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.

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.

Glicerina bruta na dieta de bovinos de corte confinados: Efeito sobre o hemograma

The aim of this study was to evaluate the hemogram in cattle fed crude glycerin. 30 Nellore steers, were used for blood sampling, which were done each 28 days. The animals were confined for 103 days and were fed with five diets containing 0, 7.5, 15, 22.5 and 30% crude glycerin based on dry matter, formulated in a forage:concentrate ratio of 30:70. Corn silage was used as forage and the concentrate was composed by corn grain, soybean hulls, sunflower meal, glycerin, limestone, dicalcium phosphate and salt. The experimental design was a randomized block with five treatments. Orthogonal contrasts were used to determine the linear, quadratic, cubic effects and gliceryn treatments × the control one. There was no treatment effect (P>0,05) on blood concentrations of erythrocytes, hematocrit, basophils, eosinophils, band neutrophils and lymphocytes, but were linearly effect on the concentrations of platelets, hemoglobin and monocytes (P=0.009, P=0.001 and P=0.043, respectivelly), and cubic effect on the concentrations of total leukocytes and segmented neutrophils (P=0.008 and P=0.004, respectivelly). Diets for beef cattle, with forage:concentrate ratio of 30:70 added with crude glycerin promote changes in the erytrhogram and leucogram of these animals.

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.

Sequential Sampling Plan for Tenuipalpus heveae Baker (Acari: Tenuipalpidae) on Rubber Tree

The objective of the present study was to develop a sequential sampling plan for the decision-making process to control Tenuipalpus heveae Baker (Acari: Tenuipalpidae), an important pest of the rubber tree crop. The experimental area was represented by 1,000 plants of the RRIM 600 clone divided in 100 plots with 10 plants each. Leaves were collected and the number of mites determined under laboratory conditions. The sequential sampling plan was developed in accordance with the Sequential Test Likelihood Ratio. The value 0.10 was pre-established for α and β representing type I and type II errors, respectively. The level of control adopted was six mites per 12 cm2. The operating characteristic curve and the curve of maximum expected sample were determined. Two lines were generated: the upper one, when the condition for chemical control is recommended (S1 = 23.3080 + 2.1972); and the lower, when chemical control is not recommended (S0 = -23.3080 + 2.1972). Sample size for the decision-making process to control T. heveae requires 6 to 18 plants. © 2013 Sociedade Entomológica do Brasil.

Global sampling reveals low genetic diversity within Compsopogon (Compsopogonales, Rhodophyta)

Twenty-five specimens of the freshwater red alga Compsopogon were collected from locations in North America, South America, Europe, Asia, Australasia and Oceania, and from an aquarium, with the goal of determining genetic diversity among specimens and ascertaining the number of phylogenetic species. Specimens were morphologically identified as having either the 'caeruleus' morphology, with regular polyhedral cortical cells, or the 'leptoclados' morphology, with irregular cortical cells with rhizoidal outgrowths. The 'leptoclados' morphology has been used by some researchers to distinguish the genus Compsopogonopsis from Compsopogon, or at least to distinguish C. leptoclados from other Compsopogon species. Sequence data for the rbcL gene and cox1 barcoding region were obtained for most specimens. In addition, SSU and partial LSU (barcode) rDNA were explored for a few specimens, but all sequences were identical. For the 25 newly generated and eight previously published rbcL gene data, there were seven unique haplotypes, but the sequence divergence was very low (≤7 bp, ≤ 0.7%). One haplotype was widespread, represented by 21 specimens from diverse locations in all regions sampled. Likewise, the 22 new and one previously published cox1 barcode region sequences yielded seven unique haplotypes with little sequence divergence (≤13 bp, ≤ 2.0%). One haplotype was widespread, being shared among 16 specimens from all regions. The combined molecular and morphological data showed no genetic differentiation between the 'caeruleus' and 'leptoclados' morphologies. The ubiquitous distribution of Compsopogon in tropical/subtropical regions and its low genetic variation are probably facilitated by the alga's ability to tolerate a wide range of stream conditions and its propagation via asexual spores. Given the findings of previous culture-based studies, morphometric research and field observations, coupled with the results of our study, we conclude there is only a single monospecific genus worldwide and that the species is correctly called C. caeruleus, since this is the oldest validly published name; all other previously described species of Compsopogon and Compsopogonopsis are synonyms. © 2013 British Phycological Society.

Influence of visual feedback sampling on obstacle crossing behavior in people with Parkinson's disease

The purpose of the current study was to investigate the role of visual information on gait control in people with Parkinson's disease as they crossed over obstacles. Twelve healthy individuals, and 12 patients with mild to moderate Parkinson's disease, walked at their preferred speeds along a walkway and stepped over obstacles of varying heights (ankle height or half-knee height), under three visual sampling conditions: dynamic (normal lighting), static (static visual samples, similar to stroboscopic lighting), and voluntary visual sampling. Subjects wore liquid crystal glasses for visual manipulation. In the static visual sampling condition only, the patients with Parkinson's disease made contact with the obstacle more often than did the control subjects. In the successful trials, the patients increased their crossing step width in the static visual sampling condition as compared to the dynamic and voluntary visual sampling conditions; the control group maintained the same step width for all visual sampling conditions. The patients showed lower horizontal mean velocity values during obstacle crossing than did the controls. The patients with Parkinson's disease were more dependent on optic flow information for successful task and postural stability than were the control subjects. Bradykinesia influenced obstacle crossing in the patients with Parkinson's disease. © 2013 Elsevier B.V.

