevents the direct application of the standard persistence results for normally hyperbolic invariant manifolds. However, as is illustrated in this paper, the theory of normally hyperbolic… (More)
The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact Rie-mannian manifold are described. We prove that the spectrum of the kinematic dynamo operator is exactly one vertical strip whose boundaries can be determined… (More)
We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase… (More)
We study the linear post-Newtonian approximation to general rela-tivity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding some significant differences between them, we find that a special nonstationary metric in GEM can be employed to show explicitly that it is… (More)
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation… (More)
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we… (More)