Relative asymptotics for orthogonal matrix polynomials

In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle. Some examples are given

Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc

22 pages, no figures.-- MSC2000 codes: Primary 42C05.MR#: MR1890494 (2002m:42023)Zbl#: Zbl 0991.42018Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product $$\langle f, g \rangle = \int_{E} f(\xi) \overline{g(\xi)} \rho (\xi) \xi \xi f(Z) A g(Z)^H,$$ where $E$ is a rectifiable Jordan curve or arc in the complex plane $$f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)),$$ $A$ is an $M \times M$ Hermitian matrix, $M=l_{1} + \cdots + l_{m} + m$, $denotes the arc length measure,$\rho$is a nonnegative function on$E$, and$z_{i} \in \Omega$,$i=1,2,\ldots,m$, where$\Omega$is the exterior region to$E$.The work of the first author was supported by the Portuguese Ministry of Science and Technology, Fundação para a Ciência e Tecnología of Portugal under grant FMRH-BSAB-109-99 and by the Centro de Matemática da Universidade de Coimbra. The second author would also like to thank the Unidade de Investigação (Matemática e Aplicações) of the University of Aveiro for their support. The work of the second and third authors was supported by the Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 96-0120-C03-01.Publicad

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ([mu]0,[mu]1) is a coherent pair of measures on the unit circle, then [mu]0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with [mu]1 is a specific rational transformation of the linear functional corresponding to [mu]0. Some examples are given.http://www.sciencedirect.com/science/article/B6WH7-4S2MJ0D-1/1/61050bb3811832f373ff40a48b7461d

Markov Chains and Multiple Orthogonality

In this work we survey on connections of Markov chains and the theory of multiple orthogonality. Here we mainly concentrate on give a procedure to generate stochastic tetra diagonal Hessenberg matrices, coming from some specific families of multiple orthogonal, such as the ones of Jacobi--Pi\~neiro and Hypergeometric Lima--Loureiro. We show that associated with a positive tetra diagonal nonnegative bounded Hessenberg matrix we can construct two stochastic tetra diagonal ones. These two stochastic tridiagonal nonnegative Hessenberg matrices are shown to be, enlightened by the Poincar\'e theorem, limit transpose of each other

Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials

This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ${}_3F_2$ and is proven using recently discovered contiguous relations. Moreover, employing the multiple Askey scheme, a bidiagonal factorization is derived for the Hahn descendants, including Jacobi-Pi\~neiro, multiple Meixner (kinds I and II), multiple Laguerre (kinds I and II), multiple Kravchuk, and multiple Charlier, all represented in terms of hypergeometric functions. For the cases of multiple Hahn, Jacobi-Pi\~neiro, Meixner of kind II, and Laguerre of kind I, where there exists a region where the recurrence matrix is nonnegative, subregions are identified where the bidiagonal factorization becomes a positive bidiagonal factorization.Comment: 14 pages, 2 figure

A case report of imported paracoccidioidomycosis

A Paracoccidioidomicose (PCM) é uma importante micose endémica na América do Sul. Na Europa a doença é muito rara e encontrada apenas em viajantes oriundos da América Latina. Os autores descrevem um caso de um jovem brasileiro de 24 anos, a viver em Portugal há 7 anos (durante o qual não regressou ao seu país natal), previamente saudável, admitido no nosso hospital com febre, perda do peso (cerca de 5Kg), dor epigástrica inespecífica, anorexia não selectiva, fadiga, linfoadenopatias periféricas e lesões cutâneas papulo- nodulares, com ulceração central, e que envolvia a cabeça, face e o tronco. Analiticamente, hypereosinofilia. Realizaram-se biopsias cirúrgicas dos gânglios linfáticos e das lesões cutâneas. O resultado anátomo-patológico foi consistente com PCM. Iniciou terapêutica antifúngica com melhoria clínica evidente

Hydrogen production by hydrolysis of sodium borohydride for PEM fuel cells feeding

In this work, hydrogen is produced by a hydrolysis process that uses sodium borohydride as a hydrogen carrier and storage media. High purity hydrogen is obtained at low temperatures with high volumetric and gravimetric storage efficiencies; reaction products are non-toxic. The produced hydrogen can be supply on-demand at specified flow by tailor made developed catalyst. Hydrogen feeding to a low power fuel cell was accomplished. According to experimental conditions conversion rates of 100% are possible. Catalyst is demonstrated to be reusable

Wearable gait analysis LAB as a biomarker of Parkinson’s disease motor stages and quality of life: a preliminary study

Bradykinetic, shuffling and shorter steps are prototypical signs of gait in Parkinson’s Disease (PD) and important indicators of Quality of Life (QoL). Advances in wearable technologies enabled their use to objectively evaluate these gait fluctuations complementing the subjective categorical clinical scales usually used by clinicians. This paper aims to study the ability of a wearable gait analysis lab, developed by our team, to serve as a biomarker of PD motor stages and an indicator of patients’ QoL. We accomplished experimental tests which involved repeated measurements of walking trials from a crosssection study with eighteen PD patients and thirteen healthy subjects. We measured gait spatiotemporal parameters and cross these data with commonly PD-scales to assess motor symptoms (UPDRS-III) and quantify patients’ QoL (PDQ39). Patients presented a bradykinetic gait with shorter steps, variability and asymmetry in spatiotemporal parameters. These prototypical signs were also observed along the disease progression considering UPDRS-III and PDQ39 levels. Positive outcomes demonstrated the feasibility and applicability of our objective wearable sensorbased gait analysis in PD to measure typical parkinsonian gait and a (bio)marker of PD motor stages and patients’ quality of life level.This work was supported in part by the FEDER Funds through the COMPETE 2020-Programa Operacional Competitividade e Internacionalizacao (POCI) and P2020 with the Reference Project SmartOs Grant POCI-01-0247-FEDER-039868, and by FCT national funds, under the national support to R&D units grant, through the reference project UIDB/04436/2020 and UIDP/04436/2020, and under the reference scholarship grant SFRH/BD/136569/2018