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In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen as a generalization of the so-called projective Reed-Muller codes. We calculate the length and the dimension of such codes, a lower bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed-Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes.

We study the asymptotic properties of a class of multiple orthogonal polynomials with respect to a Nikishin system generated by two measures $(\sigma_1, \sigma_2)$ with unbounded supports (${supp}(\sigma_1) \subset \mathbb{R}_+$, ${supp}(\sigma_2) \subset \mathbb{R}_-$), and such that the second measure $\sigma_2$ is discrete. The weak asymptotics for these polynomials was obtained previously by V. Sorokin. We use his result and the Riemann-Hilbert analysis to derive the strong asymptotics of these polynomials and of the reproducing kernel., Comment: 38 pages, 7 figures

We study the convergence of type I Hermite-Pad\'e approximation for a class of meromorphic functions obtained by adding a vector of rational functions with real coefficients to a Nikishin system of functions., Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1307.0213

We consider multiple orthogonal polynomials with respect to Nikishin systems generated by two measures $(\sigma_1, \sigma_2)$ with unbounded supports ($\mbox{supp} \, \sigma_1 \subseteq \mathbb{R}_+$, $\mbox{supp} \, \sigma_2 \subseteq \,\mathbb{R}_-$) and $\sigma_2$ is discrete. A Nikishin type equilibrium problem in the presence of an external field acting on $\mathbb{R}_+$ and a constraint on $ \mathbb{R}_-$ is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials., Comment: 47 pages, 1 figure

The description of the VV'P form factors (V,V' stands for vector particles and P for a pseudoscalar meson) for different particles virtualities remains a challenge for the theory of strong interactions. While their chiral limit is well understood, recent measurements of the gamma^* omega pi^0 and gamma^* gamma pi^0 form factors at high photon virtualities seem to depart from the simplest scaling behavior suggested by QCD. Here we attempt to describe them in their whole measured energy regimes within the Resonance Chiral Theory, a framework which naturally incorporates the chiral limit constraints and extends to higher energies by including the resonances as active fields. Specifically, we obtained an accurate description of the data up to 2 GeV on the former form factor by including three multiplets of vector resonances. Good agreement with measurements of the latter was possible even in the single resonance approximation, although we propose to measure the e^+e^- to mu^+mu^-pi^0 cross-section and di-muon invariant mass distribution to better characterize this form factor. We have then evaluated the pion exchange contribution to the muon g-2 obtaining (6.66\pm0.21)x10^{-10} with an accurate determination of the errors. We have also recalled that approximating the whole pion exchange by the pion pole contribution underestimates the corresponding result for the anomaly (by (15,20)%). Based on these results, we have predicted the eta^(\prime) transition form factors obtaining good agreement with data and obtained their respective contributions to the muon anomaly. In this way, the contribution of the three lightest pseudoscalars to it yields (10.47\pm0.54)x10^{-10}, in agreement with previous evaluations but with smaller error., Comment: 43 pages, 11 figures and 6 tables. v2: Minor changes to match version to be published in PRD

Nowadays, software artifacts are ubiquitous in our lives being an essential part of home appliances, cars, cell phones, and even in more critical activities like aeronautics and health sciences. In this context software failures may produce enormous losses, either economical or, in the worst case, in human lives. Software analysis is an area in software engineering concerned with the application of diverse techniques in order to prove the absence of errors in software pieces. In many cases different analysis techniques are applied by following specific methodological combinations that ensure better results. These interactions between tools are usually carried out at the user level and it is not supported by the tools. In this work we present HeteroGenius, a framework conceived to develop tools that allow users to perform hybrid analysis of heterogeneous software specifications. HeteroGenius was designed prioritising the possibility of adding new specification languages and analysis tools and enabling a synergic relation of the techniques under a graphical interface satisfying several well-known usability enhancement criteria. As a case-study we implemented the functionality of Dynamite on top of HeteroGenius., Comment: In Proceedings LAFM 2013, arXiv:1401.0564

The $N \to \Delta$ weak vertex provides an important contribution to the one pion production in neutrino-nucleon and neutrino-nucleus scattering for $\pi N$ invariant masses below 1.4 GeV. Beyond its interest as a tool in neutrino detection and their background analyses, one pion production in neutrino-nucleon scattering is useful to test predictions based on the quark model and other internal symmetries of strong interactions. Here we try to establish a connection between two commonly used parametrizations of the weak $N \to \Delta$ vertex and form factors (FF) and we study their effects on the determination of the axial coupling $C_5^A(0)$, the common normalization of the axial FF, which is predicted to hold 1.2 by using the PCAC hypothesis. Predictions for the $\nu_{\mu} p \to \mu^- p\pi^+$ total cross sections within the two approaches, which include the resonant $\Delta^{++}$ and other background contributions in a coherent way, are compared to experimental data., Comment: Submitted to Physics Letters B

We study the convergence of sequences of type I and type II Hermite-Pad\'e approximants for certain systems of meromorphic functions made up of rational modifications of Nikishin systems of functions.

