On universal Banach spaces of density continuum

We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).

An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

On S-asymptotically omega-periodic functions and applications

Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Quantum entanglement of bound particles under free center of mass dispersion

On the basis of the full analytical solution of the overall unitary dynamics, the time evolution of entanglement is studied in a simple bipartite model system evolving unitarily from a pure initial state. The system consists of two particles in one spatial dimension bound by harmonic forces and having its free center of mass initially localized in space in a minimum uncertainty wavepacket. The existence of such initial states in which the bound particles are not entangled is discussed. Galilean invariance of the system ensures that the dynamics of entanglement between the two particles is independent of the wavepacket mean momentum. In fact, as shown, it is driven by the dispersive center of mass free dynamics, and evolves in a time scale that depends on the interparticle interaction in an essential way.

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Nonanalyticity of the free energy in thermal field theory

We study, in a d-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar phi(4) theory as well as in QED. We find that the infrared divergent contributions induce, when d is even, a nonanalyticity in the coupling alpha of the form (alpha)((d-1)/2) whereas when d is odd the nonanalyticity is only logarithmic.

Tungiasis in a free-ranging jaguar (Panthera onca) population in Brazil

Tungiasis is an ectoparasitic disease caused by fleas of the genus Tunga. The disease is reported to occur mostly in human populations. In wildlife, however, the occurrence and impact of this disease remains uncertain. We captured and examined 12 free-ranging jaguars for the presence of Tunga penetrans in the Pantanal region of Mato Grosso do Sul state, Brazil. Tungiasis prevalence was 100% in the population; lesions were confined to the jaguar's paws. T. penetrans was identified based on the characteristics of the embedded fleas and the morphological identification of a collected free-living flea. The intensity and stage of infestation varied between individual animals. However, in general, all captured jaguars were in good health. The 100% prevalence of tungiasis may be related to the fact that all captures were performed during the dry season. Their high ecological requirements for space make jaguars potential disseminators of T. penetrans in the Pantanal region. Because cattle ranching and ecotourism are the main economic activities in the Pantanal, further studies should evaluate the risks of tungiasis to human and animal health. To the best of our knowledge, this is the first report of tungiasis in jaguars.

Left ventricular free wall impeding rupture in post-myocardial infarction period diagnosed by myocardial contrast echocardiography: Case report

Abstract Background: Left ventricular free wall rupture occurs in up to 10% of the in-hospital deaths following myocardial infarction. It is mainly associated with posterolateral myocardial infarction and its antemortem diagnosis is rarely made. Contrast echocardiography has been increasingly used for the evaluation of myocardial perfusion in patients with acute myocardial infarction, with important prognostic implications. In this case, we reported its use for the detection of a mechanical complication following myocardial infarction. Case presentation: A 50-year-old man with acute myocardial infarction in the lateral wall underwent myocardial contrast echocardiography for the evaluation of myocardial perfusion in the third day post-infarction. A perfusion defect was detected in lateral and inferior walls as well as the presence of contrast extrusion from the left ventricular cavity into the myocardium, forming a serpiginous duct extending from the endocardium to the epicardial region of the lateral wall, without communication with the pericardial space. Magnetic resonance imaging confirmed the diagnosis of impending rupture of the left ventricular free wall. While waiting for cardiac surgery, patient presented with cardiogenic shock and died. Anatomopathological findings were consistent with acute myocardial infarction in the lateral wall and a left ventricular free wall rupture at the infarct site. Conclusion: This case illustrates the early diagnosis of left ventricular free wall rupture by contrast echocardiography. Due to its ability to be performed at bedside this modality of imaging has the potential to identify this catastrophic condition in patients with acute myocardial infarction and help to treat these patients with emergent surgery.