Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces

We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called potentials of product type. We obtain explicit formulae for the leading eigenvalue, the eigenfunction (which may be discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness property of these quantities is also discussed and it is shown that there always exists a Bernoulli equilibrium state even if $f$ does not satisfy Bowen's condition. We apply these results to potentials $f:\{-1,1\}^\mathbb{N} \to \mathbb{R}$ of the form $$f(x_1,x_2,\ldots) = x_1 + 2^{-\gamma} \, x_2 + 3^{-\gamma} \, x_3 + ...+n^{-\gamma} \, x_n + \ldots$$ with $\gamma >1$. For $3/2 < \gamma \leq 2$, we obtain the existence of two different eigenfunctions. Both functions are (locally) unbounded and exist a.s. (but not everywhere) with respect to the eigenmeasure and the measure of maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ

Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as the prescribed angular velocity $\alpha(t)$ of the boundary has bounded total variation. Here we establish convergence in stronger $L^2$ and $L^p$-Sobolev spaces, allow for more singular angular velocities $\alpha$, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

In this paper we construct spectral triples $(A,H,D)$ on the symbolic space when the alphabet is finite. We describe some new results for the associated Dixmier trace representations for Gibbs probabilities (for potentials with less regularity than H\"older) and for a certain class of functions. The Dixmier trace representation can be expressed as the limit of a certain zeta function obtained from high order iterations of the Ruelle operator. Among other things we consider a class of examples where we can exhibit the explicit expression for the zeta function. We are also able to apply our reasoning for some parameters of the Dyson model (a potential on the symbolic space $\{-1,1\}^\mathbb{N}$) and for a certain class of observables. Nice results by R. Sharp, M.~Kesseb\"ohmer and T.~Samuel for Dixmier trace representations of Gibbs probabilities considered the case where the potential is of H\"older class. We also analyze a particular case of a pathological continuous potential where the Dixmier trace representation - via the associated zeta function - is not true.Comment: the tile was modified and there are two more author

Disfunção cognitiva pós-operatória

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Fractal analysis of weld defect patterns obtained by radiographic tests

This paper presents a fractal analysis of radiographic patterns obtained from specimens with three types of inserted welding defects: lack of fusion, lack of penetration, and porosity. The study focused on patterns of carbon steel beads from radiographs of the International Institute of Welding (IIW). The radiographs were scanned using a greyscale with 256 levels, and the fractal features of the surfaces constructed from the radiographic images were characterized by means of Hurst, detrended-fluctuation, and minimal-cover analyses. A Karhunen-Loeve transformation was then used to classify the curves obtained from the fractal analyses of the various images, and a study of the classification errors was performed. The obtained results indicate that fractal analyses can be an effective additional tool for pattern recognition of weld defects in radiographic tests.Comment: 7 pages, 2 figures. To appear AIP Conference Proceedings - QNDE 200

Critical aspects of biomass ashes utilization in soils: composition, leachability, PAH and PCDD/F

Bottom and fly ashes streams collected along a year in several biomass thermal plants were studied. The bulk composition of ashes and other chemical characteristics that may impact soil application showed a high variability depending on the ash stream, combustion technology and ash management practice at the power plants. The acid neutralization capacity (ANC) and metal’s availability for leaching at fixed pH 7 and 4 was performed according with EA NEN 7371, as a quick evaluation method to provide information on the long-term behavior of ashes, regarding heavy metals and also plant nutrients release. Also the pH dependence leachability study was performed according to CEN/TS 14429 for predicting the leaching behavior under different scenarios. Leachability profiles were established between pH 3 and 12, allowing to distinguish different solubility control phenomena of toxic heavy metals (Cu, Cr, Mn, Ni, Zn, Pb) as well as other salts (Ca, K, Mg, Na, Cl). The ANC of fly ashes at pH 4 (3.6–9.6 molH+/kg) were higher than that observed for the bottom ashes (1.2–2.1 molH+/kg). Ashes were also characterized for persistent organic pollutants (POP), such as polycyclic aromatic hydrocarbons (PAH) and paradibenzodioxines and furanes (PCDD/F). Contents were found to be much higher in fly ash than in bottom ash streams. None of the PAH levels did reach the current national limit value of sewage sludge application in soils or the guide value for ash in north European countries. However, PCDD/F contents, which are not regulated, varied from non-detectable levels to high amounts, regardless the level of loss on ignition (LOI) or unburned carbon content in fly ashes. Given the current ash management practices and possible use of blends of bottom and fly ash streams as soil conditioners resembles clear the urgent need to regulate ash utilization in soils, incorporating limit values both for heavy metals, PAH and PCDD/F

Development of liquid xenon detectors for medical imaging

In the present paper, we report on our developments of liquid xenon detectors for medical imaging, positron emission tomography and single photon imaging, in particular. The results of the studies of several photon detectors (photomultiplier tubes and large area avalanche photodiode) suitable for detection of xenon scintillation are also briefly described.Comment: 13 pages, 5 figures, presented on the International Workshop on Techniques and Applications of Xenon Detectors (Xenon01), ICRR, Univ. of Tokyo, Kashiwa, Japan, December 3-4, 2001 (submitted to proceedings

The pinewood nematode, Bursaphelenchus xylophilus, in Madeira Island

The environmental conditions in Madeira Island are favorable for the presence and dissemination of the pinewood nematode (PWN), Bursaphelenchus xylophilus. Five hundred Pinus pinaster wood samples were collected in several forest areas and PWN was detected in 22.8 % of the samples. Bursaphelenchus xylophilus isolates from Madeira Island displayed the species-specific diagnostic characters. A morphological variation in the female tail terminus was detected. In most females, the tail presented a broadly rounded terminus and, occasionally, a digitate terminus with a terminal nipple-like extension resembling a mucro. PCR ITS-RFLP analysis revealed that Madeira Island isolates exhibited patterns specific to the species B. xylophilus and similar to virulent isolates. Amplified ITS regions were further sequenced and no genetic diversity was found for this genomic region among 17 Portuguese isolates (Madeira Island and Continental Portugal). Phylogenetic analysis revealed that Portuguese isolates grouped with isolates from China, Korea and one isolate from Japa

Non-Gaussian velocity distributions - The effect on virial mass estimates of galaxy groups

We present a study of 9 galaxy groups with evidence for non-Gaussianity in their velocity distributions out to 4R200. This sample is taken from 57 groups selected from the 2PIGG catalog of galaxy groups. Statistical analysis indicates that non-Gaussian groups have masses significantly higher than Gaussian groups. We also have found that all non-Gaussian systems seem to be composed of multiple velocity modes. Besides, our results indicate that multimodal groups should be considered as a set of individual units with their own properties. In particular, we have found that the mass distribution of such units are similar to that of Gaussian groups. Our results reinforce the idea of non-Gaussian systems as complex structures in the phase space, likely corresponding to secondary infall aggregations at a stage before virialization. The understanding of these objects is relevant for cosmological studies using groups and clusters through the mass function evolution.Comment: 5 pages, 4 figures and 2 tables. Accepted for publication in the MNRA