Accurate calculation of the complex eigenvalues of the Schr\"{o}dinger equation with an exponential potential

We show that the Riccati--Pad\'{e} method is suitable for the calculation of the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters

Wronskian formula for confluent second-order supersymmetric quantum mechanics

The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.Comment: 7 pages, 1 figure, to be published in Physics Letters

Formality of Donaldson submanifolds

We introduce the concept of s-formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard Lefschetz property are studied for the symplectic manifolds constructed by Donaldson with asymptotically holomorphic techniques. This study permits us to show an example of a Donaldson symplectic manifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte

Characteristic cycles and Gevrey series solutions of AA-hypergeometric systems

We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze the behavior of Gevrey solution spaces of the system.Comment: 22 page

Comment on Singularity-free Cosmological Solutions with Non-rotating Perfect Fluids

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz-Senovilla and Fernandez-Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.Comment: LaTeX, 5 page

Symbolic analysis tools-the state of the art

This paper reviews the main last generation symbolic analyzers, comparing them in terms of functionality, pointing out also their shortcomings. The state of the art in this field is also studied, pointing out directions for future research

Memory: A Self-Referential Account

This book offers a philosophical account of memory. Memory is remarkably interesting from a philosophical point of view. Our memories interact with mental states of other types in a characteristic way. They also have some associated feelings that other mental states lack. Our memories are special in terms of their representational capacity too, since we can have memories of objective events, and we can have memories of our own past experiences. Finally, our memories are epistemically special, in that beliefs formed on the basis of our memories are protected from certain errors of misidentification and justified in a way which does not rely on any cognitive capacity other than memory. The aim of the book is to explain these features of memory. It proposes that memories have a particular functional role which involves past perceptual experiences and beliefs about the past and suggests that memories have a particular content as well; they represent themselves as having a certain causal origin. The book then accounts for the feelings associated with our memories as the experience of some of the things that our memories represent; things such as our own past experiences, or the fact the memories originate in those experiences. It also accounts for the special justification for belief afforded by our memories in terms of the content that memories have. The resulting picture is a unified account of several philosophically interesting aspects of memory

Using ages and kinematic traceback: the origin of young local associations

Over the last decade, several groups of young (mainly low-mass) stars have been discovered in the solar neighbourhood (closer than ~100 pc), thanks to cross-correlation between X-ray, optical spectroscopy and kinematic data. These young local associations offer insights into the star formation process in low-density environments, shed light on the substellar domain, and could have played an important role in the recent history of the local interstellar medium. Ages estimates for these associations have been derived in the literature by several ways. In this work we have studied the kinematic evolution of young local associations and their relation to other young stellar groups and structures in the local interstellar medium, thus casting new light on recent star formation processes in the solar neighbourhood. We compiled the data published in the literature for young local associations, including the astrometric data from the new Hipparcos reduction. Using a realistic Galactic potential we integrated the orbits for these associations and the Sco-Cen complex back in time. Combining these data with the spatial structure of the Local Bubble and the spiral structure of the Galaxy, we propose a recent history of star formation in the solar neighbourhood. We suggest that both the Sco-Cen complex and young local associations originated as a result of the impact of the inner spiral arm shock wave against a giant molecular cloud. The core of the giant molecular cloud formed the Sco-Cen complex, and some small cloudlets in a halo around the giant molecular cloud formed young local associations several million years later. We also propose a supernova in young local associations a few million years ago as the most likely candidate to have reheated the Local Bubble to its present temperature.Comment: 9 pages, 5 figures. Invited talk, to appear in "The Ages of Stars", Proceedings of the IAU Symposium 258, Baltimore USA 13-17 Oct 2008, eds D. Soderblom et al., CUP in pres