Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Chaotic synchronization in general network topology for scene segmentation

Chaotic synchronization has been discovered to be an important property of neural activities, which in turn has encouraged many researchers to develop chaotic neural networks for scene and data analysis. In this paper, we study the synchronization role of coupled chaotic oscillators in networks of general topology. Specifically, a rigorous proof is presented to show that a large number of oscillators with arbitrary geometrical connections can be synchronized by providing a sufficiently strong coupling strength. Moreover, the results presented in this paper not only are valid to a wide class of chaotic oscillators, but also cover the parameter mismatch case. Finally, we show how the obtained result can be applied to construct an oscillatory network for scene segmentation.

An alternative approach for general covariant Horava-Lifshitz gravity and matter coupling

Recently, in [3] Horava and Melby-Thompson proposed a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduces the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of. to be lambda = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general lambda.

A general treatment of geometric phases and dynamical invariants

Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.

THE SOUTHERN BRAZILIAN SHELF: GENERAL CHARACTERISTICS, QUATERNARY EVOLUTION AND SEDIMENT DISTRIBUTION

Extending from latitude 34 degrees S to 22 degrees S the Southern Brazilian shelf constitutes the only part of the Brazilian shelf with a subtropical to temperate environment. The studies on the different geological aspects of the area began in the 1960`s and have recently been reassessed after studies related to the determination of the Economic Exclusive Zone. In terms of morphology, the Southern Brazilian shelf may be divided into three sectors, the Sao Paulo Bight, the Florianopolis-Mostardas Sector and the Rio Grande Cone, characterized by conspicuous differences in terms of geological determining factors, bathymetry, declivities and the presence of canyons and channels. Despite the existence of hundreds of radiocarbon datings the sea level changes curve of southern Brazil during the Last Glacial Cycle is still a matter of debate. A recent controversy on the Middle and late Holocene sea level changes curve raised the question of the amplitude of the oscillations which occurred in the period. Also, a few but relatively consistent radiocarbon datings suggest the occurrence of a high sea level during Isotope Stage 3. In terms of sedimentary cover the Southern Brazilian shelf exhibits a very strong hydrodynamic control, both latitudinal and bathymetrical. The sector southward from 25 degrees S is characterized by the influence of the plume of water carrying sediments originating from the Rio de La Plata. Actually its presence is conspicuous up to 28 degrees S, with the area between this latitude and 25 degrees S constituting a transitional zone. In terms of bathymetry the outer shelf is marked by the ""floor-polisher"" effect of the Brazil Current, which is responsible for the maintenance of a relict facies in areas deeper than 100 meters.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

A two-component system, an anti-sigma factor and two paralogous ECF sigma factors are involved in the control of general stress response in Caulobacter crescentus

The extracytoplasmic function sigma factor sigma(T) is the master regulator of general stress response in Caulobacter crescentus and controls the expression of its paralogue sigma(U). In this work we showed that PhyR and NepR act, respectively, as positive and negative regulators of sigma(T) expression and function. Biochemical data also demonstrated that NepR directly binds sigma(T) and the phosphorylated form of PhyR. We also described the essential role of the histidine kinase gene CC3474, here denominated phyK, for expression of sigma(T)-dependent genes and for resistance to stress conditions. Additionally, in vivo evidence of PhyK-dependent phosphorylation of PhyR is presented. This study also identified a conserved cysteine residue (C95) located in the periplasmic portion of PhyK that is crucial for the function of the protein. Furthermore, we showed that PhyK, PhyR and sigma(T) regulate the same set of genes and that sigma(T) apparently directly controls most of its regulon. In contrast, sigma(U) seems to have a very modest contribution to the expression of a subset of sigma(T)-dependent genes. In conclusion, this report describes the molecular mechanism involved in the control of general stress response in C. crescentus.