Base change for Elliptic Curves over Real Quadratic Fields

Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve readabilit

A multi-Frey approach to Fermat equations of signature (r,r,p)(r,r,p)

In this paper, we give a resolution of the generalized Fermat equations $$x^5 + y^5 = 3 z^n \text{ and } x^{13} + y^{13} = 3 z^n,$$ for all integers $n \ge 2$, and all integers $n \ge 2$ which are not a multiple of $7$, respectively, using the modular method with Frey elliptic curves over totally real fields. The results require a refined application of the multi-Frey technique, which we show to be effective in new ways to reduce the bounds on the exponents $n$. We also give a number of results for the equations $x^5 + y^5 = d z^n$, where $d = 1, 2$, under additional local conditions on the solutions. This includes a result which is reminiscent of the second case of Fermat's Last Theorem, and which uses a new application of level raising at $p$ modulo $p$.Comment: Includes more details regarding the connection of this paper with its sequel 'Some extensions of the modular method and Fermat-equations of signature (13,13,n)'. More precisely: extended Remark 7.4; added details on the computational parts of the proofs of Proposition 9 and Theorem 2; included new comments and polished the auxiliary Magma files for Proposition 9 and Theorem

Comment on "Effective of the q-deformed pseudoscalar magnetic field on the charge carriers in graphene"

We point out a misleading treatment in a recent paper published in this Journal [J. Math. Phys. (2016) 57, 082105] concerning solutions for the two-dimensional Dirac-Weyl equation with a q-deformed pseudoscalar magnetic barrier. The authors misunderstood the full meaning of the potential and made erroneous calculations, this fact jeopardizes the main results in this system.Comment: 7 pages, 2 figure

Nectaries and reproductive biology of croton sarcopetalus (euphorbiaceae)

Flower morphology, nectary structure, nectar chemical composition, breeding system, floral visitors and pollination were analysed in Croton sarcopetalus, a diclinous-monoecious shrub from Argentina. Male flowers have five receptacular nectaries, with no special vascular bundles, that consist of a uniserial epidermis with stomata subtended by a secretory parenchyma. Female flowers bear two different types of nectaries: inner (IN) and outer (ON) floral nectaries. IN, five in all, are structurally similar to the nectaries of male flowers. The five ON are vascularized, stalked, and composed of secretory, column-shaped epidermal cells without stomata subtended by secretory and ground parenchyma. In addition, ON act as post-floral nectaries secreting nectar during fruit ripening. Extrafloral nectaries (EFN) are located on petioles, stipules and leaf margins. Petiolar EFN are patelliform, stalked and anatomically similar to the ON of the female flower. Nectar sampled from all nectary types is hexose dominant, except for the ON of the female flower at the post-floral stage that is sucrose dominant. The species is self-compatible, but geitonogamous fertilization is rarely possible because male and female flowers are not usually open at the same time in the same individual, i.e. there is temporal dioecism. Flowers are visited by 22 insect species, wasps being the most important group of pollinators. No significant differences were found in fruit and seed set between natural and hand pollinated flowers. This pattern indicates that fruit production in this species is not pollen/pollinator limited and is mediated by a wide array of pollinators. © 2001 The Linnean Society of London.Fil: Freitas, Leandro. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: Bernardello, Gabriel Luis Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Galetto, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Paoli, Adelita. Universidade Estadual Paulista Julio de Mesquita Filho; Brasi

Derrame pleural maligno

Trabalho final de mestrado integrado em Medicina área cientifica de Pneumologia, apresentado à Faculdade de Medicina da Universidade de CoimbraIntrodução: A patologia oncológica ocupa cada vez mais um lugar de destaque na prática clínica em todo o mundo, dado o número crescente de casos. Uma das complicações mais frequentes nos pacientes com neoplasias avançadas é o derrame pleural maligno, sendo o cancro de pulmão a causa mais comum; no entanto, o cancro da mama, ovário, do tracto gastrointestinal e os linfomas são agentes etiológicos com alguma frequência. O prognóstico nestes doentes é geralmente reservado dado que a presença de derrame pleural traduz frequentemente disseminação da doença e a resposta à terapêutica sistémica é variável, comprometendo significativamente a qualidade de vida dos doentes, nomeadamente por sintomas como dispneia, tosse e dor torácica. Objectivos: A presente revisão visa abordar a problemática do derrame pleural associado à patologia neoplásica, procurando integrar a informação disponibilizada pelos vários autores nos últimos 10 anos. A metodologia escolhida baseou-se na pesquisa de artigos indexados na PubMed. Desenvolvimento: Avanços consideráveis foram feitos no diagnóstico de derrames pleurais malignos, através do recurso à análise do líquido pleural e dos estudos imagiológicos que melhoraram a execução das biópsias pleurais. A obliteração da cavidade pleural com talco continua a ser o gold standard no tratamento; no entanto, dependendo do prognóstico do doente, a abordagem varia, podendo passar por uma toracocentese para alívio sintomático ou então procedimentos mais invasivos como cateteres pleurais de longa duração. Conclusões: Apesar da existência de múltiplas técnicas bem toleradas para o controlo e tratamento destes derrames pleurais, as estratégias actuais estão claramente inadequadas. Mais pesquisa deve ser feita no sentido de encontrar novas abordagens e modalidades terapêuticas para este problema de incidência crescente.Introduction: The oncologic pathology occupies an increasingly prominent place on clinical practice in the world, due to the increasing number of cases. One of the most common complications in patients with advanced cancer is malignant pleural effusion, being the lung cancer the most common cause; however, breast cancer, ovarian, gastrointestinal tract and lymphomas are pathogens with some frequency. The prognosis in these patients is usually reserved as the pleural effusion often means spread disease and the response to systemic therapy is variable, significantly compromising the quality of life for patients, particularly for symptoms such as dyspnea, cough and chest pain. Objectives: This review aims to address the issue of pleural effusion in the context of malignancy, by integrating the information provided by various authors in the last 10 years. The methodology chosen was based on the research of articles indexed in PubMed. Results: Considerable progress has been made in the diagnosis of malignant pleural effusions by using pleural fluid analysis and imaging studies that have improved the performance of pleural biopsies. The obliteration of pleural cavity with talc remains the gold standard in treatment; however, depending on the patient's prognosis, the approach varies, and may undergo a thoracentesis for symptomatic relief or else more invasive procedures such as pleural catheters for long periods. Conclusions: Despite the existence of multiple techniques well tolerated for the control and treatment of pleural effusions, the current strategies are clearly inadequate. More research must be done in order to find new approaches and therapeutic modalities for this problem of increasing incidence