Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Preferential location of prilocaine and etidocaine in phospholipid bilayers: A molecular dynamics study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Preferential location of lidocaine and etidocaine in lecithin bilayers as determined by EPR, fluorescence and H-2 NMR

We have examined the effect of the uncharged species of lidocaine (LDC) and etidocaine (EDC) on the acyl chain moiety of egg phosphatidylcholine liposomes. Changes in membrane organization caused by both anesthetics were detected through the use of EPR spin labels (5, 7 and 12 doxyl stearic acid methyl ester) or fluorescence probes (4, 6, 10, 16 pyrene-fatty acids). The disturbance caused by the LA was greater when the probes were inserted in more external positions of the acyl chain and decreased towards the hydrophobic core of the membrane. The results indicate a preferential insertion of LDC at the polar interface of the bilayer and in the first half of the acyl chain, for EDC. Additionally, 2 H NMR spectra of multilamellar liposomes composed by acyl chain-perdeutero DMPC and EPC (1:4 mol%) allowed the determination of the segmental order (S-mol) and dynamics (T-1) of the acyl chain region. In accordance to the fluorescence and EPR results, changes in molecular orientation and dynamics are more prominent if the LA preferential location is more superficial, as for LDC while EDC seems to organize the acyl chain region between carbons 2-8, which is indicative of its positioning. We propose that the preferential location of LDC and EDC inside the bilayers creates a "transient site", which is related to the anesthetic potency since it could modulate the access of these molecules to their binding site(s) in the voltage-gated sodium channel. (C) 2007 Elsevier B.V. All rights reserved.

Evaluation of the influence of location of osseointegrated implants associated with mandibular removable partial dentures

Purpose: The aim of this research was to assess, by means of, the bi-dimensional finite element method, the best implant location in the alveolar edge, through stress distribution and support structure displacement of a distal extension removable partial denture associated with an osseointegrated implant of 10.0 x .75 mm, acting as abutment for the denture base.Methods and Materials: Five models in sagittal cut were used to represent: model A-hemi arch containing natural tooth 33 and the distal alveolar edge; model B-similar to model A, but with a conventional removable partial denture to replace the absent teeth; model C (MC)-similar to the previous one, with an implant in the distal region of the edge under the denture base; model D-similar to MC, with the implant in the central region of the edge; model E-similar to MC, with an implant in the mesial region of the edge. With the aid of the finite element program ANSYS 8.0, the models were loaded with strictly vertical forces of 50 N on each cusp tip. Displacement and von Mises Maps were plotted for visualization of results.Results: The introduction of implant diminished the tendency of intrusion of the removable partial denture in all situations. The maximum stress was observed on implant in all situations. Approximating implant in direction of support teeth was benefit for stress distribution.Conclusion: Model D presented the lowest value for maximum tendency to displacement when compared with those found in the other models; model E demonstrated better relief with regard to demand from the abutment tooth; locating the implant near of the abutment tooth influenced positively the distribution of stresses on the analyzed structures.

Location of the mandibular foramen according to the amount of dental alveoli

The aim of this study was to analyze the anatomotopographic location of the mandibular foramen in the right and left ramus, and to verify the influence of the amount of dental alveoli on the foramen position. Thirty-five adult dry human mandibles of Araraquara Dental School, UNESP - São Paulo State University were assessed, with or without dental alveoli. Measurements were obtained, using a ruler and a digital caliper. The following distances were measured: Fl - distance between the lowest point of the mandibular incisure and the mandibular foramen (F point); FB - distance between the mandibular base and F point; FP - distance between the posterior margin of the ramus and F point; FA - distance between the anterior margin of the ramus and F point; FT - distance between the apex of the retromolar trigone and F point. The Mann-Whitney test was used to compare each measurement according to hemi-arch, and the Kruskal-Wallis test was used to analyze the influence of the presence of alveoli on the measures. For multiple comparison, Dunn's method was used. There was no statistically significant difference in the location of the mandibular foramen when compared to the right and left hemi-arches. The amount of dental alveoli influenced, significantly, only on FA and FP distances. Thus, it was concluded that the right and left mandibular ramus showed symmetry in the location of the mandibular foramen, and the amount of alveoli influenced on the distances of the anterior and posterior margins of the mandibular rams, in relation to the mandibular foramen.

Chromosomal location of heterochromatin and 45S rDNA sites in four South American triatomines (Heteroptera: Reduviidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotics of zeros of polynomials arising from rational integrals

We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All rights reserved.

Monotonicity of zeros of Jacobi polynomials

Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved.

On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity of zeros of Laguerre polynomials

Denote by X(nk)(alpha), k = 1, ..., n, the zeros of the Laguerre polynomial L(n)((alpha))(X). We establish monotonicity with respect to the parameter at of certain functions involving X(nk)(alpha). As a consequence we obtain sharp upper bounds for the largest zero of L(n)((alpha))(X). (C) 2009 Elsevier B.V. All rights reserved.

Distances between critical points and midpoints of zeros of hyperbolic polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)