41,480 research outputs found

    Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

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    In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.P.A. is partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific projects PEstOE/MAT/UI0208/2013 and PTDC/MAT-CAL/4334/2014. R.F. was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.info:eu-repo/semantics/publishedVersio

    Influence of Lorentz-violating terms on a two-level system

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    The influence of Lorentz- and CPT-violating terms of the extended Standard Model on a semi-classical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.Comment: 13 pages, 6 figures, revtex style

    Synthesis and properties of Co-doped titanate nanotubes and their optical sensitization with methylene blue

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    Here we report on a novel chemical route to synthesize homogenous cobalt doped titanate nanotubes (CoTNT), using an amorphous Co-doped precursor. The influence of the synthesis temperature, autoclave dwell time and metal doping on the structural and microstructural as well as on the optical properties of the synthesized titanate nanotubes is studied and discussed. The optical band gaps of the CoTNT samples are red shifted in comparison with the values determined for the undoped samples, such red shifts bringing the absorption edge of the CoTNT samples into the visible region. CoTNT materials also demonstrate particular high adsorption ability for methylene blue, the amount of the adsorbed dye being higher than the one predictable for a monolayer formation. This suggests the possibility of intercalation of the dye molecule between the TiO6 layers of the TNT structure. It is also shown that the methylene blue sensitized Co-doped nanostructures are highly stable under UV radiation and present a strong and broad absorption in the visible region.Comment: 31 pages, 3 tables, 7 figure
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