By adopting the above described point of view, which means to reinterpret general relativity as a gauge theory for the Lorentz group, the aim of the present paper will be to show that the **angular** **momentum** and the energy-**momentum** tensors of a general matter field can be defined as the Noeth- er currents associated to the invariance of the action integral under local transformations taking place not in spacetime, but in the tangent space. We begin in Sec. II with a review of the Lorentz transformation properties. In Sec. III we intro- duce the gauge potentials, define the Lorentz covariant de- rivative, and show how a very special tetrad field naturally shows up in this formalism. This tetrad, as we are going to see, depends on the spin connection, and this dependency will be crucial for obtaining the covariant conservation laws. In Sec. IV we obtain the gauge transformations of both the spin connection and the tetrad field. The roles played by the spin and the orbital parts of the Lorentz generators in these transformations will also be analyzed. In Sec. V we show how the **angular** **momentum** conservation can be obtained as the Noether current associated to a transformation generated by the spin generator of the Lorentz group. Then, by consid- ering the Lorentz transformation of the tetrad field, we show in Sec. VI how the energy-**momentum** conservation can be obtained as the Noether current associated to a transforma- tion generated by the orbital generator of the Lorentz group. Finally, in Sec. VII, we comment on the results obtained.

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The Hamiltonian formulation of the TEGR, with no a priori restriction on the tetrad fields, has recently been estab- lished @18#. Its canonical structure is different from that ob- tained in Ref. @13#, since it is not given in the standard Arnowitt-Deser-Misner ~ADM! form @19#. In this framework we again arrive at an expression for the gravitational energy, in strict similarity with the procedure adopted in Ref. @16#, namely, by interpreting the Hamiltonian constraint equation as an energy equation for the gravitational field. Likewise, the gravitational **momentum** can be defined. The constraint algebra of the theory suggests that certain **momentum** com- ponents are related to the gravitational **angular** **momentum**. It turns out to be possible to define, in this context, the **angular** **momentum** of the gravitational field.

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Testing the true nature of black holes —the no-hair hypothesis—will become increasingly more precise in the next few years as new observational data is collected in both the gravitational-wave channel and the electromagnetic channel. In this paper we consider numerically generated spacetimes of Kerr black holes with synchronized scalar hair and build stationary models of magnetized thick disks (or tori) around them. Our approach assumes that the disks are not self-gravitating, they obey a polytropic equation of state, the distribution of their specific **angular** **momentum** is constant, and they are marginally stable, i.e., the disks completely fill their Roche lobe. Moreover, contrary to existing approaches in the literature, our models are thermodynamically relativist, as the specific enthalpy of the fluid can adopt values significantly larger than unity. We study the dependence of the morphology and properties of the accretion tori on the type of black hole considered, from purely Kerr black holes with varying degrees of spin parameter, namely from a Schwarzschild black hole to a nearly extremal Kerr case, to Kerr black holes with scalar hair with different Arnowitt-Deser-Misner mass and horizon **angular** velocity. Comparisons between the disk properties for both types of black holes are presented. The sequences of magnetized, equilibrium disks around Kerr black holes with scalar hair discussed in this study are morphologically and thermodynamically different than their Kerr black hole counterparts, namely their vertical size is larger, the high-density central region is more extended, and the fluid is more relativistic. Therefore, we expect significant differences to appear when these sequences are used as initial data for numerical relativity codes to investigate their dynamical (nonlinear) stability and used in tandem with ray-tracing codes to obtain synthetic images of black holes (i.e., shadows) in astrophysically relevant situations where the light source is provided by an emitting accretion disk.

