Discrete-Time Fractional Variational Problems

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when $h$ tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.Comment: Submitted 24/Nov/2009; Revised 16/Mar/2010; Accepted 3/May/2010; for publication in Signal Processing

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

Resposta diferencial de genótipos de sorgo para tolerância ao alumínio em solução nutritiva.

Neste trabalho utilizou-se de uma tecnica de solucao nutritiva para identificar, dentre 391 linhagens de sorgo (BAG-Sorgo; 181), CNPMS: 71, SEPON/ICRISAT: 17 e Sacarino: 122, os genotipos que apresentam tolerancia ao aluminio. A avaliacao do comportamento diferencial dessas linhagens baseou-se no crescimento da raiz seminal primaria de plantas jovens de sorgo, em solucao nutritiva contendo niveis variados de Al (0,0, 2,25 e 4,5 mg de Al/1 para sorgo granifero e 0,0, 2,25 e 5,0 mg de Al/1 para sorgo sacarino). A caracteristica usada para a comparacao entre genotipos foi o Comprimento Relativo da Raiz Seminal (CRSS = CRS + AL/CRS - Al, onde CRS = comprimento da Raiz Seminal). Baseando-se na distribuicao percentual dos valores de CRRS obtidos para as diferentes linhagens e nos valores de CRRS encontrados para os materiais controles SC 298 (sensivel ao Al) e SC 283 (tolerante ao Al) tres classes de resposta ao aluminio foram definidas: Sensivel (CRRS 0,70). Dentre os materiais avaliados as seguintes linhagens apresentaram tolerancia aos niveis de 4,5 ou 5,0 mg de Al/1: IS 3625, IS 7173 C (SC 283), IS 12666, 5DX61/6/2, 3DX57/1/1910, 156-P-5-Serere-1, 9DX9/11, Brandes, MN 4004 e MN 1204

Reptilia, Squamata, Tropiduridae, <i>Stenocercus sinesaccus</i> Torres–Carvajal, 2005: Distribution extension

The present study reports the easternmost known record for the tropidurid lizard Stenocercussinesaccus Torres–Carvajal, 2005, at Floresta Nacional de Silvânia, state of Goiás, Brazil, in a transition areabetween cerrado sensu strictu and gallery fores

Dermoscopic and Reflectance Confocal Microscopic Presentation of Relapsing Eccrine Porocarcinoma

info:eu-repo/semantics/publishedVersio

Registo da avaliação da dor em sistema de informação: um projeto em desenvolvimento

Poster apresentado nas I Jornadas do Mestrado em Enfermagem de Saúde Infantil e Pediatria, organizadas pela Escola Superior de Enfermagem do Port

Thermal difference reflectivity of tilted 2D Dirac materials

Deviation from perfect conical dispersion in Dirac materials, such as the presence of mass or tilting, enhances control and directionality of electronic transport. To identify these signatures, we analyze the thermal derivative spectra of optical reflectivity in doped massive tilted Dirac systems. The density of states and chemical potential are determined as preliminary steps to calculate the optical conductivity tensor at finite temperature using thermal convolution. Changes in reflection caused by temperature variations enable clear identification of critical frequencies in the optical response. By measuring these spectral features in the thermoderivative spectrum, energy gaps and band structure tilting can be determined. A comparison is presented between the spectra of various low-energy Dirac Hamiltonians. Our findings suggest that thermal difference spectroscopy holds promise as a valuable technique for probing interband transitions of 2D Dirac fermion