Why does the recently proposed simple empirical formula for the lowest excitation energies work so well?

It has recently been shown that a simple empirical formula, in terms of the mass number and the valence nucleon numbers, is able to describe the main trends of the lowest excitation energies of the natural parity even multipole states up to $10^+$ in even-even nuclei throughout the entire periodic table. In an effort to understand why such a simple formula is so capable, we investigate the possibility of associating each term of the empirical formula with the specific part of the measured excitation energy graph.Comment: 9 pages, 3 figure

Spin-dependent empirical formula for the lowest excitation energies of the natural parity states in even-even nuclei

We present an empirical expression which holds for the lowest excitation energy of the natural parity states in even-even nuclei throughout the entire periodic table. This formula contains spin-dependent factors so that it is applied to different multipole states with the same model parameters in contrast to the recently proposed empirical expression where the model parameters had to be fitted for each multipole separately.Comment: 9 pages, 5 figure

A loss function approach to model specification testing and its relative efficiency

The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable nonparametric inference procedure. In this paper, we show that although it inherits many advantages of the parametric maximum likelihood ratio (LR) test, the GLR test does not have the optimal power property. We propose a generally applicable test based on loss functions, which measure discrepancies between the null and nonparametric alternative models and are more relevant to decision-making under uncertainty. The new test is asymptotically more powerful than the GLR test in terms of Pitman's efficiency criterion. This efficiency gain holds no matter what smoothing parameter and kernel function are used and even when the true likelihood function is available for the GLR test.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1099 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

UV Upturn in Elliptical Galaxies: Theory

The UV upturn is the rising flux with decreasing wavelength between the Lyman limit and 2500\AA found virtually in all bright spheroidal galaxies. It has been a mystery ever since it was first detected by the OAO-2 space telescope (Code & Welch 1979) because such old metal-rich populations were not expected to contain any substantial number of hot stars. It was confirmed by following space missions, ANS (de Boer 1982), IUE (Bertola et al. 1982) and HUT (Brown et al. 1997). The positive correlation between the UV-to-optical colour (i.e., the strength of the UV upturn) and the Mg2 line strength found by Burstein et al. (1987) through IUE observations has urged theorists to construct novel scenarios in which metal-rich ($\gtrsim Z_{\odot}$) old ($\gtrsim$ a few Gyr) stars become UV bright (Greggio & Renzini 1990; Horch et al. 1992). Also interesting was to find using HUT that, regardless of the UV strength, the UV spectral slopes at 1000--2000\AA in the six UV bright galaxies were nearly identical suggesting a very small range of temperatures of the UV sources in these galaxies (Brown et al. 1997), which corresponds to $T_{\rm eff} \approx 20,000 \pm 3,000$ K. This, together with other evidence, effectively ruled out young stars as the main driver of the UV upturn. A good review on the observational side of the story is given in the next article by Tom Brown, as well as in the recent articles of Greggio & Renzini (1999) and O'Connell (1999).Comment: 6 figures; belated paper from Keele Conferenc