Pad\'e approximation has two natural extensions to vector rational approximation through the so called type I and type II Hermite-Pad\'e approximants. The convergence properties of type II Hermite-Pad\'e approximants have been studied. For such approximants Markov and Stieltjes type theorems are available. To the present, such results have not been obtained for type I approximants. In this paper, we provide Markov and Stieltjes type theorems on the convergence of type I Hermite-Pad\'e approximants for Nikishin systems of functions., Comment: 20 pages

In this Technical Design Report (TDR) we describe the SuperB detector that was to be installed on the SuperB e+e- high luminosity collider. The SuperB asymmetric collider, which was to be constructed on the Tor Vergata campus near the INFN Frascati National Laboratory, was designed to operate both at the Upsilon(4S) center-of-mass energy with a luminosity of 10^{36} cm^{-2}s^{-1} and at the tau/charm production threshold with a luminosity of 10^{35} cm^{-2}s^{-1}. This high luminosity, producing a data sample about a factor 100 larger than present B Factories, would allow investigation of new physics effects in rare decays, CP Violation and Lepton Flavour Violation. This document details the detector design presented in the Conceptual Design Report (CDR) in 2007. The R&D and engineering studies performed to arrive at the full detector design are described, and an updated cost estimate is presented. A combination of a more realistic cost estimates and the unavailability of funds due of the global economic climate led to a formal cancelation of the project on Nov 27, 2012., Comment: 495 pages

We carry out a detailed study of the branching fractions and lepton pair invariant-mass spectrum of \tau^- ->\pi^- \nu_\tau l^+l^- decays (l=e,\mu). In addition to the model-independent (QED) contributions, we include the structure-dependent (SD) terms, which encode information on the hadronization of QCD currents. The form factors describing the SD contributions are evaluated by supplementing Chiral Perturbation Theory with the inclusion of the lightest multiplet of spin-one resonances as active degrees of freedom. The Lagrangian couplings have been determined demanding the known QCD short-distance behaviour to the relevant Green functions and associated form factors in the limit where the number of colours goes to infinity. As a result, we predict BR(\tau^- ->\pi^-\nu_\tau e^+e^-)= (1.7^{+1.1}_{-0.3})x10^{-5} and BR(\tau^- -> \pi^-\nu_\tau \mu^+\mu^-) = [0.03,1.0]x10^{-5}. According to this, the first decay could be measured in the near future, which is not granted for the second one., Comment: 18 pages, 6 figures. It matches version accepted for publication in PRD

Starting from the orthogonal polynomial expansion of a function $F$ corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Pad\'{e}-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of $F.$ Thereby, we obtain analogues of the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin., Comment: 26 pages

An empirical formula relating the physical masses of elementary particles and the Fermi constant is proposed. Although no mechanism or theoretical model behind this formula is advocated, we seek for a possible physical interpretation. If not a simple numerical coincidence, this formula may motivate theorists to search for relations among the different sectors of the Electroweak Standard model., Comment: 2 pages

The study of neutrinoless double beta decays of nuclei and hyperons require the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units \Delta Q=2 . Using a low energy effective Lagrangian that induces these transitions, we compute these hadronic matrix elements in the framework of the MIT bag model. As an illustrative example we evaluate the amplitude and transition rate of \Sigma- -> p e- e-, a decay process that violates lepton number by two units (\Delta L=2). The relevant matrix element is evaluated without assuming the usual factorization approximation of the four-quark operators and the results obtained in both approaches are compared., Comment: 13 pages, 2 .eps figures

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided., Comment: 27 pages

We consider row sequences of simultaneous rational approximations constructed in terms of Fourier expansions and prove a Montessus de Ballore type theorem., Comment: 16 pages

We give a Montessus de Ballore type theorem for row sequences of Hermite-Pad\'e approximations of vector valued analytic functions refining some results in this direction due to P.R. Graves-Morris and E.B. Saff. We do this introducing the notion of incomplete Pad\'e approximation which contains, in particular, simultaneous Pad\'e approximation and may be applied in the study of other systems of approximants as well., Comment: 20 pages

