129 research outputs found
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
- …