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difference between two pump modes. The high OAM harmonics result from the **angular** **momentum** cascading from the modes with lower OAM to the modes with higher OAM. This is an unexpected and unexplored behavior, which is profoundly related to the role of the plasma wave as a spiral phase element. Thus, similar mechanisms are expected when dealing with waves or oscillations in other nonlinear media, e.g., phonons or molecular vibrations. We confirm the analytical predictions numerically through ab initio three- dimensional OSIRIS simulations [29,30]. OSIRIS employs

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event horizons should occur generically in large families of space-times, with the exterior region approaching a Kerr-Newman metric asymptotically with time. Now, mass and Maxwell charges are conserved quantities, and the same is true for **angular** **momentum** if one further assumes axisymmetry, so the inequality (1.1) follows for all initial data for such a collapse. Besides its intrinsic interest, our inequality provides some support for this “standard picture”, and in particular for weak cosmic censorship.

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DIPOLE-DIPOLE OPERATOR IN **ANGULAR** **MOMENTUM** BASIS: A COMPLEMENTARY STUDY IN NUCLEAR MAGNETIC RESONANCE. The relationship between the magnetic dipole-dipole potential energy function and its quantum analogue is presented in this work. It is assumed the reader is familiar with the classical expression of the dipolar interaction and has basic knowledge of the quantum mechanics of **angular** **momentum**. Except for these two points only elementary steps are involved.

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The first example is given by a slab-shaped dense light beam. The beam propagates in the z-direction of a rectangul- ar frame (x, y, z), has a core region defined by −a < x < a, and two narrow boundary regions at −b < x < − a and a < x < b. Within the core there is a homogeneous conven- tional electromagnetic wave field. This field is matched to the electromagnetic field in the inhomogeneous boundary regions as shown elsewhere [3, 8]. The analysis is here restricted to these regions within which the inhomogeneity in the x-direction requires the revised field equations to be used. In an analogous beam of circular cross-section, the source of **angular** **momentum** becomes localized to a corresponding inhomogeneous boundary region [3, 8].

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Since Michel Mayor and his student Didier Queloz’s pioneer announcement, in 1995, of the existence of a planet orbiting the star 51 Peg, up to present date, 695 extrasolar planets orbiting stars of spectral type F, G, K and M have been discovered. A study on the behavior of the total **angular** **momentum** of the planetary systems known up to present date becomes relevant when we know that about 98% of the **angular** **momentum** of the solar system is associated with the planets, although they represent only 0.15 percent of the mass of the whole system. In this dissertation we study the behavior of stellar **angular** **momentum**, orbital **angular** **momentum** and total **angular** **momentum** in a sample of 282 stars harboring planets, including 40 multiple systems. We observed that planetary systems containing more than one known planet have both higher orbital **angular** **momentum** and total **angular** **momentum** compared to those who have only one planet. This analysis shows that multiplanet systems tend to have higher momenta, suggesting that the planets in such systems that contribute to the greater portion momenta have been found. Thus, planetary systems with lower values for the momenta represent the best candidates to the discovery of new planets.

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Por outro lado, estudos realizados recentemente defendem que os resultados das estratégias **momentum** são insignificantes durante a última década, apontando para o desaparecimento contínuo da anomalia (Daniel & Moskowitz 2014; Hwang & Rubesam 2015). No mesmo sentido, Pinto (2014) aplicou a estratégia **momentum** 6meses/6meses para Reino Unido entre 1997 e 2013. Através de uma análise repartida em dois momentos temporais, concluiu que a rentabilidade desta estratégia é significativa apenas até 2008, altura da crise financeira, passando a ser negativa após essa data. De outro ponto de vista, Cremers and Pareek (2015) defendem uma análise mais pormenorizada destas estratégias, alegando diferenças entre as suas rentabilidades. Segundo os autores, as estratégias **momentum** são mais lucrativas para períodos de detenção mais curtos, passando a ser insignificantes em períodos longos. Por último, Grobys (2016) estudou a rentabilidade de três estratégias **momentum** para o mercado alemão entre 2000 e 2014. Os seus resultados apontam para a continuidade dos lucros no período pós-crise.

