A CHEBYSHEV-TYPE QUADRATURE RULE WITH SOME INTERESTING PROPERTIES

We give here an n-point Chebyshev-type rule of algebraic degree of precision n - 1, but having nodes that can be given explicitly. This quadrature rule also turns out to be one with an ''almost'' highest algebraic degree of precision.

Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials

Let C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the zeros of C-n(lambda)(x) enumerated in decreasing order. In this short note, we prove that, for any n is an element of N, the product (lambda + 1)(3/2)x(n1)(lambda) is a convex function of lambda if lambda greater than or equal to 0. The result is applied to obtain some inequalities for the largest zeros of C-n(lambda)(x). If X-nk(alpha), k = 1,...,n, are the zeros of Laguerre polynomial L-n(alpha)(x), also enumerated in decreasing order, we prove that x(n1)(lambda)/(alpha + 1) is a convex function of alpha for alpha > - 1. (C) 2002 Published by Elsevier B.V. B.V.

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

Intersubband plasmon-phonon modes in quantum wires at high temperatures

Coupled intersubband plasmon-phonon modes are studied in a multisubband parabolic quantum wire at room temperatures. These modes are found by calculating the spectral weight function which is related to the inelastic Raman spectra. We use a 13 subband model. The plasmon-phonon coupling strongly modifies the dispersion relation of the intersubband modes in the vicinity of the optical phonon frequency omega(LO). Extra modes show up as a result of the electron-phonon interaction. We carefully study the density and temperature dependence of these extra modes. We also show that coupled intersubband plasmon-phonon modes should be observed for temperatures as high as 300 K.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

Obtenção das distribuições de carga/massa e momentos no 'INTPOT. 4 HE' com o método de coordenadas geradoras

Pós-graduação em Física - IFT

Sentidos de percepção e educação matemática: geometria dinâmica e ensino de funções com auxílio de representações dinâmicas

Pós-graduação em Educação Matemática - IGCE

On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

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

Effects of a muscarinic type-2 antagonist on cardiorespiratory function and intestinal transit in horses anesthetized with halothane and xylazine

Objective-To evaluate the cardiorespiratory and intestinal effects of the muscarinic type-2 (M-2) antagonist, methoctramine, in anesthetized horses.Animals-6 horses.Procedure-Horses were allocated to 2 treatments in a randomized complete block design. Anesthesia was maintained with halothane (1% end-tidal concentration) combined with a constant-rate infusion of xylazine hydrochloride (1 mg/kg/h, IV) and mechanical ventilation. Hemodynamic variables were monitored after induction of anesthesia and for 120 minutes after administration of methoctramine or saline (0.9% NaCl) solution (control treatment). Methoctramine was given at 10-minute intervals (10 mug/kg, IV) until heart rate (HR) increased at least 30% above baseline values or until a maximum cumulative dose of 30 mug/kg had been administered. Recovery characteristics, intestinal auscultation scores, and intestinal transit determined by use of chromium oxide were assessed during the postanesthetic period.Results-Methoctramine was given at a total cumulative dose of 30 mug/kg to 4 horses, whereas 2 horses received 10 mug/kg. Administration of methoctramine resulted in increases in HR, cardiac output, arterial blood pressure, and tissue oxygen delivery. Intestinal auscultation scores and intestinal transit time (interval to first and last detection of chromium oxide in the feces) did not differ between treatment groups.Conclusions and Clinical Relevance-Methoctramine improved hemodynamic function in horses anesthetized by use of halothane and xylazine without causing a clinically detectable delay in the return to normal intestinal motility during the postanesthetic period. Because of their selective positive chronotropic effects, M-2 antagonists may represent a safe alternative for treatment of horses with intraoperative bracycardia.

