Zeros of polynomials orthogonal with respect to a signed weight

AbstractIn this paper we consider the monic polynomial sequence (Pnα,q(x)) that is orthogonal on [−1,1] with respect to the weight function x2q+1(1−x2)α(1−x),α>−1,q∈N; we obtain the coefficients of the tree-term recurrence relation(TTRR) by using a different method from the one derived in Atia et al. (2002) [2]; we prove that the interlacing property does not hold properly for (Pnα,q(x)); and we also prove that, if xn,nα+i,q+j is the largest zero of Pnα+i,q+j(x), x2n−2j,2n−2jα+j,q+j<x2n−2i,2n−2iα+i,q+i,0≤i<j≤n−1

A Survey on q-Polynomials and their Orthogonality Properties

In this paper we study the orthogonality conditions satisfied by the classical q-orthogonal polynomials that are located at the top of the q-Hahn tableau (big q-jacobi polynomials (bqJ)) and the Nikiforov-Uvarov tableau (Askey-Wilson polynomials (AW)) for almost any complex value of the parameters and for all non-negative integers degrees. We state the degenerate version of Favard's theorem, which is one of the keys of the paper, that allow us to extend the orthogonality properties valid up to some integer degree N to Sobolev type orthogonality properties. We also present, following an analogous process that applied in [16], tables with the factorization and the discrete Sobolev-type orthogonality property for those families which satisfy a finite orthogonality property, i.e. it consists in sum of finite number of masspoints, such as q-Racah (qR), q-Hahn (qH), dual q-Hahn (dqH), and q-Krawtchouk polynomials (qK), among others. -- [16] R. S. Costas-Santos and J. F. Sanchez-Lara. Extensions of discrete classical orthogonal polynomials beyond the orthogonality. J. Comp. Appl. Math., 225(2) (2009), 440-451Comment: 3 Figures, 3 tables, in a 22 pages manuscrip

The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(\lambda)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$_S= +\lambda <{{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}>,$$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $\lambda$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez lagomasino on the occasion of his 60th birthday, accepted in Journal of Approximation Theor

Palynological study of the endemic woody sonchus from de Flora of Madeira.A morphological and molecular approach

info:eu-repo/semantics/publishedVersio

The effect of level of knowledge accuracy of results on learning of motor skills in children and adults

The level of knowledge accuracy of results (KR) is a variable that interferes with the learning of motor skills, however such interference does not work the same way in adults and children. This study examined the effects of KR in children and adults during learning of a manipulative task with target accuracy. Forty adults (female = 21.13 ± 2.26 years; male = 20.97 ± 2.17 years) and forty children (female = 9.10 ± .83 years; male = 9.70 ± .48 years) practiced a task of hitting a target placed on a table by the thrown of metal discs. There were six experimental groups and two control groups (without KR) containing 10 subjects each. Experimental groups differed according to the individual's KR (less precise KR, precise KR and very precise KR) and development level (children and adult). Performance measure was the absolute error (AE). A three-way (age × groups × blocks) and two-way (groups × blocks) analysis of variance for the stabilization and adaptation phases were used. Results showed that adults perform better than children in low and intermediate KR and in high KR adults and children showed similar performance

Extensions of discrete classical orthogonal polynomials beyond the orthogonality

It is well known that the family of Hahn polynomials $\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $\Delta$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all n\in \XX N_0. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.Comment: 2 figures, 20 page

Survey Of Acarin Fauna In Dust Samplings Of Curtains In The City Of Campinas, Brazil.

The aim of this study was to investigate the mite fauna present in 33 living room and 22 bedroom curtain dust samples from 41 different homes in the southern Brazilian city of Campinas, SP. A total of 148 mite bodies were found. Of these, 83 were found in living-room curtain samples (56.1% of total) and 65 were in bedroom curtain dust samples (43.9%). The most frequently observed mite suborders were: Acaridida (n = 79; 53.4%), Actinedida (n=53; 35.8%), Oribatida (n=14; 9.5%), and Gamasida (n=2; 1.3%). The most frequent families were Pyroglyphidae (n=61; 41.2%), Eriophyidae (n=25; 16.9%), Tarsonemidae (n=15; 10.1%), and Glycyphagidae (n=13; 8.8%). No statistical difference was observed between the number of mites found in the samples from living room and bedroom curtains.651252