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the Market State (MKT) and Market Volatility (Vol) as predictors of **Momentum** Returns (MoM_Reg). Reported results show that Market State (MKT) is not a statistically significant predictor of the **momentum** returns whereas Market Volatility (Vol) is a significant predictor. This set of results contrasts with those reported in WX with respect to the predictor MKT. That difference arises from the fact that WX use a shorter sample period and also due to some corrections in the data that occurred since they finished their work. 4

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In total, t-tests for four investment strategies will be run for this paper. The first strategy is individual stock **momentum** where stocks per country and industry are used to determine if **momentum** exists within the indices. The returns of individual companies within each stock index were used for the **momentum** return calculations. When looking at the AEX (The Netherlands), for example, all 25 companies listed on the exchange were ranked and the top and bottom 10 percent were tracked for three and six months respectively to create the zero- cost portfolios and obtain their returns. The result is the significance per country or industry. To be able to compare individual stock **momentum** with the other strategies that rank countries or industries as opposed to companies, a second investment strategy is based on the individual stock **momentum** strategy to obtain an overall overview; the so-called ‘all industries / all countries’. Here, an average will be taken of the monthly **momentum** returns across the already ranked companies within the countries and industries (so no additional ranking). The importance of this strategy will become clear in the next chapter when individual stock **momentum** for industries will be compared to macromomentum. The third strategy is called macromomentum or ‘country / industry’ where the countries or industries themselves will be ranked each month based on the monthly returns of each country or industry. The top and bottom 10 percent 13 will be used to create the equally weighted zero-cost portfolio as explained before. The fourth investment strategy is based on the ranking of ETFs. Each MSCI index will

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Several sources of systematic uncertainties are taken into ac- count. The most signiﬁcant source is the muon eﬃciency that includes the trigger, track reconstruction, isolation, and identi- ﬁcation. The statistical uncertainties of the measured eﬃciency scale factors are taken into account by simulating 500 pseudo- experiments in which the templates are reformed, each time vary- ing the scale factors randomly within the given uncertainty. The systematic uncertainties in the extraction of the eﬃciency (e.g., background estimates) are also included. Another signiﬁcant uncer- tainty stems from the statistical precision of the templates, which is estimated using pseudo-experiments. The pileup uncertainty is estimated by varying the cross section of the minimum bias events by ± 5%. The muon **momentum** bias is measured in data and sim- ulation, and corresponding corrections are applied [35] . The statis- tical uncertainties in the muon **momentum** correction factors are propagated to a systematic uncertainty using pseudo-experiments. In addition, a systematic uncertainty is assessed to take into ac- count possible global offsets from the peak position of the Z boson mass. The systematic uncertainties for the background are esti- mated by varying the normalization scale factor of the e μ sample by 10% and the yields of WZ and ZZ events by 50%. The sta-

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Generically, the risk-return profile of **momentum** strategies is a double- edged sword. On one hand, the strategy offers very attractive risk-adjusted returns, frequently outperforming those of strategies based on the market, value, or size factors. However, **momentum** strategies are highly exposed to the ‘crash’ risk, i.e., severe downside risk in rare occasions. In this dissertation, we aim to improve the implementation of a **momentum** strategy in the U.S. equity market (NYSE, NASDAQ and AMEX). With that purpose, and for the first time in the literature, we make use of information on the S&P500 index option- implied correlation of the index constituents returns. We conclude that by using the 2-month moving average of a proxy for the term structure of expected correlations across the S&P500 index constituents, implied in their option prices, it is possible to improve significantly the performance of **momentum** strategies. We denominate this strategy as Dynamic **momentum** strategy. It optimises the exposure to the upside potential of the **momentum** factor but continues to be exposed to the momentum’s crash risk. In order to manage this risk exposure, we propose another **momentum** strategy which we denominate by Hybrid **momentum** strategy, which combines the Dynamic **momentum** strategy and the Risk-managed **momentum** strategy, as proposed by Barroso and Santa-Clara (2015). This Hybrid **momentum** strategy can be implemented on real-time (i.e. only uses information available to the trader), generating returns with positive skewness and a Sharpe ratio that more than triples versus that of the plain-vanilla **momentum** strategy.

