Can simple models explain Zipf’s law for all exponents?

H. Simon proposed a simple stochastic process for explaining Zipf’s law for word frequencies. Here we introduce two similar generalizations of Simon’s model that cover the same range of exponents as the standard Simon model. The mathematical approach followed minimizes the amount of mathematical background needed for deriving the exponent, compared to previous approaches to the standard Simon’s model. Reviewing what is known from other simple explanations of Zipf’s law, we conclude there is no single radically simple explanation covering the whole range of variation of the exponent of Zipf’s law in humans. The meaningfulness of Zipf’s law for word frequencies remains an open question.Peer ReviewedPostprint (published version

Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds

For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to the representation given by the composition of the lift of the holonomy representation defined by \eta, and the n-dimensional, irreducible, complex representation of SL(2,C). In the present work, we focus on two aspects of this invariant: its asymptotic behavior and its relationship with the complex-length spectrum of the manifold. Concerning the former, we prove that for suitable spin structures, log(\tau_n(M; \eta)) grows as -n^2 Vol(M)/4\pi, extending thus the result obtained by W. Mueller for the compact case. Concerning the latter, we prove that the sequence {\tau_n(M; \eta)} determines the complex-length spectrum of the manifold up to complex conjugation

A numerical study on active control for tiltrotor whirl flutter stability augmentation

The use of active control to augment whirl flutter stability of tiltrotor aircraft is studied by means of a multibody simulation. The numerical model is based on a 1/5 scale semi-span aeroelastic wind tunnel model of a generic tiltrotor concept and possesses a gimballed, stiff-in-plane rotor that is windmilling. A single-input single-output controller and two types of multi-input multi-output algorithms, Linear Quadratic Gaussian Control and Generalized Predictive Control, are studied. They are using measured wing deflections in order to calculate appropriate swashplate input. Results on the closed-loop behavior of three wing and two gimbal natural modes are given. Robustness analyses with respect to major parameters like wing natural frequencies or structural damping are also briefly discussed. The rotor shear force is shown in the uncontrolled condition and in presence of a controller in order to illustrate the whirl flutter mechanism. The single-input single-output controller yielded substantial gain in stability and turned out to be most suitable for industrial application, whereas the Linear Quadratic Gaussian Regulator yielded even higher damping and still had good robustness characteristics

Los tipos nomenclaturales de Scilla autumnalis L. y Urginea maritima (L.) Baker (Liliaceae)

Se proponen los tipos nomenclaturales de Scilla autumnalis L. y Urginea maritima (L.) Baker (Liliaceae) a partir del material original de Linneo conservado en los herbarios UPS y L.Nomenclatural types of Scilla autumnalis L. and Urginea maritima (L.) Baker (Liliaceae). Nomenclatural types of Scilla autumnalis L. and Urginea maritima (L.) Baker (Liliaceae) are proposed from Linnaeus’ original material preserved in the herbaria UPS and L