Stability analysis of cosmological models through Liapunov's method

We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides information not only about the asymptotic stability of a given equilibrium point but also about its basin of attraction. This cannot be obtained by the usual methods found in the literature, such as linear stability analysis or first order perturbation techniques. Moreover, Liapunov's method is also applicable to non-autonomous systems. We use this advantadge to investigate the mechanism of reheating for the inflaton field in FRW models.Comment: Latex file, 8 pages, no figures, accepted for publication in Class. & Quant. Gra

Generic stability of dissipative non-relativistic and relativistic fluids

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.Comment: 22 page

Fake Superpotential for Large and Small Extremal Black Holes

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities. Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov). Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point. This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space. In particular the W function for small non-BPS black holes can always be computed analytically, unlike for the large black-hole case.Comment: 30 pages, LaTeX source. Discussion on the radial evolution of the scalar fields, in relation to the symmetries of the W-function, extended. Table 1 added. Typos correcte

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

European survey on criteria of aesthetics for periodontal evaluation: The ESCAPE study

Objective: The ESCAPE multicentre survey was designed to (a) compare the agreement of three relevant aesthetic scoring systems among different centres, and (b) evaluate the reproducibility of each question of the questionnaires. / Materials and Methods: EFP centres (n = 14) were involved in an e‐survey. Forty‐two participants (28 teachers, 14 postgraduate students) were asked to score the one‐year aesthetic outcomes of photographs using the Before–After Scoring System (BASS), the Pink Esthetic Score (PES) and the Root coverage Esthetic Score (RES). Mean values of kappa statistics performed on each question were provided to resume global agreement of each method. / Results: Between teachers, a difference of kappa ≥ 0.41 (p = .01) was found for BASS (75%) and PES (57%). Similarly, RES (84%) and PES (57%) were different (p < .001). No difference was found between BASS (75%) and RES (84%). No difference was found between students, whatever the scoring system. Questions of each scoring system showed differences in their reproducibility. / Conclusions: The outcomes of this study indicate that BASS and RES scoring systems are reproducible tools to evaluate aesthetic after root coverage therapies between different centres. Among the various variables, lack of scar, degree of root coverage, colour match and gingival margin that follows the CEJ show the best reliability