Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Analytical functions for the calculation of hyperspherical potential curves of atomic systems

We present angular basis functions for the Schrödinger equation of two-electron systems in hyperspherical coordinates. By using the hyperspherical adiabatic approach, the wave functions of two-electron systems are expanded in analytical functions, which generalizes the Jacobi polynomials. We show that these functions, obtained by selecting the diagonal terms of the angular equation, allow efficient diagonalization of the Hamiltonian for all values of the hyperspherical radius. The method is applied to the determination of the 1S e energy levels of the Li + and we show that the precision can be improved in a systematic and controllable way. ©2000 The American Physical Society.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

Constrained intervals and interval spaces

Constrained intervals, intervals as a mapping from [0, 1] to polynomials of degree one (linear functions) with non-negative slopes, and arithmetic on constrained intervals generate a space that turns out to be a cancellative abelian monoid albeit with a richer set of properties than the usual (standard) space of interval arithmetic. This means that not only do we have the classical embedding as developed by H. Radström, S. Markov, and the extension of E. Kaucher but the properties of these polynomials. We study the geometry of the embedding of intervals into a quasilinear space and some of the properties of the mapping of constrained intervals into a space of polynomials. It is assumed that the reader is familiar with the basic notions of interval arithmetic and interval analysis. © 2013 Springer-Verlag Berlin Heidelberg.

Synthesis, characterization, x-ray structure, DNA cleavage, and cytotoxic activities of palladium(ii) complexes of 4-phenyl-3-thiosemicarbazide and triphenylphosphane

Complexes of the type [PdX(PPh3)(1)]X [1 = 4-phenyl-3- thiosemicarbazide; X = Cl- (2), Br- (3), I- (4), and SCN- (5)] have been synthesized and characterized by elemental analyses and IR, UV/Vis, and 1H and 13C NMR spectroscopy. The molecular structure of complex 4 was determined by single-crystal X-ray diffraction. The binding of the complexes with a purine base (guanosine) was investigated by 1H NMR spectroscopy and mass spectrometry, which showed the complexes to coordinate to guanosine through N7. A gel electrophoresis assay demonstrated the ability of 2-5 to cleave DNA plasmid. All the complexes were tested in vitro by means of the MTT assay for their cytotoxicity against two murine cell lines, LM3 (mammary adenocarcinoma) and LP07 (lung adenocarcinoma), and compared with cisplatin. Complexes 2-5 exhibited good cytotoxicity that surpasses that of cisplatin in the case of LM3. A series of thiosemicarbazide/phosphane palladium(II) complexes have been synthesized and fully characterized. These complexes are able to cleave DNA plasmid and show cytotoxicity against adenocarcinoma (mammary LM3 and lung LP07), surpassing the cytotoxicity of cisplatin in the case of LM3. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Viabilidade e longevidade de sementes de tabebuia aurea benth. & hook. submetidas a diferentes métodos de armazenamento

Seeds Tabebuia aurea (syn. Handroanthus aureus Mattos), The seeds of Tabebuia aurea (syn. Handroanthus Mattos aureus), have low metabolic rates, which favors their storage conditions and freezing temperatures when stored at room temperature, there is a progressive decline in viability. Therefore, this study aims to determine the viability and longevity of seeds of Tabebuia aurea subjected to different storage methods. There were used 6100 seeds. In 2400 seeds were stored refrigerator, which in 1200 placed in transparent plastic bag and 1200 in Kraft paper bags. 3600 Other seeds were placed in room temperature and 1200 seeds in clear plastic bag, 1200 in Kraft paper bags and tray open in 1200. For each treatment, four replicates of 25 seeds for 12 months, with design was completely randomized. The average germination, normal seedlings and speed germination index were transformed into (x+1)(-1/2). The data were submitted to ANOVA and means compared by Tukey test at 5%. Also regressions polynomials were modeled for the variables study in function of the periods of storage of the seeds. The seeds stored in the refrigerator at 13 C maintained a high germination rate and normal seedling germination rate during the 360 days of evaluation. The method suitable for the seed storage of Tabebuia aurea is in the refrigerator at 13 degrees C, both in plastic and paper.

Quantitative phase analysis from X-ray diffraction in Y-TZP dental ceramics: A critical evaluation

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

Goppa codes over certain semigroups

A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.

Schur-Szegö composition of entire functions

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

Perfil hematológico de cabras Saanen e mestiças (1/2 Saanen e 1/2 Anglo-nubiana) criadas em clima tropical do Ceará

The aim of this study was to determine the influence of climatic conditions on the hematological profile of Saanen and mixed-breed (1/2 Saanen x 1/2 Anglo-Nubian) goats, as well as to define reference values for these animals bred in Ceara, Brazil. Thirty goats were utilized and blood samples were collected monthly during the rainy (February to May) and dry (August to November) periods to obtain an erythrogram a leukogram. The averange were compared by the t-Student test and Mann Whitney test, with parametric and non-parametric distribution of the data, respectively, where p<0.05 was considered significant. A study was carried out of simple Pearson correlations of the hematological parameters with environmental and physiological variables. The number of red blood cells (RBCs) was higher in the Saanen goats and in the rainy period, while the hematocrit was higher in the dry period (p<0.05). The leukocytes and lymphocytes were higher in the 1/2S1/2 AN goats in the two periods (p<0.05). In the two genotypes, the leukocytes and lymphocytes were higher in the dry season and the segmented neutrophils higher in the rainy season (p<0.05). The other parameters did not differ (p>0.05). The RBCs and segmented neutrophils displayed a negative correlation with air temperature, but positive with relative humidity and rectal temperature (p<0.05). The hematocrit positively correlated with air temperature and respiratory rate (p<0.05). The leukocytes and lymphocytes showed a negative correlation with rectal temperature (p<0.05). It was therefore concluded that Saanen females are more affected by climatic variations and that the rainy season has a greater negative impact on hematological parameters. The values obtained could serve as a reference for these genotypes in Ceara.

Reproductive efficiency of Nellore cows nursing Nellore or crossbred Simmental x Nellore calves

The objective of this study was to analyze the influence of genetic group (GG) of the calf during gestation, mobilization of body reserves and period of postpartum anestrus in Nellore cows. Thirty-seven primiparous and multiparous cows were used: 24 gave birth to Nellore (NEL), and 13 gave birth to 1/2 Simmental x 1/2 Nellore (SIM) calves. According to the date of calving, cows were divided into three blocks, with intervals of 20 days between blocks. The body condition (BC) of the cows was estimated subjectively on a scale from 0 to 5 points, with intermediate grading of 0.5 points. We measured the thickness of subcutaneous fat (SF) between the 12th and 13th ribs and rump by ultrasound. Blood samples from each cow were collected weekly from the third week after birth until weaning, to analyze the level of progesterone; in the samples collected until 16 weeks postpartum, we analyzed the concentration of nonesterified fatty acids(NEFA). The gestation period of mothers of NEL calves was eight days longer, on average. The variables relating to the mobilization of body reserves (NEFA, BC and SF) were not influenced by calf GG, with the only significant effects being the number of days postpartum, witha peak in the concentration of NEFA between the sixth and eighth weeks and linear decrease in BC and NF. Mothers of NEL calves remained in anestrus for 4.6 weeks longer than the mothers of crossbred calves.

A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Die Ekstase der alttestamentlichen Propheten

W. Jacobi