Lepton number violation (LNV) can be induced by Majorana neutrinos in four-body decays of the neutral B meson and the top quark. We study the effects of Majorana neutrinos in these |\Delta L|=2 decays in an scenario where a single heavy neutrino can enhance the amplitude via the resonant mechanism. Using current bounds on heavy neutrino mixings, the most optimistic branching ratios turn out to be at the level of 10^{-6} for \bar{B} -> D^+e^-e^-\pi^+ and t -> bl^+l^+W^- decays. Searches for these LNV decays at future facilities can provide complementary constraints on masses and mixings of Majorana neutrinos., Comment: 15 pages, 6 figures, "Added comments on sensitivities. Version accepted for publication"

Light tensor mesons (T = a_2, f_2 and K_2^*) can be produced in decays of tau leptons. In this paper we compute the branching ratios of tau --> T pi nu decays by assuming the dominance of intermediate virtual states to model the form factors involved in the relevant hadronic matrix element. The exclusive f_2(1270) pi^- decay mode turns out to have the largest branching ratio, of O(10^-4) . Our results indicate that the contributions of tensor meson intermediate states to the three-pseudoscalar channels of tau decays are rather small., Comment: 10 pages, 1 figure. Version accepted for publication in PRD, some typos are corrected and comments are added in section 4. Conclusions remain unchanged

K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Pad\'{e} approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and non-intersecting consecutive supports contained on the real line, are perfect. Here, we prove that they are also perfect when the supports of the generating measures are unbounded or touch at one point. As an application, we give a version of Stieltjes' theorem in the context of simultaneous Hermite-Pad\'e approximation., Comment: 26 pages

We present kinematic data for 211 bright planetary nebulae in eleven Local Group galaxies: M31 (137 PNe), M32 (13), M33 (33), Fornax (1), Sagittarius (3), NGC 147 (2), NGC 185 (5), NGC 205 (9), NGC 6822 (5), Leo A (1), and Sextans A (1). The data were acquired at the Observatorio Astron\'omico Nacional in the Sierra de San Pedro M\'artir using the 2.1m telescope and the Manchester Echelle Spectrometer in the light of [\ion{O}{3}]$\lambda$5007 at a resolution of 11 km/s. A few objects were observed in H$\alpha$. The internal kinematics of bright planetary nebulae do not depend strongly upon the metallicity or age of their progenitor stellar populations, though small systematic differences exist. The nebular kinematics and H$\beta$ luminosity require that the nebular shells be accelerated during the early evolution of their central stars. Thus, kinematics provides an additional argument favoring similar stellar progenitors for bright planetary nebulae in all galaxies., Comment: Accepted for publication in the October 2010 issue of the Revista Mexicana de Astronom\'ia y Astrof\'isica

We describe some recent results on isospin breaking corrections which are of relevance for predictions of the leading order hadronic contribution to the muon anomalous magnetic moment (amuhadLO) when using tau lepton data. When these corrections are applied to the new combined data on the pi^+pi^0 spectral function, the prediction for amuhadLO based on tau lepton data gets closer to the one obtained using e^+e^- data., Comment: 6 pages, 3 figures, Proceedings of the PhiPsi09 Workshop, Oct. 13-16, 2009, Beijing, China. Some typos corrected, and the FSR correction used in a previous work is added to Table 1

K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite-Pade approximation of analytic functions. We prove that Nikishin systems are perfect providing, by far, the largest class of systems of functions for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov's theorem to simultaneous Hermite-Pade approximation, a general result on the convergence of simultaneous quadrature rules of Gauss-Jacobi type, the logarithmic asymptotics of general sequences of multiple orthogonal polynomials, and an extension of the Denisov-Rakhmanov theorem for the ratio asymptotics of mixed type multiple orthogonal polynomials., Comment: 39 pages

Observing charge-parity (CP) or time-reversal (T) violations in the leptonic sector will give useful information to elucidate the nature of neutrinos. CP-violating couplings in charged leptonic currents carry out the weak phases necessary to break these symmetries. Here we study the interference of $W^{\pm}$ and $H^{\pm}$ bosons mediated amplitudes as the origin of possible CP and T violation in semileptonic decays of $K^{\pm}$ mesons and $\tau^{\pm}$ leptons. We use the experimental bound on the T-odd transverse polarization asymmetry in $K^+_{\mu 3}$ decays to predict an upper limit on the CP violating effects in $\tau \to K \pi \nu$ decays. In the framework of this model with scalar-mediated interactions, we find that current limits on the former process indicate that the CP violating effects in the latter are much smaller than the limits reported so far., Comment: 9 pages, 2 figures

