A new approach to the asymptotics for Sobolev orthogonal polynomials

In this paper we deal with polynomials orthogonal with respect to an inner product involving derivatives, that is, a Sobolev inner product. Indeed, we consider Sobolev type polynomials which are orthogonal with respect to $$(f,g)=\int fg d\mu +\sum_{i=0}^r M_i f^{(i)}(0) g^{(i)}(0), \quad M_i \ge 0,$$ where $\mu$ is a certain probability measure with unbounded support. For these polynomials, we obtain the relative asymptotics with respect to orthogonal polynomials related to $\mu$, Mehler--Heine type asymptotics and their consequences about the asymptotic behaviour of the zeros. To establish these results we use a new approach different from the methods used in the literature up to now. The development of this technique is highly motivated by the fact that the methods used when $\mu$ is bounded do not work.Comment: 31 page

Neutral and charged pion production in the S-matrix approach

The S-matrix approach is applied to charged and neutral pion production in pp collisions, in which the spin/isospin channels filter differently the rescattering mechanism. The chiral perturbation theory rescattering amplitude is employed. The contributions from the single-nucleon, Z-diagrams and Delta-isobar mechanisms are also included. For the reactions investigated, the convergence of the partial wave series is quite satisfactory and J=0 is enough to describe the data close to threshold.Comment: To appear in the proceedings of the 6th International Conference on Nuclear Physics at Storage Rings (STORI'05), Julich - Bonn, Germany, 23-26 May 200

Short-range three-nucleon forces and low-energy constants

The 3N forces due to pi-rho, pi-sigma and pi-omega exchanges following from the nucleon Born diagrams and diagrams with an intermediate N^{*}(1440) are re-analyzed. The cancellation between pi-sigma and pi-omega forces is rather sensitive to the values of the coupling constants and to the form of the piNN vertex. Experimental uncertainties in the parameters of the TM pi-pi potential are assessed. They lead to uncertainties in theoretical predictions of the triton binding energy of about 0.4 MeV. The low-energy limit of pi-sigma and pi-omega potentials is performed. It defines the coupling constants of effective contact piNNNN vertices, which are compared with the corresponding contact vertices of Chiral Perturbation Theory.Comment: 41 pages, 3 figures (4 *.eps files

Pion re-scattering operator in the S-matrix approach

The pion re-scattering operator for pion production, derived recently in time-ordered perturbation theory, is compared with the one following from the simple S-matrix construction. We show that this construction is equivalent to the on-shell approximation introduced in previous papers. For a realistic NN interaction, the S-matrix approach, and its simplified fixed threshold-kinematics version, work well near threshold.Comment: 17 pages, 7 figure

Three-dimensional angular momentum projected relativistic point-coupling approach for the low-lying excited states in 24^{24}Mg

A full three-dimensional angular momentum projection on top of a triaxial relativistic mean-Geld calculation is implemented for the first time. The underlying Lagrangian is a point coupling model and pairing correlations are taken into account by a monopole force. This method is applied for the low-lying excited states in 24Mg. Good agreement with the experimental data is found for the ground state properties. A minimum in the potential energy surface for the 2+ state, with beta = 0.55, gamma = 10 deg, is used as the basis to investigate the rotational energy spectrum as well as the corresponding B(E2) transition probabilities as compared to the available data.Comment: 10 pages, 5 figure

Aspects of the T-duality construction for the Supermembrane theory

In this note we explicitly show how the generalization of the T-duality symmetry of the supermembrane theory compactified in M9xT2 can be reduced to a parabolic subgroup of SL(2,Z) that acts non-linearly on the moduli parameters and on the KK and winding charges of the supermembrane. This is a first step towards a deeper understanding of the dual relation between the parabolic type II gauged supergravity in nine dimensions.Comment: 6 pages, Latex, Proceedings for the XIX Simposio Chileno de Fisica, SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chil

T-duality Invariance of the Supermembrane

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in the limit when the torus degenerate into a circle and the M2 mass operator restricts to the string-like configurations, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered. Moreover if we just restrict M2 mass operator to string-like configurations but we perform a generalized T-duality we find the SL(2,Z) non-perturbative multiplet of IIA.Comment: 8pages, Latex. Proceeding of the XXI International Workshop on Geometry and Physics held at U.Burgos, Spai

Characterizing the variability of Melotte 111 AV 1224: a new variable star in the Coma Berenices open cluster

A search for new pulsating stars in the Coma Berenices open cluster was carried out. As a result of this search the cluster member Melotte 111 AV 1224 presented clear indications of photometric variability. In order to determine its physical parameters Str\"omgren standard indices and low-resolution spectra were acquired. In this work we present the preliminary results of these observations.Comment: To be published in conference proceedings of IAU Symposium 301: Precision Asteroseismology, held in Wroclaw, Poland, August 201

Charged and neutral pion production in the S-matrix approach

The S-matrix approach is used to calculate charged as well as neutral pion production reactions from NN scattering, with the same set of underlying processes and interactions. The chiral perturbation theory piN scattering amplitude is used. For the nucleon-nucleon distortions a newly developed realistic potential within the Bonn family of potentials, valid well above the pion production threshold, is considered. In the pi+ production case, the NN potential, the piN relative p-waves and the treatment of the exchanged pion energy build up the observed cross-section strength.Comment: 8 pages, 5 figure

Searching for short-period variable stars in the direction of Coma Berenices and Upgren 1 open clusters: Melotte 111 AV 1224 a new eclipsing binary star

We report the results of CCD photometric observations in the direction of the Coma Berenices and Upgren 1 open clusters with the aim at searching for new short-period variable stars. A total of 35 stars were checked for variability. As a result of this search the star designated in the SIMBAD database as Melotte 111 AV 1224 was found to be a new eclipsing binary star. Follow-up Str\"omgren photometric and spectroscopic observations allowed us to derive the spectral type, distance, reddening and effective temperature of the star. A preliminary analysis of the binary light curve was performed and the parameters of the orbital system were derived. From the derived physical parameters we conclude that Melotte 111 AV 1224 is most likely a W UMa eclipsing binary that is not a member of the Coma Berenices open cluster. On other hand, we did not find evidence of brightness variations in the stars NSV 5612 and NSV 5615 previously catalogued as variable stars in Coma Berenices open cluster.Comment: 9 pages, 9 figures, 4 tables, accepted for publication in New Astronom