Colors and Mass-to-Light Ratios of Bulges and Disks of Nearby Spiral Galaxies

We investigate colors and mass-to-light ratios ($M/L$s) of the bulges and disks for 28 nearby spiral galaxies with various morphological types of Sab to Scd, using images in optical and near-infrared ($V$, $I$, and $J$) bands and published rotation curves. It is shown that the observed colors and $M/L$s generally agree with the galaxy formation model with an exponentially declining star formation rate and shallow slope (ex. Scalo) initial mass function (IMF) for both the bulges and the disks. We find that the bulge $M/L$ is generally higher than the disk $M/L$ and that the galaxies with larger bulge-to-total luminosity ratio tend to have a smaller bulge $M/L$. The fact indicates that the luminosity-weighted average age of bulges for early-type spirals is younger than that of later-type spirals. These results support a formation scenario that produces young stars for the bulges of middle-type and early-type spirals.Comment: 33 pages, 24 figures, PASJ accepte

Generation of continuous-wave broadband Einstein-Podolsky-Rosen beams using periodically-poled lithium niobate waveguides

Continuous-wave light beams with broadband Einstein-Podolsky-Rosen correlation (Einstein-Podolsky-Rosen beams) are created with two independent squeezed vacua generated by two periodically-poled lithium niobate waveguides and a half beam splitter.Comment: 4 pages, 3 figure

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from "quasi-normal" modes of the self-similar system as well as "high-frequency" waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation, and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.Comment: 20 pages, 7 figures, references added to match the published versio

Uniform hyperbolicity of a class of scattering maps

In recent years fractal Weyl laws and related quantum eigenfunction hypothesis have been studied in a plethora of numerical model systems, called quantum maps. In some models studied there one can easily prove uniform hyperbolicity. Yet, a numerically sound method for computing quantum resonance states, did not exist. To address this challenge, we recently introduced a new class of quantum maps. For these quantum maps, we showed that, quantum resonance states can numerically be computed using theoretically grounded methods such as complex scaling or weak absorbing potentials. However, proving uniform hyperbolicty for this class of quantum maps was not straight forward. Going beyond that work this article generalizes the class of scattering maps and provides mathematical proofs for their uniform hyperbolicity. In particular, we show that the suggested class of two-dimensional symplectic scattering maps satisfies the topological horseshoe condition and uniform hyperbolicity. In order to prove these properties, we follow the procedure developed in the paper by Devaney and Nitecki. Specifically, uniform hyperbolicity is shown by identifying a proper region in which the non-wandering set satisfies a sufficient condition to have the so-called sector bundle or cone field. Since no quantum map is known where both a proof of uniform hyperbolicity and a methodologically sound method for numerically computing quantum resonance states exist simultaneously, the present result should be valuable to further test fractal Weyl laws and related topics such as chaotic eigenfunction hypothesis.Comment: 50 pages, 23 figure

Risco de crédito e alocação ótima para uma carteira de debêntures

A debênture vem se tornando um instrumento de captação cada vez mais importante para empresas não financeiras no mercado brasileiro e uma alternativa às elevadas taxas de juros cobradas pelos bancos comerciais em uma operação de financiamento. Um aspecto-chave para o desenvolvimento do mercado secundário deste instrumento é o correto tratamento do risco de crédito, que ocorre quando o emissor não cumpre suas obrigações contratuais. Este trabalho propõe e testa uma metodologia que determina a magnitude deste risco para uma carteira de debêntures de empresas emissoras brasileiras. A abordagem utilizada baseia-se no Modelo de Merton (1974) para bônus corporativos, que utiliza as fórmulas de Black-Scholes para o cálculo do preço de opções. Também são utilizadas técnicas de otimização para a determinação do risco da carteira. Adotando um modelo simples e de baixo custo computacional, chegamos a uma medida de risco mais conservadora do que a obtida com o tradicional modelo VaR (value at risk). Além disso, apresentamos uma metodologia para a obtenção da composição ótima da carteira de debêntures.The debenture (corporate bond) is considered a fantastic financial instrument in terms of funding for the non-financial firms in the Brazilian market. The intermediation would be done in the capital market instead of through the commercial banks. The key issue for the development of this market is the financial engineering involving the credit risk (chance that the corporate issuer can default on its debt obligation). This paper proposes and tests a methodology to quantify this risk in a cross-section of Brazilian debentures. Our approach is based on Merton’s (1974) asset pricing model that uses the Black-Schole’s put option formula. The consequent optimization techniques allow us to infer the risk of debentures. By using a simple and low-cost model, we find a risk measure that is more conservative than the usual VaR (value at risk). Thus, we present a methodology for obtaining the optimum portfolio composed of debentures subject to the default risk