We revisit the procedure for comparing the pi pi spectral function measured in tau decays to that obtained in e+e- annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the tau- --> pi- pi0 nu_tau branching fraction measurement and its prediction using the isospin-breaking-corrected e+e- --> pi+pi- spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g-2 using e+e- and tau data with the new corrections, and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement., Comment: 10 pages, 6 figures, submitted to Eur. Phys. J. C; (v2): Revised version with improved and uniform treatment of tau and e+e- data with HVPTools and a few minor bug fixes; (v3): Final version accepted for publication

We find formulas for the birational maps from a Kummer surface K and its dual K^* to their common minimal desingularization S. We show how the nodes of K blow up. Then we give a description of the group of linear automorphisms of S., Comment: 22 pages

We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an associated vector valued equilibrium problem for the logarithmic potential. The ratio asymptotic is described by means of a conformal representation of an appropriate Riemann surface of genus zero onto the extended complex plane., Comment: 46 pages

Current predictions for the ratio of phi -> K^+K^-/K_LK_S decay rates exceed the corresponding experimental value in about five standard deviations. By far, the dominant sources of isospin breaking to this ratio are the phase-space (52%) and the electromagnetic radiative (4.3%, computed within scalar QED) corrections. Here we estimate the effects of the electromagnetic structure of kaons and other model-dependent contributions into the radiative corrections., Comment: 8 pages, Latex, 2 .eps figures

The \tau -> (\omega, \phi)P^-\nu decays, where P^-=\pi^-, K^-, are considered within a phenomenological model with dominance of meson intermediate states. We assume SU(3) flavor symmetry to fix some of the unknown strong interaction couplings. Our predictions for the \tau -> \phi (\pi^-, K^-)\nu branching fractions are in good agreement with recent measurements of the BABAR and BELLE Collaborations., Comment: 15 pages, 3 figures

We compute the rates of semileptonic B_A \to B_Bl^-l^- (l=e or \mu) hyperon transitions in a model where intermediate states involve loops of baryons and a Majorana neutrino. These rates turn out to be well below present experimental bounds and other theoretical estimates. From the experimental upper limit on the \Xi^- \to p\mu^-\mu^- decay, we derive the bound < 22 TeV for the effective Majorana mass of the muon neutrino. Also, an estimate of background contributions for these decays due to the allowed B_A \to B_Bl^-l^-\bar{\nu}\bar{\nu} decays are provided., Comment: 10 pages, 1 figure

We compute the difference in decay widths of charged and neutral \rho(770) vector mesons. The isospin breaking arising from mass differences of neutral and charged \pi and \rho mesons, radiative corrections to \rho -> \pi\pi, and the \rho -> \pi\pi\gamma decays are taken into account. It is found that the width difference \Delta \Gamma_rho is very sensitive ot the isospin breaking in the $\rho$ meson mass \Delta m_\rho. This result can be useful to test the correlations observed between the values of these parameters extracted from experimental data., Comment: 16 pages, 4 figures

Based on the description of unstable $K_{L,S}$ particles in quantum field theory (QFT), we compute the time-dependent probabilities for transitions between asymptotic states in $\tau^{\pm} \to [\pi^+\pi^-]_K\pi^{\pm}\nu$ decays, where the pair $[\pi^+\pi^-]_K$ is the product of (intermediate state) neutral kaon decays. Then we propose a definition of $\tau$ decays into $K_L$ and $K_S$ states, which reflects into the cancellation between their CP rate asymmetries, thus solving in a natural way the paradox pointed out previously in litterature. Since our definition of $K_{L,S}$ final states in $\tau$ decays is motivated on experimental grounds, our predictions for the integrated CP rate asymmetries can be tested in a dedicated experiment., Comment: 4 pages, 1 figure

The long-distance electromagnetic radiative corrections to tau- -> pi- pi0 nu are re-evaluated. A meson dominance model is used to describe the emission of real photons in this decay. Results obtained for the hadronic spectrum and the decay rate in photon inclusive reactions are compared with previous calculations based on the chiral resonance theory. Independent tests in tau -> pi pi nu gamma that can help to validate the predictions of one of the two models are briefly discussed., Comment: 5 pages, 4 figures, talk given by GLC at the 9th International Workshop on Tau Lepton Physics, Pisa (Italy), september 2006