The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved

We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.Comment: 10 pages, 5 figure

Short-range nuclear effects on axion emissivities by nucleon-nucleon bremsstrahlung

The rates of axion emission by nucleon-nucleon (NN) bremsstrahlung are reconsidered by taking into account the NN short range correlations. The analytical formulas for the neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) processes with the inclusion of the full momentum dependence of an one- and two- pion exchange nuclear potentials, in the non-degenerate limit, are explicitly given. We find that the two-pion exchange (short range) effects can give a significant contribution to the emission rates, and are temperature dependent. Other short range nuclear effects like effective nucleon mass, polarization effects and use of correlated wave functions, are discused as well. The trend of all these nuclear effects is to diminish the corresponding axion emission rates. Further, we estimate that the values of the emission rates calculated with the inclusion of all these effects can differ from the corresponding ones derived with constant nuclear matrix elements by a factor of $\sim 24$. This leads to an uncertainty factor of $\sim 4.9$ when extracting bounds of the axion parametersComment: 11 pages, 4 figure

No-Core shell model for A = 47 and A = 49

We apply an {\it ab-initio} approach to the nuclear structure of odd-mass nuclei straddling $^{48}Ca$. Starting with the NN interaction, that fits two-body scattering and bound state data we evaluate the nuclear properties of $A = 47$ and $A = 49$ nuclei in a no-core approach. Due to model space limitations and the absence of 3-body interactions, we incorporate phenomenological terms determined by fits to $A = 48$ nuclei in a previous effort. Our modified Hamiltonian produces reasonable spectra for these odd mass nuclei. In addition to the differences in single-particle basis states, the absence of a single-particle Hamiltonian in our no-core approach obscures direct comparisons with valence effective NN interactions. Nevertheless, we compare the fp-shell matrix elements of our initial and modified Hamiltonians in the harmonic oscillator basis with a recent model fp-shell interaction, the GXPF1 interaction of Honma, Otsuka, Brown and Mizusaki. Notable differences emerge from these comparisons. In particular, our diagonal two-body $T = 0$ matrix elements are, on average, about 800-900keV more attractive. Furthermore, while our initial and modified NN Hamiltonian fp-shell matrix elements are strongly correlated, there is much less correlation with the GXPF1 matrix elements.Comment: 17 pages including 14 figure

Model Order Selection Rules For Covariance Structure Classification

The adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper. This represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties. The considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of Model Order Selection (MOS) is exploited to devise suitable decision rules. Several MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed. At the analysis stage, illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules