Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 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)(&alpha;, &beta;) (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 < &beta; (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).

Search for pair production of second generation scalar leptoquarks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New antifungal terpenoid glycosides from Alibertia edulis (Rubiaceae)

Phytochemical investigation from the stems of Alibertia edulis led to the isolation and identification of a new iridoid 6 beta-hydroxy-7-epigardoside methyl ester (1) and a new saponin 3 beta-O-[alpha-L-rhamnopyranosyl-(1 -> 2)-O-beta-D-glucopyranosyl-(1 -> 2)-O-beta-D-glucopyranosyl]-28-O-beta-D-glucopyranoside pomolate (2), along with three known compounds, shanzhiside methyl ester (3), ixoside (4), and 3,4,5-trimethoxyphenyl 1-O-beta-D-apiofuranosyl-(1 -> 6)-O-beta-D-glucopyranoside (5). The structures of 1 and 2 were established on the basis of their spectroscopic data. Iridoid 1 and saponin 2 exhibited moderate inhibitory activities against Candida albicans and C krusei in a dilution assay.

Characterization of esterases in a Brazilian population of Zaprionus indianus (Diptera : Drosophilidae)

The aim of this study was to characterize esterases in Zaprionus indianus, a drosophilid recently introduced into Brazil. A further aim was study the variation of activity of esterases in the presence of inhibitors and their expression according to sex, sexual activity and age of individual flies. Polymorphisms were detected in two esterase loci (Est-2 and Est-3) and monomorphisms in four others (Est-1, Est-4, Est-5 and Est-6). Biochemical tests using alpha- and beta-naphthyl acetate and the inhibitors malathion, eserine sulphate and PMSF allowed us to classify EST-2 and EST-5 as beta-esterases, both carboxyl-esterases, and EST-1, EST-3, EST-4 and EST-6 as alpha-esterases. EST-1 and EST-3 were classified as carboxyl-esterases and EST-4 and EST-6 as cholinesterases. EST-5 activity was more pronounced in males and EST-2 was restricted to them or to recently copulated females. EST-4, rarely detected, was not characterized. Based on their biochemical characteristics possible roles for these enzymes are suggested.

PHENYLBUTANOID AND TAXANE-LIKE METABOLITES FROM NEEDLES OF TAXUS-BREVIFOLIA

The structures for brevifoliol and three baccatin VI derivatives were revised to possess the novel 11(15 --> 1)-abeotaxane tricylic skeleton based on X-ray crystallographic studies. Four more new rearranged taxane derivatives related to brevifoliol and the unusual phenylbutanoid, (-)-rhododendrol, were isolated from the needles of Taxus breuifolia. Their structures were established as 10 beta-benzoxy-5 alpha-(3'-dimethylamino-3'-phenyl)-propanoxy-1 beta-hydroxy- 7 beta,9 alpha,13 alpha-triacetoxy-11(15 --> 1)-abeotaxa-4(20),11-diene; 10 beta-benzoxy-1 beta-hydroxy-5 alpha-(3'-methylamino-3'-phenyl)- propanoxy-7 beta,9 alpha,l3 alpha-triacetoxy-11(15 --> 1)-abeotaxa-4(20),11-diene; 10 beta-benzoxy-5 alpha-cinnamoxy-1 beta-hydroxy-7 beta,9 alpha,13 alpha-triacetoxy-1 1(15 --> 1)-abeotaxa-4(20),11-diene; 10 beta-benzoxy-1 beta,5 alpha-dihydroxy-7 beta,9 alpha,13 alpha-triacetoxy-11(15 --> 1)-abeotaxa-4(20),11-diene and 2(R)-hydroxy-4-(4'-hydroxyphenyl)-butane.

Triterpenes from Maytenus macrocarpa and evaluation of their anti-HIV activity

A set of pentacyclic triterpenes has been isolated from the bark of Maytenus macrocarpa (Celastraceae). It includes two new olean-12-ene derivatives, namely 3 beta, 22(alpha-dihydroxy-olean-12-en-30-oic acid (1) and 22 alpha-hydroxy-olean-12-en-3-oxo-30-oic acid (2), and the new urs-12-ene derivative 3-(E)-coumaroyluvaol (7), along with 10 known compounds possessing olean-12ene, urs-12-ene, lupane and friedelane skeletons. The structures have been elucidated by extensive spectroscopic methods including ID- and 2D-NMR experiments, as well as ESI-MS analysis. All isolated compounds were tested for anti-HIV activity in C8166 cells infected with HIV-1(MN), the most active compound was 22(alpha-hydroxy-12-en-3-oxo-29-oic acid (triterpenonic acid A, 4), with an EC50 value of I mu g/mL and a selectivity index of 35.