Modelling energy utilization for laying type Pullets

Three trials were carried out to determine energy metabolized (EM) requirement model for starting and growing pullets from different strains, at five ambient temperatures and different percentage feather coverage. In Trial I, metabolizable energy requirements for maintenance (MEm) and efficiency of energy utilization were estimated using 64 birds of two different strains, Hy-Line W36 (HLW36) and Hy-Line Semi-heavy (HLSH), from 9 to 13 weeks of age. The effects of ambient temperature (12, 18, 24, 30 and 36ºC) and percentage feather coverage (0, 50 and 100%) on MEm were assessed in the second trial, using 48 birds per temperature per strain (HLSH and HLW36) from 9 to 13 weeks of age. Trial III evaluated ME requirements for weight gain (MEg) using 1,200 birds from two light strains (HLW36 and Hisex Light, HL) and two semi-heavy strains (HLSH and Hisex Semi-heavy, HSH) reared until 18 weeks of age. According to the prediction models, MEm changed as a function of temperature and feather coverage, whereas MEg changed as a function of age and bird strain. Thus, two models were developed for birds aged 1 to 6 weeks, one model for the light strain and one for the semi-heavy strain. Energy requirements (ER) were different among strains from 7 to 12 weeks, and therefore 4 models were elaborated. From 13 to 18 weeks, one single model was produced for semi-heavy birds, since ER between semi-heavy strains were not different, whereas two different models were elaborated for the light layers. MEg of light birds was higher than MEg of semi-heavy birds, independent of age.

Evaluation of Philips and Ziegler-Natta high-density polyethylene degradation during processing in an internal mixer using the chain scission and branching distribution function analysis

The oxidative and thermo-mechanical degradation of HDPE was studied during processing in an internal mixer under two conditions: totally and partially filled chambers, which provides lower and higher concentrations of oxygen, respectively. Two types of HDPEs, Phillips and Ziegler-Natta, having different levels of terminal vinyl unsaturations were analyzed. Materials were processed at 160, 200, and 240 degrees C. Standard rheograrns using a partially filled chamber showed that the torque is much more unstable in comparison to a totally filled chamber which provides an environment depleted of oxygen. Carbonyl and transvinylene group concentrations increased, whereas vinyl group concentration decreased with temperature and oxygen availability. Average number of chain scission and branching (n(s)) was calculated from MWD curves and its plotting versus functional groups' concentration showed that chain scission or branching takes place depending upon oxygen content and vinyl groups' consumption. Chain scission and branching distribution function (CSBDF) values showed that longer chains undergo chain scission easier than shorter ones due to their higher probability of entanglements. This yields macroradicals that react with the vinyl terminal unsaturations of other chains producing chain branching. Shorter chains are more mobile, not suffering scission but instead are used for grafting the macroradicals, increasing the molecular weight. Increase in the oxygen concentration, temperature, and vinyl end groups' content facilitates the thermo-mechanical degradation reducing the amount of both, longer chains via chain scission and shorter chains via chain branching, narrowing the polydispersity. Phillips HDPE produces a higher level of chain branching than the Ziegler-Natta's type at the same processing condition. (c) 2006 Elsevier Ltd. All rights reserved.

Weight vector estimation of circular arrays of antennas using Artificial Neural Networks

This paper presents a model for the control of the radiation pattern of a circular array of antennas, shaping it to address the radiation beam in the direction of the user, in order to reduce the transmitted power and to attenuate interference. The control of the array is based on Artificial Neural Networks (ANN) of the type RBF (Radial Basis Functions), trained from samples generated by the Wiener equation. The obtained results suggest that the objective was reached.

Grip and load force coordination in cyclical isometric manipulation task is not affected by the feedback type

Background: The relationship between normal and tangential force components (grip force - GF and load force - LF, respectively) acting on the digits-object interface during object manipulation reveals neural mechanisms involved in movement control. Here, we examined whether the feedback type provided to the participants during exertion of LF would influence GF-LF coordination and task performance. Methods. Sixteen young (24.7 ±3.8 years-old) volunteers isometrically exerted continuously sinusoidal FZ (vertical component of LF) by pulling a fixed instrumented handle up and relaxing under two feedback conditions: targeting and tracking. In targeting condition, FZ exertion range was determined by horizontal lines representing the upper (10 N) and lower (1 N) targets, with frequency (0.77 or 1.53 Hz) dictated by a metronome. In tracking condition, a sinusoidal template set at similar frequencies and range was presented and should be superposed by the participants' exerted FZ. Task performance was assessed by absolute errors at peaks (AEPeak) and valleys (AEValley) and GF-LF coordination by GF-LF ratios, maximum cross-correlation coefficients (r max), and time lags. Results: The results revealed no effect of feedback and no feedback by frequency interaction on any variable. AE Peak and GF-LF ratio were higher and rmax lower at 1.53 Hz than at 0.77 Hz. Conclusion: These findings indicate that the type of feedback does not influence task performance and GF-LF coordination. Therefore, we recommend the use of tracking tasks when assessing GF-LF coordination during isometric LF exertion in externally fixed instrumented handles because they are easier to understand and provide additional indices (e.g., RMSE) of voluntary force control. © 2013 Pedão et al.; licensee BioMed Central Ltd.