As equações de campo da gravitação

Tradução a partir do original alemão “Die Feldgleichungen der Gravitation”, A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 844-847, 25.11.1915 (As equações de campo da gravitação, A. Einstein, Atas da Academia Prussiana das Ciências de Berlim). Este artigo é continuação do trabalho “Zur allgemeinen Relativitätstheorie” de A. Einstein publicado nas Atas XLIV da Academia Prussiana das Ciências de Berlim com o título “Sobre a teoria da relatividade geral”. Em particular, o artigo faz referência às pp. 778-786 e às equações (21)e(22)dotrabalhopublicadonasAtasXLIV,ecitaestasequaçõescomo (21)loc.cit. e(22)loc.cit.. AtraduçãodotrabalhopublicadonasAtasXLIV junta-se aqui a seguir à tradução deste artigo.info:eu-repo/semantics/publishedVersio

Conformal transformations in general relativistic elasticity

Conformal transformations are applied in the context of general relativistic elasticity. Expressions relating relativistic elastic quantities and tensors are obtained for two conformal spacetimes, whose material metrics are also conformally related. Non-static shear-free spherically symmetric elastic solutions of the Einstein field equations are constructed by performing conformal transformations of spacetime and material metrics of a known non-static shear-free spherically symmetric elastic solution.Funds from the Fundação para a Ciência e a Tecnologia", through the Project PEstOE/MAT/UI0013/201

A portfolio stock selection model based on expected utility, entropy and variance

In the context of investment decision-making, the selection of stocks is important for a successful construction of portfolios. In this paper the expected utility, entropy and variance (EU-EV) model is applied for stock selection, which can be used as preselection model for mean-variance portfolio optimization problems. Based on the EU-EV risk, stocks are ranked and the best ranked stocks with lower risk are selected in order to form subsets of stocks, which are then used to construct portfolios. The EU-EV model is applied to the PSI 20 index, to the Euro Stoxx 50 index and to the Nasdaq 100 index. Subsets of selected stocks are analysed and their portfolios' efficiencies are compared with those of the portfolios obtained from the whole set of stocks using the mean-variance model. The results reveal that the EU-EV model is an adequate stock selection model for building up efficient portfolios with a lower number of stocks.The author thanks the reviewers for helpful comments. The author thanks support from FCT (“Fundação para a Ciência e a Tecnologia”) through the Projects UIDB/00013/2020 and UIDP/00013/2020

General relativistic elasticity : statics and dynamics of spherically symmetric metrics

An introduction is provided to the theory of elasticity in general relativity. Important tensors appearing in this context are presented. In particular, attention is focussed on the elasticity difference tensor, for which an algebraic analysis is performed. Applications are given to static and non-static spherically symmetric configurations. For the latter, dynamical equations are obtained characterizing the space-time in the context of general relativistic elasticity

Mathematical properties of the elasticity difference tensor

A tetrad, adapted to the principal directions of the unstrained reference tensor, is chosen and the elasticity difference tensor, as introduced in [1], is decomposed along those directions. The second order tensors obtained are studied and an example is presented

Generating elastic solutions of the Einstein field equations from the Schwarzschild vacuum solution

PreprintThe problem of generating solutions of the Einstein field equations with an elastic energy-momentum tensor from the Schwarzschild vacuum solution by means of conformal transformations is analyzed. Applying the formulation of relativistic elasticity, suitable conformal factors are obtained for static and non-static elastic spacetime configurations and particular solutions are presented. This work shows that the technique used here permits generating new elastic matter solutions from a vacuum spacetime.The author thanks support from FCT ("Fundacao para a Ciencia e Tecnologia"), through the projects UID/MAT/00013/2013 and PTDC/MAT-ANA/1275/2014

Performance Evaluation of Portfolio Stocks Selected with the EU-EV Risk Model

In this paper, the performance of portfolios consisting of stocks selected with the recently proposed expected utility, entropy and variance (EU-EV) risk model is analysed. The portfolios were constructed using data of the PSI 20 index, from January 2019 to December 2020, by reducing the number of stock components to the half with the EU-EV risk model. The effciency of these portfolios in terms of the mean-variance model was shown to be approximately equal to the effciency of portfolios obtained from the whole set of stocks. The aim is to evaluate the performance of the constructed portfolios, by comparing their in-sample and out-of-sample results with those of the benchmark. For that purpose, cumulative returns in the in-sample period from January 2019 to December 2020 and in the out-of-sample period from January 2021 to December 2022, considering both an one-year and a two-year time horizon, as well as different performance metrics, such as Sharpe ratio, Sortino ratio, Beta and Alpha, are analysed. The results reveal that the portfolios constructed with the EU-EV risk model outperform the benchmark portfolio in the given periods, where a better performance was obtained in the one-year out-of-sample period. These results suggest that the strategy of constructing portfolios using the best ranked stocks according to the EU-EV risk model can be useful for short-term investment objectives.FCT -Fundação para a Ciência e a Tecnologia(UIDB/00013/2020

Relating material and space-time metrics within relativistic elasticity : a dynamical example

Given a space-time and a continuous medium with elastic properties described by a 3-dimensional material space, one can ask whether they are compatible in the context of relativistic elasticity. Here a non-static, spherically symmetric spacetime metric is considered and we investigate the conditions for that metric to correspond to different 3-dimensional material metrics

Sobre a teoria da relatividade geral

Tradução a partir do original alemão “Zur allgemeinen Relativitätstheorie”, A. Einstein, Sitzungsberichte XLIV der Preussischen Akademie der Wissenschaften zu Berlin, 778-786, 4.11.1915 (Sobre a teoria da relatividade geral, A. Einstein, Atas XLIV da Academia Prussiana das Ciências de Berlim). Em anexo a esta tradução são apresentadas as equações de “Die formale Grundlage der allgemeinen Relativitätstheorie” (O fundamento formal da teoria de relatividade geral, A. Einstein, Atas XLI, 1066-1077, 1914) citadas neste artigo (por “loc. cit.”).info:eu-repo/semantics/publishedVersio

Analyzing and classifying risks: a case-study in the furniture industry

In this work we propose a methodology which permits the risk analysis and classification of occupational accidents in industrial settings. Data used in this study corresponds to accidents that occurred in the furniture industry in Portugal in 2010. A loss random variable is constructed in order to model the number of lost days implied by different contact modes of injuries in industry. The corresponding risk measures, such as Value-at-Risk, expected loss, loss variance and exceedance probabilities are determined in order to analyze and classify the contact modes according to their risk level, allowing the identification of the most problematic and the less problematic accident category in this industry. Contact with cutting, sharp, rough material was the most problematic whereas contact with electrical current, temperature, hazardous substance was the one with lower risk level.Fundação para a Ciência e a Tecnologia(UID/MAT/00013/2013