Sharp Turán inequalities via very hyperbolic polynomials

We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results may be considered as extensions of the classical Turán inequalities. © 2010 Elsevier Inc.

Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤apolynomials {Qn}, defined by ∫a bt-n+sQn(t)dψ(t)=0, s=0,1,⋯,n-1, is known to exist. We refer to these polynomials as the L-orthogonal polynomials with respect to the strong positive measure ψ. The purpose of this manuscript is to consider some properties of the kernel polynomials associated with these L-orthogonal polynomials. As applications, we consider the quadrature rules associated with these kernel polynomials. Associated eigenvalue problems and numerical evaluation of the nodes and weights of such quadrature rules are also considered. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.

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.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

Rumen microbial diversity under influence of a polyclonal antibody preparation against lactate-producing and proteolytic bacteria in cows fed different energy sources

Nine ruminally cannulated cows fed different energy sources were used to evaluate an avianderived polyclonal antibody preparation against specific ruminal bacteria and monensin on microbial community diversity. The experimental design was three Latin squares 3 x 3 distinguished by the main energy source in the diet [dry-ground corn grain, high moisture corn silage or citrus pulp]. Inside each Latin square, animals received one of the feed additives per period [control, monensin or polyclonal antibody preparation]. Each period lasted 21 days where 20 were used for treatments adaptation and the last one for sampling collection. Microbial diversity was evaluated by protozoa counts and denaturing gradient gel electrophoresis. Polyclonal antibodies plus citrus pulp (CiPu) addition in the diet resulted in an increase of relative counting of Isotricha protozoa that indicates a possible effect on this ruminal ciliate population. In general lines, in the present experiment, it was not possible to assign that there was a pattern in the structures of amplification of Bacteria and Archaea communities of the ruminal content. Oral passive immunization is a technology that arises as an effective alternative for feed additive production. Further research is still necessary to better understand its mechanisms of action.

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Address by Honourable D.F. Martina Prime Minister and Minister of General Affairs of the Netherlands Antilles at the inaugural ceremony of the CDCC Seventh Session, Monday 24 January 1983

Discurso del Primer Ministro de las Antillas Holandesas en el cual destaca la labor del CDCC como instrumento de los paises del Caribe para articular sus necesidades e intereses y coordinar sus relaciones y actividades para la cooperacion regional.

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Pulmonary and hepatic lesions caused by the dehydropyrrolizidine alkaloid-producing plants Crotalaria juncea and Crotalaria retusa in donkeys

The effects and susceptibility of donkeys to Crotalaria juncea and Crotalaria retusa poisoning were determined at high and low doses. Seeds of C. juncea containing 0.074% of dehydropyrrolizidine alkaloids (DHPAs) (isohemijunceines 0.05%, trichodesmine 0.016%, and junceine 0.008%) were administered to three donkeys at 0.3, 0.6 and 1g/kg body weight (g/kg) daily for 365 days. No clinical signs were observed and, on liver and lung biopsies, the only lesion was a mild liver megalocytosis in the donkeys ingesting 0.6 and 1g/kg/day. Two other donkeys that received daily doses of 3 and 5g seed/kg showed initial respiratory signs 70 and 40 days after the start of the administration, respectively. The donkeys were euthanized following severe respiratory signs and the main lung lesions were proliferation of Clara cells and interstitial fibrosis. Three donkeys ingested seeds of C. retusa containing 5.99% of monocrotaline at daily doses of 0.025, 0.05 and 0.1g/kg for 365 days. No clinical signs were observed and, on liver and lung biopsies, the only lesion was moderate liver megalocytosis in each of the three donkeys. One donkey that received a single dose of 5g/kg of C. retusa seeds and another that received 1g/kg daily for 7 days both showed severe clinical signs and died with diffuse centrilobular liver necrosis. No lung lesions were observed. Another donkey that received a single dose of 2.5g/kg of C. retusa seeds showed no clinical signs. The hepatic and pneumotoxic effects observed are consistent with an etiology involving DHPAs. Furthermore, the occurrence of lung or liver lesions correlates with the type of DHPAs contained in the seeds. Similarly as has been reported for horses, the data herein suggest that in donkeys some DHPAs are metabolized in the liver causing liver disease, whereas others are metabolized in the lung by Clara cells causing lung disease. © 2013 Elsevier Ltd.

Bacille Calmette-Guérin/DNAhsp65 prime-boost is protective against diabetes in non-obese diabetic mice but not in the streptozotocin model of type 1 diabetes

Type I diabetes is a disease caused by autoimmune destruction of the beta cells in the pancreas that leads to a deficiency in insulin production. The aim of this study was to evaluate the prophylactic potential of a prime-boost strategy involving bacille Calmette-Guérin (BCG) and the pVAXhsp65 vaccine (BCG/DNAhsp65) in diabetes induced by streptozotocin (STZ) in C57BL/6 mice and also in spontaneous type 1 diabetes in non-obese diabetic (NOD) mice. BCG/DNAhsp65 vaccination in NOD mice determined weight gain, protection against hyperglycaemia, decreased islet inflammation, higher levels of cytokine production by the spleen and a reduced number of regulatory T cells in the spleen compared with non-immunized NOD mice. In the STZ model, however, there was no significant difference in the clinical parameters. Although this vaccination strategy did not protect mice in the STZ model, it was very effective in NOD mice. This is the first report demonstrating that a prime-boost strategy could be explored as an immunomodulatory procedure in autoimmune diseases. © 2013 British Society for Immunology.

Soil and crop residue CO2-C emission under tillage systems in sugarcane-producing areas of southern Brazil

Appropriate management of agricultural crop residues could result in increases on soil organic carbon (SOC) and help to mitigate gas effect. To distinguish the contributions of SOC and sugarcane (Saccharum spp.) residues to the short-term CO2-C loss, we studied the infl uence of several tillage systems: heavy offset disk harrow (HO), chisel plow (CP), rotary tiller (RT), and sugarcane mill tiller (SM) in 2008, and CP, RT, SM, moldboard (MP), and subsoiler (SUB) in 2009, with and without sugarcane residues relative to no-till (NT) in the sugarcane producing region of Brazil. Soil CO2-C emissions were measured daily for two weeks after tillage using portable soil respiration systems. Daily CO2-C emissions declined after tillage regardless of tillage system. In 2008, total CO2-C from SOC and/or residue decomposition was greater for RT and lowest for CP. In 2009, emission was greatest for MP and CP with residues, and smallest for NT. SOC and residue contributed 47% and 41%, respectively, to total CO2-C emissions. Regarding the estimated emissions from sugarcane residue and SOC decomposition within the measurement period, CO2-C factor was similar to sugarcane residue and soil organic carbon decomposition, depending on the tillage system applied. Our approach may define new emission factors that are associated to tillage operations on bare or sugarcane-residue-covered soils to estimate the total carbon loss.

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.