AN OLEANANE ACID FROM ALIBERTIA-EDULIS

A new oleanane, 3 beta,19 alpha,23,24-tetrahydroxy-12-oleanen-28-oic acid, was isolated together with nine known triterpene compounds from the leaves of Alibertia edulis, Rubiaceae.

Host-guest complexation of a nitroheterocyclic compound with cyclodextrins: a spectrofluorimetric and molecular modeling study

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

Interclonal Variations in the Molecular Karyotype of Trypanosoma cruzi: Chromosome Rearrangements in a Single Cell-Derived Clone of the G Strain

Trypanosoma cruzi comprises a pool of populations which are genetically diverse in terms of DNA content, growth and infectivity. Inter- and intra-strain karyotype heterogeneities have been reported, suggesting that chromosomal rearrangements occurred during the evolution of this parasite. Clone D11 is a single-cell-derived clone of the T. cruzi G strain selected by the minimal dilution method and by infecting Vero cells with metacyclic trypomastigotes. Here we report that the karyotype of clone D11 differs from that of the G strain in both number and size of chromosomal bands. Large chromosomal rearrangement was observed in the chromosomes carrying the tubulin loci. However, most of the chromosome length polymorphisms were of small amplitude, and the absence of one band in clone D11 in relation to its reference position in the G strain could be correlated to the presence of a novel band migrating above or below this position. Despite the presence of chromosomal polymorphism, large syntenic groups were conserved between the isolates. The appearance of new chromosomal bands in clone D11 could be explained by chromosome fusion followed by a chromosome break or interchromosomal exchange of large DNA segments. Our results also suggest that telomeric regions are involved in this process. The variant represented by clone D11 could have been induced by the stress of the cloning procedure or could, as has been suggested for Leishmania infantum, have emerged from a multiclonal, mosaic parasite population submitted to frequent DNA amplification/deletion events, leading to a 'mosaic' structure with different individuals having differently sized versions of the same chromosomes. If this is the case, the variant represented by clone D11 would be better adapted to survive the stress induced by cloning, which includes intracellular development in the mammalian cell. Karyotype polymorphism could be part of the T. cruzi arsenal for responding to environmental pressure. © 2013 Lima et al.

Caracterização da radioatividade das águas do aquífero Guarani

This research aimed to evaluate the quality of “Aquifer Guarani’s” waters in the context of the current legislation related to the radioactive aspects, besides correlating the values obtained with chemical data already available, seeking to make an integrated analysis of the data in order to establish possible tendencies with directions of underground flow. The determinations of the total radioactivity beta and alpha were accomplished through the employment of the available infrastructure at the LABIDRO – Laboratory of Isotope and Hydrochemistry of the Petrology and Metallogeny of UNESP’s Institute of Geosciences and Exact Sciences, largely implanted through resources supplied by FAPESP and CNPq. The systems were gauged for the determinations of interest with tracer of known activity. Preliminaries tests were accomplished with high radioactivity samples of water to check the applicability of the methods. It was ended that the waters analyzed possess low radioactivity, as much alpha as total beta, and, therefore, they are appropriate for the human consumption; that there is not lineal relationship between the obtained data and the chemical data already available; and that the direction of the underground flow of the Aquifer doesn't check any tendency to the generated data.

Determination of estrogenic mycotoxins in environmental water samples by low-toxicity dispersive liquid-liquid microextraction and liquid chromatography-tandem mass spectrometry

A novel, simple, rapid and eco-friendly method based on dispersive liquid-liquid microextraction using a bromosolvent was developed to determine six estrogenic mycotoxins (zearalenone, zearalanone, alpha-zearalanol, beta-zearalanol, alpha-zearalenol and beta-zearalenol) in water samples by liquid chromatography-electrospray ionization tandem mass spectrometry in the negative mode (LC-ESI-MS/MS). The optimal conditions for this method include the use of 100 mu L bromocyclohexane as an extraction solvent (using a non-dispersion solvent), 10 mL of aqueous sample (adjusted to pH 4), a vortex extraction time of 2 min, centrifugation for 10 min at 3500 rpm and no ionic strength adjustment. The calibration function was linear and was verified by applying the Mandel fitting test with a 95% confidence level. No matrix effect was observed. According to the relative standard deviations (RSDs), the precision was better than 13% for the repeatability and intermediate precision. The average recoveries of the spiked compounds ranged from 81 to 118%. The method limits of detection (LOD) and quantification (LOQ) considering a 125-fold pre-concentration step were 4-20 and 8-40 ng L-1, respectively. Next, the method was applied to the analysis of the environmental aqueous samples, demonstrating the presence of beta-zearalanol and zearalanone in the river water samples. (C) 2015 Elsevier B.V. All rights reserved.

Domínios de potências fracionárias de operadores matriciais segundo Lasiecka-Triggiani

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.