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abstract The Capital Market, in a European level, have suffered large shocks in recent years, causing major changes in reactions and in investor sentiment. Thus, the objective of this work is to understand how do markets, as well as investors react to news disclosed by companies from different sectors and different markets, in a time interval between April 22, 2010 to April 20, 2012. With a total of 24 European companies, and using daily data for the period mentioned above, we try to answer questions that explain the overreaction of investors and the **Momentum** Effect, if there are differences in the sensitivity of the investor in face of companies from different sectors and if the news have an immediate impact on investors. Centred on the literature, the analysis method is based on the study of events. From the empirical analysis provide it appears that markets react in the most positive way, but differently to news

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Segundo Cardoso e Freire (2002), o cajueiro pode ser afetado por mais de 20 doenças, sendo a maioria causada por fungos. Dentre as doenças fúngicas destacam-se a antracnose (Colletotrichum gloeosporiodes Penz.), a resinose e a podridão-preta-da-haste, ambas causadas pelo mesmo patógeno (Lasiodiplodia theobromae (Pat.) Griffon), o mofo-preto (Pelgeriella anacardii (Bat. et al.) Von Arx e Müller), a requeima (Phytophthora hevea Thompson e P. nicotiana Breda de Haan) e o oídio (Oidium anacardii Noack.) (ARAÚJO; SILVA, 1995; FREIRE et al., 2002) e, dentre as de origem bacteriana, destacam-se a mancha **angular** e a mancha de xanthomonas, ambas causadas pela bactéria Xanthomonas campestris pv. mangiferaeindicae (Patel et al.) Robbs et al. (VIANA et al., 2006a; VIANA et al., 2006b; VIANA et al., 2007).

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We propose a decision tree procedure with four steps in order to assess whether network separation is an adequate regulatory response: [1] “Is there significant market powe[r]

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de ocorrência severa destas doenças foram feitas em genótipos altamente susceptíveis. A ramulose e a mancha **angular** ocorrem com maior severidade sob condições de alta umidade, temperatura elevada e dias nublados (CASSETARI NETO & MACHADO, 2000; CIA & SALGADO, 1997), enquanto a murcha de Verticillium é mais severa sob temperaturas mais baixas, (18-22ºC), tanto em linhagens tolerantes como susceptíveis, independente do grau de agressividade do patógeno (CIA & SALGADO, 1997).

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Entre as cultivares, observou-se uma ligeira diferença, sendo a severidade levemente maior na cv. Rosinha (Figura 1B) que na cv. Carioca (Figura 1A). Como a severidade é dependente do tamanho de lesões e da freqüência de infecção, já era esperado que houvesse diferença entre as cultivares Rosinha (altamente suscetível) e Carioca (moderadamente suscetível). Verificou-se que também para a mancha **angular** a temperatura exerce efeito significativo em todas as fases do ciclo das relações patógeno-hospedeiro. Os dados obtidos neste trabalho foram semelhantes aos resultados de Bassanezi et al. (1998), que verificaram comportamento diferente entre as cultivares testadas, Carioca e Rosinha, quanto à severidade máxima observada (Tabela 1).

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the corresponding **angular** distribution, as given in Eq. (1). The templates are based on recon- structed muons, and thereby incorporate the effects of resolution, efficiency and acceptance. A template is also built for the term ( 1 + cos 2 θ ∗ ) of Eq. (1). An additional template, with shape and normalization fixed, is developed for fitting the backgrounds. A binned maximum- likelihood method with Poisson uncertainties is employed for the fit. The **angular** coefficients A 5 , A 6 , and A 7 are predicted to be very small; they are set to zero and excluded from the fit.

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