An extremal nonnegative sine polynomial

For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each Pi 1 ≤ P ≤ ∞ and for any 27π-periodic function f ∈ Lp [-π, π], the sequence of convolutions Kn * f is proved to converge to f in Lp[-ππ]. The pointwise and almost everywhere convergences are also consequences of our construction.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Evaluation of the combined solar TiO2/photo-Fenton process using multivariate analysis

The effect of combining the photocatalytic processes using TiO 2 and the photo-Fenton reaction with Fe3+ or ferrioxalate as a source of Fe2+ was investigated in the degradation of 4-chlorophenol (4CP) and dichloroacetic acid (DCA) using solar irradiation. Multivariate analysis was used to evaluate the role of three variables: iron, H2O2 and TiO2 concentrations. The results show that TiO2 plays a minor role when compared to iron and H2O2 in the solar degradation of 4CP and DCA in the studied conditions. However, its presence can improve TOC removal when H2O2 is totally consumed. Iron and peroxide play major roles, especially when Fe(NO3)3 used in the degradation of 4CP. No significant synergistic effect was observed by the addition of TiO 2 in this process. On the other hand, synergistic effects were observed between FeOx and TiO2 and between H 2O2 and TiO2 in the degradation of DCA. © IWA Publishing 2004.

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.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Modelación para ajuste de la curva de lactación usando función lineal, no lineal y polinomios segmentados en ganados con alto grado de sangre Brown Swiss

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

Uso de polinômios segmentados para o estudo da curva de lactação de búfalos da raça Murrah e seus mestiços em sistema de criação semi-intensivo, no estado de São Paulo

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

Concerning the stability of BDF methods

We present an analysis of A0-stability of BDF methods and proof that zero-stable BDF methods are A0-stable using the Schur-Cohn criterion. With this result we have that zero-stable BDF methods are stiffly-stable. © 2008 American Institute of Physics.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Estimación de parámetros genéticos para la producción de leche en el día del control empleando un modelo de regresión aleatoria para primeras lactancias en búfalos de la costa norte de Colombia

A total of 5575 monthly test-day yield records from 796 lactations buffaloes first in the north coast of Colombia. The model included random direct additive genetic and permanent environment effects. As fixed effects were included, contemporary groups, and age of cow at calving as covaraible, linear and quadratic effects. Test-day (PLDC) yield was 3.89 ± 1.14 kg. The PLDC ranged from 2.86 kg to 4.26 kg while the highest values towards the middle of lactation. The heritability estimates obtained for PLDC ranged from 0.23 to 0.47. Genetic correlations between PLDC, declining steadily increased the distance between PLDC. Phenotypic variances were higher in the initial PLDC and decreasing towards the end of lactation. The results found in this study indicate that there is a high genetic variability for the PLDC in the population studied using a random regression model.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co)variances with age adequately and larger breeding value accuracies can be expected using this model. © South African Society for Animal Science.

Inversor CS Boost monofásico em aplicações com fontes renováveis

This paper presents a new methodology for the operation and control of a single-phase current-source (CS) Boost Inverter, considering that the conventional current-source inverter (CSI) has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the known non-minimum-phase effects. In this context, a special design with low boost inductance and a multi-loop control is developed in order to assure stable and very fast dynamics. Furthermore, the Inverter presents output voltage with very low total harmonic distortion (THD), reduced components and high power density. Therefore, this paper presents the inverter operation, the proposed control technique, and main simulation and experimental results in order to demonstrate the feasibility of the proposal. © 2010 IEEE.

Head and neck carcinogenesis: Impact of MTHFD1 G1958A polymorphism

Objective: To investigate the MTHFD1 G1958A polymorphism involved in the folate metabolism as a risk for head and neck cancer, and to find the association of the polymorphism with the risk factors and clinical and histopathological characteristics. Methods: Retrospective study investigating MTHFD1 G1958A polymorphism in 694 subjects (240 patients in the Case Group and 454 in the Control Group) by Restriction Fragment Length Polymorphism (RFLP) Analysis. Multiple logistic regression and chi-square tests were used in the statistical analysis. Results: Multivariable analysis showed that smoking and age over 42 years were disease predictors (p < 0.05). MTHFD1 1958GA or AA genotypes were associated with smoking (p = 0.04) and alcoholism (p = 0.03) and were more ofen found in more advanced stage tumors (p = 0.04) and in patients with a shorter survival (p = 0.03). Conclusion: Te presence of MTHFD1 G1948A polymorphism associated with smoking and alcoholism raises the head and neck cancer risk.

Evolución de las emisiones industriales potenciales en América Latina, 1970-2000

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