Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

Multimilligram enantioresolution of sulfoxide proton pump inhibitors by liquid chromatography on polysaccharide-based chiral stationary phase

The enantiomers of sulfoxide proton pump inhibitors - omeprazole, lansoprazole, rabeprazole and Ro 18-5364 - were enantiomerically separated by liquid chromatography at multimilligram scale on a poly saccharide-based chiral stationary phase using normal and polar organic conditions as mobile phase. The values of the recovery and production rate were significant for each enantiomer; better results were achieved using a solid-phase injection system. However, this system was applied just for the enantionteric separation of omeprazole to demonstrate the applicability of this injection mode at milligram scale. The chiroptical characterization of the compounds was performed using a polarimeter and a circular dichroism detector. The higher enantiomeric purity obtained for the isolated enantiomers suggests that the methods here described should be considered as a simple and rapid way to obtain enantiomeric pure standards for analytical purpose. (C) 2007 Elsevier B.V. All rights reserved.

Identification of cause of impairment in spiral drawings, using non-stationary feature extraction approach

Parkinson’s disease is a clinical syndrome manifesting with slowness and instability. As it is a progressive disease with varying symptoms, repeated assessments are necessary to determine the outcome of treatment changes in the patient. In the recent past, a computer-based method was developed to rate impairment in spiral drawings. The downside of this method is that it cannot separate the bradykinetic and dyskinetic spiral drawings. This work intends to construct the computer method which can overcome this weakness by using the Hilbert-Huang Transform (HHT) of tangential velocity. The work is done under supervised learning, so a target class is used which is acquired from a neurologist using a web interface. After reducing the dimension of HHT features by using PCA, classification is performed. C4.5 classifier is used to perform the classification. Results of the classification are close to random guessing which shows that the computer method is unsuccessful in assessing the cause of drawing impairment in spirals when evaluated against human ratings. One promising reason is that there is no difference between the two classes of spiral drawings. Displaying patients self ratings along with the spirals in the web application is another possible reason for this, as the neurologist may have relied too much on this in his own ratings.

The latitude dependent irradiation distribution in Europe and its implication for the design of stationary concentrators

When a stationary solar concentrator is designed, the spatial distribution of the available irradiation is of vital interest. An irradiation distribution based only on solar geometry will look similar at different sites. The only difference is that the distribution of the incident irradiation is shifted to lower solar altitudes when latitude is increased. However, real irradiation distribution will show strong asymmetry at high latitude sites, since the winter irradiation is reduced by absorption and scattering in the atmosphere, and by seasonal changes in the climate. The reduced winter irradiation at high latitudes implies that the available annual radiation is concentrated to a narrower angular interval. This means that the degree of concentration that is possible increases with latitude.In the paper examples of irradiation distribution from different sites in Europe from latitude 38°N to 65°N are shown. The origin of the reduced winter irradiation with increased latitude is discussed, and numerical examples on the performance of different types of stationary concentrators for different latitudes are given.

Robustness of stationary tests under long-memory alternatives

This paper investigates the presence of long memory in financiaI time series using four test statistics: V/S, KPSS, KS and modified R/S. There has been a large amount of study on the long memory behavior in economic and financiaI time series. However, there is still no consensus. We argue in this paper that spurious short-term memory may be found due to the incorrect use of data-dependent bandwidth to estimating the longrun variance. We propose a partially adaptive lag truncation procedure that is robust against the presence of long memory under the alternative hypothesis and revisit several economic and financiaI time series using the proposed bandwidth choice. Our results indicate the existence of spurious short memory in real exchange rates when Andrews' formula is employed, but long memory is detected when the proposed lag truncation procedure is used. Using stock market data, we also found short memory in returns and long memory in volatility.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

The impact on the stationary state income of a pay-as-you-go system of social security

A model of overlapping generations in continuous time is composed. IndividuaIs pass through two distinct time periods during their life times. During the first period, they work, save and have a death probability equal to zero. During the second, from the periods T after birth, their probability of death changes to p and then they retire. Capital stock and the stationary state in come are calculated for two situations: in the first, people live from their accumulated capital after retirementj in the second, they live from a state transfer payment through income taxo To simplify matters, in this preliminary version, it is supposed that there is no population growth and that the instantaneous elasticity substitution of consumption is unitary.

Qual a evolução do tecido empresarial da RAM a nível sectorial no período pós-adesão à CE (1988-2008)?

O presente estudo tem como principal objectivo analisar o desempenho global e por sector de actividade do tecido empresarial da RAM no período 1988-2008 através da análise de dados financeiros. A relevância do estudo baseia-se na reflexão da resposta dada pelo tecido empresarial regional aos desafios que foram surgindo ao longo do período referido, e na análise do espírito empresarial e das linhas estratégicas de actuação que pautaram o tecido empresarial a nível das diferentes actividades na RAM. Para a realização deste estudo quantitativo utilizamos uma amostra de conveniência que contêm dados contabilísticos anuais de 545 empresas do tecido empresarial regional, que participaram na iniciativa anual das 100 Maiores Empresas da RAM ao longo dos 21 anos em estudo e que constituem, eventualmente, a única base de dados de cariz semipúblico da região. Os dados foram obtidos através de recolha exaustiva nas instituições responsáveis pelo tratamento da informação disponibilizada pelas empresas concorrentes (Previsão, ECAM), consolidada por pesquisa em jornais (DN, JM), revistas e dados recolhidos no arquivo regional. Estas fontes constituem-se como um precioso instrumento de recolha de dados financeiros de difícil acesso. No tratamento dos dados foram utilizados métodos de estatística descritiva, taxas de crescimento e números índices de base fixa e aplicado teste de correlação de «Pearson». Obteve-se como principais resultados a evolução anual positiva do indicador Volume de Negócios (7,95%) e Activo Líquido (12,23%), Capital Próprio (11,04%), Cash-Flow (12,40%) e Produtividade (2,51%). Os resultados obtidos permitem concluir que houve crescimento empresarial na RAM no período em estudo. As actividades industriais, comerciais e de serviços cresceram a ritmos diferenciados ao longo do período de análise, com predominância para o crescimento do sector terciário, alicerçada nas actividades comerciais e de serviços, que evidenciaram crescimento superiores à actividade industrial.