Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page

KamLAND and Solar Antineutrino Spectrum

We use the recent KamLAND observations to predict the solar antineutrino spectrum at some confidence limits. We find that a scaling of the antineutrino probability with respect to the magnetic field profile --in the sense that the same probability function can be reproduced by any profile with a suitable peak field value-- can be utilised to obtain a general shape of the solar antineutrino spectrum. This scaling and the upper bound on the solar antineutrino event rate, that can be derived from the data, lead to: 1) an upper bound on the solar antineutrino flux, 2) the prediction of their energy spectrum, as the normalisation of the spectrum can be obtained from the total number of antineutrino events recorded in the experiment. We get $\phi_{\bar\nu}<3.8\times 10^{-3}\phi(^8B)$ or $\phi_{\bar\nu} <5.5\times 10^{-3}\phi(^8B)$ at 95% CL, assuming Gaussian or Poissonian statistics, respectively. And for 90% CL these become $\phi_{\bar\nu}<3.4 \times 10^{-3}\phi(^8B)$ and $\phi_{\bar\nu}<4.9\times 10^{-3}\phi(^8B)$. It shows an improvement by a factor of 3-5 with respect to existing bounds. These limits are quite general and independent of the detailed structure of the magnetic field in the solar interior.Comment: Based on talk given at NANP'03, JINR Dubna, Russia, June 2003. To be published in "Physics of Atomic Nuclie

Muon anomalous magnetic moment in supersymmetric scenarios with an intermediate scale and nonuniversality

We analyze the anomalous magnetic moment of the muon (a_{\mu}) in supersymmetric scenarios. First we concentrate on scenarios with universal soft terms. We find that a moderate increase of a_{\mu} can be obtained by lowering the unification scale M_{GUT} to intermediate values 10^{10-12} GeV. However, large values of \tan \beta are still favored. Then we study the case of non-universal soft terms. For the usual value M_{GUT}~10^{16} GeV, we obtain a_{\mu} in the favored experimental range even for moderate \tan \beta regions \tan\beta ~ 5$. Finally, we give an explicit example of these scenarios. In particular, we show that in a D-brane model, where the string scale is naturally of order 10^{10-12} GeV and the soft terms are non universal, a_{\mu} is enhanced with low \tan\beta.Comment: Final version to appear in Phys. Rev. D. Conventions clarified, results in the figures improve

A model for fermion masses and lepton mixing in SO(10) x A4

The discrete flavor symmetry A4 explains very well neutrino data at low energy, but it seems difficult to extend it to grand unified models since in general left-handed and right-handed fields belong to different A4 representations. Recently it has been proposed a model where all the fermions equally transform under A4. We study here a concrete SO(10) realization of such a model providing small neutrino masses through the seesaw mechanism. We fit at tree level the charged fermion masses run up to the unification scale. Some fermion masses properties come from the SO(10) symmetry while lepton mixing angles are consequence of the A4 properties. Moreover, our model predicts the absolute value of the neutrino masses, these ones are in the range $m_\nu\simeq 0.005-0.052 eV$.Comment: 15 pages. V2: Final version to appear in the journa

Revisión de las colecciones de rocas riolíticas catalanas del Museu de Geologia y de la Facultat de Geologia de la Universitat de Barcelona

