Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Generalized nonuniform dichotomies and local stable manifolds

We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.Comment: 18 pages. New version with minor corrections and an additional theorem and an additional exampl

Unit root tests for panel data: a survey and an application

The importance of a priori check of the existence of unit roots in the panel data comes from the already known effect that the presence of unit roots in time series may cause a misinterpretation of estimated results. Adding the cross-section dimension to the time series dimension offers an advantage in testing for nonstationary and cointegration since cross-section increases the data set used in those tests, thus improving their power. However, the cross-section dimension also brings some new problems into question, namely the existence of cross-section dependency which can bias usual panel data unit root test results in small samples. This paper presents a survey of panel unit root tests, evidencing the most recent developments on the issue, including those that account for the presence of contemporaneous cross-correlation as well as for the presence of heterogeneous serial correlation. Parallel to the developments of panel unit root tests, great attention has also been given to cointegration tests. We briefly review the most widely referred cointegration tests. We apply the reviewed panel unit root tests on an EU social variable which represents the population weight over than 65 years of age. We consider data running from 1970 to 2001. The panel unit root test results reveal to be sensitive to the prior assumptions regarding contemporaneous cross-correlation and heterogeneous serial correlation in small samples. The usual battery of panel unit root tests appear not to be adequate when a panel is composed by a mix of a stationary and nonstationary time series

Estudo numérico e experimental de modos de falha em placas de aço aparafusadas

Neste trabalho será apresentado um modelo numérico utilizando o software Ansys para estudo não linear do comportamento de placas em aço, aparafusadas, quando submetidas a esforços para além da sua capacidade elástica. Serão utilizados elementos finitos sólidos e de contacto, que permitirão obter resultados dos modos de falha que ocorrem nas juntas aparafusadas sobrepostas. Serão apresentados resultados experimentais em placas com as mesmas características. Os modos de falha obtidos nos ensaios realizados, permitirão observar a resistência última das ligações, e comprovar que a resistência ao corte nas ligações, aumenta com o aumento do comprimento da zona lisa do parafuso

The Impact of COVID-19 on Physical Activity and Sedentary Behavior in Children: A Pilot Study

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Topological pressure of simultaneous level sets

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space and to a conditional variational principle. We use this to recover information on the topological entropy and Hausdorff dimension of the level sets. Our approach is thermodynamic in nature, requiring only existence and uniqueness of equilibrium states for a dense subspace of potential functions. Using an idea of Hofbauer, we obtain results for all continuous potentials by approximating them with functions from this subspace. This technique allows us to extend a number of previous multifractal results from the $C^{1+\epsilon}$ case to the $C^1$ case. We consider ergodic ratios $S_n \phi/S_n \psi$ where the function $\psi$ need not be uniformly positive, which lets us study dimension spectra for non-uniformly expanding maps. Our results also cover coarse spectra and level sets corresponding to more general limiting behaviour.Comment: 32 pages, minor changes based on referee's comment

Fire protection efficiency of intumescent coatings

This paper presents an experimental study about the fire protection efficiency of a material produced of an emulsion of intumescent coating with granulated cork. The analysis is performed at the micro scale level, with TG and DSC tests at elevated temperatures, and in a mass loss calorimeter with protected steel plates, with temperatures representative of a fire scenario. The results indicate that an increased protection is obtained when the granular cork particle size is smaller and a cork mass fraction of 5% is used.info:eu-repo/semantics/publishedVersio

Realistic clocks, universal decoherence and the black hole information paradox

Ordinary quantum mechanics is formulated on the basis of the existence of an ideal classical clock external to the system under study. This is clearly an idealization. As emphasized originally by Salecker and Wigner and more recently by other authors, there exist limits in nature to how ``classical'' even the best possible clock can be. When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate. This improves on a previous calculation we presented with a sub-optimal clock in which only part of the information was lost by the time of evaporation.Comment: 3 Pages, RevTex, no figure

Unknown Primary Merkel Cell Carcinoma With Cutaneous Spread

The authors present the case of a woman in the seventh decade of life with medical history of: left nephrectomy for renal tuberculosis and non-Hodgkin's lymphoma treated with chemotherapy (QT) and radiotherapy. She presented with a 2-month history of non-tender, left inguinal lymph node enlargement. Positron Emission Tomography (PET)-CT -scanshowed hypermetabolic inguinal and retroperitoneal lymphadenopathies, no primary tumour. On the second dermatological examination a pink, 2 cm plaque on the anterior left knee was noted. The histopathological analysis revealed Merkel cell carcinoma. The patient underwent two lines of systemic QT, with life-threatening toxicities limiting treatment. Followed overwhelming disease progression with lymphoedema and numerous skin metastases in the left lower limb. The patient received palliative care until death. The rare incidence of such neoplasia and its uncommon clinical presentation justifies reporting this case and highlights the importance of multidisciplinary teams in the management of cancer patients.info:eu-repo/semantics/publishedVersio