An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.Comment: LaTex, 22 page

Neural networks and spectra feature selection for retrival of hot gases temperature profiles

Proceeding of: International Conference on Computational Intelligence for Modelling, Control and Automation, 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, Vienna, Austria 28-30 Nov. 2005Neural networks appear to be a promising tool to solve the so-called inverse problems focused to obtain a retrieval of certain physical properties related to the radiative transference of energy. In this paper the capability of neural networks to retrieve the temperature profile in a combustion environment is proposed. Temperature profile retrieval will be obtained from the measurement of the spectral distribution of energy radiated by the hot gases (combustion products) at wavelengths corresponding to the infrared region. High spectral resolution is usually needed to gain a certain accuracy in the retrieval process. However, this great amount of information makes mandatory a reduction of the dimensionality of the problem. In this sense a careful selection of wavelengths in the spectrum must be performed. With this purpose principal component analysis technique is used to automatically determine those wavelengths in the spectrum that carry relevant information on temperature distribution. A multilayer perceptron will be trained with the different energies associated to the selected wavelengths. The results presented show that multilayer perceptron combined with principal component analysis is a suitable alternative in this field.Publicad

Faint emission lines in the Galactic H II regions M16, M20 and NGC 3603

We present deep echelle spectrophotometry of the Galactic {\hii} regions M16, M20 and NGC 3603. The data have been taken with the Very Large Telescope Ultraviolet-Visual Echelle Spectrograph in the 3100 to 10400 \AA range. We have detected more than 200 emission lines in each region. Physical conditions have been derived using different continuum and line intensity ratios. We have derived He$^{+}$, C$^{++}$ and O$^{++}$ abundances from pure recombination lines as well as abundances from collisionally excited lines for a large number of ions of different elements. We have obtained consistent estimations of the temperature fluctuation parameter, {\ts}, using different methods. We also report the detection of deuterium Balmer lines up to D$\delta$ (M16) and to D$\gamma$ (M20) in the blue wings of the hydrogen lines, which excitation mechanism seems to be continuum fluorescence. The temperature fluctuations paradigm agree with the results obtained from optical CELs and the more uncertain ones from far IR fine structure CELs in NGC 3603, although, more observations covering the same volume of the nebula are necessary to obtain solid conclusions.Comment: 22 pages, 13 Tables, 7 Figures. Accepted for publication by MNRA

On the abundance discrepancy problem in HII regions

The origin of the abundance discrepancy is one of the key problems in the physics of photoionized nebula. In this work, we analize and discuss data for a sample of Galactic and extragalactic HII regions where this abundance discrepancy has been determined. We find that the abundance discrepancy factor (ADF) is fairly constant and of the order of 2 in all the available sample of HII regions. This is a rather different behaviour than that observed in planetary nebulae, where the ADF shows a much wider range of values. We do not find correlations between the ADF and the O/H, O++/H+ ratios, the ionization degree, Te(High), Te(Low)/ Te(High), FWHM, and the effective temperature of the main ionizing stars within the observational uncertainties. These results indicate that whatever mechanism is producing the abundance discrepancy in HII regions it does not substantially depend on those nebular parameters. On the contrary, the ADF seems to be slightly dependent on the excitation energy, a fact that is consistent with the predictions of the classical temperature fluctuations paradigm. Finally, we obtain that Te values obtained from OII recombination lines in HII regions are in agreement with those obtained from collisionally excited line ratios, a behaviour that is again different from that observed in planetary nebulae. These similar temperature determinations are in contradiction with the predictions of the model based on the presence of chemically inhomogeneous clumps but are consistent with the temperature fluctuations paradigm. We conclude that all the indications suggest that the physical mechanism responsible of the abundance discrepancy in HII regions and planetary nebulae are different.Comment: 14 pages, 8 figures, 9 tables. Accepted for publication in the Ap