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.

Evaluation of three sampling methods for the microbiological analysis of broiler carcasses after immersion chilling

Countries have different official programs and implement different sampling methods for the detection of Salmonella on poultry carcasses. In Brazil, a 25-g sample of skin and muscle excision (SME) from the wings, neck, and pericloacal parts is used; in the European Union (EU), a 25-g sample of neck skin (NSE) is used; and, in the United States, the whole carcass is rinsed with 400 ml of diluent (WCR). In the present study, these methods were evaluated to compare Salmonella occurrence and counts of hygiene indicator microorganisms (Escherichia coli, Enterobacteriaceae, and total viable count of aerobic mesophilic bacteria) using different carcasses from the same flock and also using different analytical units taken from the same carcass. Eighty flocks, with four broiler carcasses from each, were included in this study; three broilers were sampled according to protocols from Brazil, the EU, and the United States, and the last one by all three methods. SME, NSE, and WCR provided equivalent results (P > 0.05) for Salmonella detection on broiler carcasses when using different carcasses from the same flock and when using the same carcass. The predominant serovar was Salmonella Enteritidis. For the enumeration of hygiene indicator microorganisms, WRC provided higher counts than SME or NSE (P < 0.05), when using both the same or different carcasses. Therefore, it is possible to directly compare Salmonella results in poultry carcasses when using the methods recommended by the legislative bodies of Brazil, the United States, and the EU. However, WCR provides the best results for hygiene indicator microorganisms. Copyright © International Association for Food Protection.

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.

Multiple-trait random regression models for the estimation of genetic parameters for milk, fat, and protein yield in buffaloes

In this study, genetic parameters for test-day milk, fat, and protein yield were estimated for the first lactation. The data analyzed consisted of 1,433 first lactations of Murrah buffaloes, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, with calvings from 1985 to 2007. Ten-month classes of lactation days were considered for the test-day yields. The (co)variance components for the 3 traits were estimated using the regression analyses by Bayesian inference applying an animal model by Gibbs sampling. The contemporary groups were defined as herd-year-month of the test day. In the model, the random effects were additive genetic, permanent environment, and residual. The fixed effects were contemporary group and number of milkings (1 or 2), the linear and quadratic effects of the covariable age of the buffalo at calving, as well as the mean lactation curve of the population, which was modeled by orthogonal Legendre polynomials of fourth order. The random effects for the traits studied were modeled by Legendre polynomials of third and fourth order for additive genetic and permanent environment, respectively, the residual variances were modeled considering 4 residual classes. The heritability estimates for the traits were moderate (from 0.21-0.38), with higher estimates in the intermediate lactation phase. The genetic correlation estimates within and among the traits varied from 0.05 to 0.99. The results indicate that the selection for any trait test day will result in an indirect genetic gain for milk, fat, and protein yield in all periods of the lactation curve. The accuracy associated with estimated breeding values obtained using multi-trait random regression was slightly higher (around 8%) compared with single-trait random regression. This difference may be because to the greater amount of information available per animal. © 2013 American Dairy Science Association.

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.

Análise e síntese de um processador digital wavelet

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimization of the sampling scheme for maps of physical and chemical properties estimated by kriging

The sampling scheme is essential in the investigation of the spatial variability of soil properties in Soil Science studies. The high costs of sampling schemes optimized with additional sampling points for each physical and chemical soil property, prevent their use in precision agriculture. The purpose of this study was to obtain an optimal sampling scheme for physical and chemical property sets and investigate its effect on the quality of soil sampling. Soil was sampled on a 42-ha area, with 206 geo-referenced points arranged in a regular grid spaced 50 m from each other, in a depth range of 0.00-0.20 m. In order to obtain an optimal sampling scheme for every physical and chemical property, a sample grid, a medium-scale variogram and the extended Spatial Simulated Annealing (SSA) method were used to minimize kriging variance. The optimization procedure was validated by constructing maps of relative improvement comparing the sample configuration before and after the process. A greater concentration of recommended points in specific areas (NW-SE direction) was observed, which also reflects a greater estimate variance at these locations. The addition of optimal samples, for specific regions, increased the accuracy up to 2 % for chemical and 1 % for physical properties. The use of a sample grid and medium-scale variogram, as previous information for the conception of additional sampling schemes, was very promising to determine the locations of these additional points for all physical and chemical soil properties, enhancing the accuracy of kriging estimates of the physical-chemical properties.