The Museu de Geologia de Barcelona and the Faculty of Geology of the University of Barcelona own twin collections of rhyolitic volcanic rocks from the Catalonian Pyrenees, permo-carboniferous in age. Samples of these collections are currently exposed in the museum and used for didactic purposes at the university (petrography and hand sample studies). This revision corroborates that the collections have a initial common origin in the San Miguel de la Cámara collection (1934). The university' collection consists of lavic rocks from the Gréixer-Coll de Pi sector, rhyolitic in composition, and with textural evidence (perlitic textures, skeletal phenocrysts, thermal shocked quartz, etc.) of magma-water interaction during the mise-en-place process. Despite of their age these rocks show fine preservation of the original textural features, but they seem unadequate for didactic purposes in introductory courses of petrography because of several facts (peraluminous character expressed in phenocrysts, presence of specific textures of magma-water interaction, advanced stage of devetrification and silicification, etc.). These samples seem more idoneous for advanced didactic purposes (second cycle or PhD level studies). The Museu de Geologia contains two groups of samples: the aforementioned lavic rocks, and pyroclastic rocks from several localities of the catalonian Pyrenees. The pyroclastic rocks offer evidence of their character related to explosive volcanism (shards, pumice, crystal fragments, etc.) but they are deeply transformed and therefore inadequated for didactic purposes. Most of the thin slides are in fact too thick to allow a correct study of pyroclastic textures. The petrographic features allow us to suspect not only rhyolitic terms but also rhyodacitic and dacitic ones. The available data (bibliography and this study) shows some inconsistences in the current interpretation of the lavic silicic rocks. We offer a synthetic tentative explanation that could be tested in future research. Key words: volcanic rock, Upper Paleozoic, Catalonian Pyrenees, rhyolite, subaqueous environment, didactics, Museu de Geologia de Barcelona, Universitat de Barcelona, Spain.El Museu de Geologia de Barcelona y la Facultat de Geologia de la Universitat de Barcelona poseen sendas colecciones 'gemelas' de rocas volcánicas riolíticas de edad permo-carbonífera, procedentes del Pirineo catalán. Algunas muestras forman parte de la exposición permanente del museo y muchas de las de la colección universitaria son utilizadas regularmente en la didáctica de petrología ígnea en la universidad (petrografía y muestras de mano). Esta revisión permite confirmar la inicial procedencia común de ambas colecciones en la inicial de San Miguel de la Cámara (1934). La colección universitaria está constituida por rocas lávicas del sector de Gréixer-Coll de Pi, son riolitas, y presentan evidencias texturales claras de emplazamiento en medio subacuático (texturas perlíticas, fenocristales esqueléticos, fenocristales de cuarzo afectados de choque térmico, etc.). A pesar de su edad presentan un excelente estado de conservación de sus texturas, pero algunas de sus características (carácter peralumínico expresado en los fenocristales, texturas excesivamente específicas de interacción agua-magma, avanzado estado de desvitrificación y silicificación, etc.) desaconsejan su empleo didáctico en cursos introductorios de petrología ígnea y sugieren que su desplazamiento hacia cursos más avanzados (segundo ciclo o doctorado) sería más adecuado. El Museu de Geologia posee dos tipos de muestras: las lávicas antes descritas, y un segundo grupo de tipo piroclástico procedente de diferentes localidades del Pirineo catalán. Las rocas piroclásticas ofrecen evidencias inequívocas de su carácter genético (volcanismo explosivo), tales como presencia de pumitas, shards, fragmentos de cristales, etc. Sin embargo, han sufrido transformaciones importantes que las hacen inadecuadas en usos didácticos. Por otra parte, la mayoría de las láminas estudiadas son excesivamente gruesas, lo que impide un correcto estudio de las texturas piroclásticas. Las características petrográficas sugieren que existen términos riodacíticos y dacíticos además de los riolíticos. Finalmente, el conjunto de datos disponibles al final del estudio muestra que existen inconsistencias en la interpretación comúnmente aceptada para las rocas lávicas. Se ofrece en el trabajo una solución de compromiso compatible con las evidencias conocidas, que debe ser entendida como una hipótesis a corroborar en futuras investigaciones. Palabras clave: roca volcánica, Paleozoico Superior, Pirineo catalán, riolita, ambiente subacuático, didáctica, Museu de Geologia de Barcelona, Universitat de Barcelona. España

Las colecciones de anortositas canadienses del Museu de Geologia de Barcelona y de la Facultat de Geologia de la Universitat de Barcelona

Este trabajo aporta algunas precisiones sobre el origen y características petrográficas de las colecciones gemelas de rocas anortosíticas canadienses del Museu de Geologia de Barcelona y la Facultat de Geologia de la Universitat de Barcelona, así como sobre su idoneidad a efectos museísticos y didácticos. Palabras clave: Canadá, Québec, Anortosita de Langelier, Anortosita de Lac de Saint-Jean, cantera de Alma, petrografia, meta-anortosita, didáctica, colecciones de anortositas, Museu de Geologia, Universitat, Barcelona.This work provides new insights on the origin and petrographic features of the twin collections of canadian anorthositic rocks from Museu de Geologia of Barcelona and Faculty of Geology of University of Barcelona, as well as some considerations on its interest as exhibition and didactic samples. Key words: Canada, Québec, Langelier anorthosite, Lac de Saint-Jean anorthosite, Alma quarry petrography, meta-anorthosite, didactics, anorthosite collections, Museu de Geologia, Universitat, Barcelona.Este trabajo aporta algunas precisiones sobre el origen y características petrográficas de las colecciones gemelas de rocas anortosíticas canadienses del Museu de Geologia de Barcelona y la Facultat de Geologia de la Universitat de Barcelona, así como sobre su idoneidad a efectos museísticos y didácticos. Palabras clave: Canadá, Québec, Anortosita de Langelier, Anortosita de Lac de Saint-Jean, cantera de Alma, petrografia, meta-anortosita, didáctica, colecciones de anortositas, Museu de Geologia, Universitat, Barcelona

r-norm bounds and metric properties for zero loci of real analytic functions

We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed

Initial Scales, Supersymmetric Dark Matter and Variations of Neutralino-Nucleon Cross Sections

The neutralino-nucleon cross section in the context of the MSSM with universal soft supersymmetry-breaking terms is compared with the limits from dark matter detectors. Our analysis is focussed on the stability of the corresponding cross sections with respect to variations of the initial scale for the running of the soft terms, finding that the smaller the scale is, the larger the cross sections become. For example, by taking $10^{10-12}$ GeV rather than $M_{GUT}$, which is a more sensible election, in particular in the context of some superstring models, we find extensive regions in the parameter space with cross sections in the range of $10^{-6}$--$10^{-5}$ pb, i.e. where current dark matter experiments are sensitive. For instance, this can be obtained for \tan\beta\gsim 3