Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Efficiency of extrinsic and intrinsic charge-carrier photogeneration processes obtained from the steady-state photocurrent action spectra of poly(p-phenylene vinylene) derivatives

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interaction of amphiphilic derivatives of chitosan with DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine)

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

In vitro exposure to fullerene C60 influences redox state and lipid peroxidation in brain and gills from Cyprinus carpio (Cyprinidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fullerene and omega-3 and omega-6 fatty acids on fish brain antioxidant status

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hamilton-Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made. (C) 2007 Elsevier B.V. All rights reserved.

Speciation of butyltin derivatives in surface sediments of three southern Brazilian harbors

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Re-examination of the anion derivatives of isoflavones by radical fragmentation in negative electrospray ionization tandem mass spectrometry: experimental and computational studies

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

Nitro derivatives and other constituents of Aristolochia melastoma

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

In vitro Trypanocidal Activity of Phenolic Derivatives from Peperomia obtusifolia

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

Alkyl Hydroxybenzoic Acid Derivatives that Inhibit HIV-1 Protease Dimerization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Geranylation of benzoic acid derivatives by enzymatic extracts from Piper crassinervium (Piperaceae)

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

Piperamides and their derivatives as potential anti-trypanosomal agents

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

Antinociceptive profile of 2,3,6-trisubstituted piperidine alkaloids: 3-O-acetyl-spectaline and semi-synthetic derivatives of (-)-spectaline

In early studies, we have reported the antinociceptive profile of (-)-spectaline, a piperidine alkaloid from Cassia spectabilis. The present study describes the synthesis, the antinociceptive and anti-inflammatory activities of a series of 2,3,6-trialkyl-piperidine alkaloids: the natural (-)-3-O-acetyl-spectaline (LASSBio-755) and ten semi-synthetic spectaline derivatives. Structure-activity relationship (SARs) studies were performed. The structures of all synthesized derivatives were confirmed by means of nuclear magnetic resonance. Compounds were evaluated for their analgesic (acetic acid-induced mouse abdominal constrictions, hot-plate test, formalin-induced pain test) and some of them for the anti-inflammatory activities (carrageenan-induced rat paw edema test). The pharmacological results showed that several of the new compounds given orally at a dose of 100 mu mol/kg significantly inhibited the acetic acid-induced abdominal constrictions, but they were less active than (-)-spectaline. LASSBio-755 and LASSBio-776 were the most actives with 37% and 31.7% of inhibition. In the formalin-induced pain only LASSBio-776 was able to inhibit by 34.4% the paw licking response of the inflammatory phase, (-)-spectaline and LASSBio-755 did show any activity. In the carrageenan-induced rat paw edema, only (-)-spectaline exhibited an anti-inflammatory profile, showing an ED(50) value of 56.6 mu mol/kg. Our results suggest different mechanisms of action for the analgesic activity observed for LASSBio-776 (3-O-Bocspectaline), LASSBio-755 (3-O-acetyl-spectaline) and (-)-spectaline (LASSBio-754). The antinociceptive profile of some of the semi-synthetic spectaline derivatives extends our research concerning the chemical and pharmacological optimization of isolated natural products in the search of new drug candidates from brazilian biodiversity.

Phenolic Derivatives from Fruits of Dipteryx lacunifera DUCKE and Evaluation of Their Antiradical Activities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)