Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

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.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

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.

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.

Um modelo para orientação de imagens orbitais baseado em feições retas

The aim of this paper is to present a model for orientation of pushbroom sensors that allows estimating the polynomial coefficients describing the trajectory of the platform, using linear features as ground control. Considering that pushbroom image acquisition is not instantaneous, six EOP (Exterior Orientation Parameters) for each scanned line must be estimated. The sensor position and attitude parameters are modeled with a time dependent polynomial. The relationship between object and image space is established through a mathematical model based on the equivalence between the vector normal to the projection plane in the image space and to the vector normal to the rotated projection plane in the object space. The equivalence property between planes was adapted to consider the pushbroom geometry. Some experiments with simulated data corresponding to CBERS scene (China-Brazil Earth Resource Satellite) were accomplished in order to test the developed model using straight lines. Moreover, experiments with points ground with the model based on collinearity equations adapted to the pushbroom geometry were also accomplished. The obtained results showed that the proposed model can be used to estimate the EOP of pushbroom images with suitable accuracy.

Identification of structural parameters for active vibration control

The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.

Freezing point and thermal conductivity of tropical fruit pulps: Mango and papaya

The freezing point depression of mango and papaya pulps was measured by using a simple apparatus, consisting of two major sections: a freezing vessel and a data acquisition system. The thermal conductivity of both pulps as a function of frozen water fraction and temperature was also investigated by using a coaxial dual-cylinder apparatus. Thermal conductivity above the initial freezing point was well fitted by polynomial equations. Below the freezing point, the thermal conductivity was strongly affected by both the frozen water fraction and temperature. Simple equations in terms of frozen water fraction and temperature could be fitted to the experimental data of freezing point depression and thermal conductivity.

Qualidade fisiológica de sementes de Sebastiania commersoniana (Baill.) Smith & Downs (branquilho - Euphorbiaceae) durante o armazenamento

This paper aims to evaluate the physiological quality of Sebastiania commersoniana seeds stored in cloth bag, plastic bag and glass container and kept in two conditions: laboratory workbench and cold chamber (4 ± 2°C e 80% relative humidity - RH) for 531 days. Periodically, samples were taken in order to determine the moisture content and to perform germination tests. The experimental design was completely randomized, in factorial scheme of 3 × 2 (wrappings × conditions), for each period of storage evaluated (0, 158, 271, 389 and 531 days of storage). Supplementary, a polynomial regression was adjusted in order to describe the physiological quality of the seeds for the different conditions during the experimental period. The results lead to the following considerations: a) storage under variable temperature and air humidity (laboratory workbench) can be used for periods of over five and a half months, with the seeds stored in cloth bag, plastic bag or glass container; b) the physiological quality of the seeds was not hardly altered when stored in cold chamber in cloth bag, plastic bag and glass container for over 18 months.

Uso de modelos lineales y no lineales para el estudio de la curva de lactancia en búfalos Murrah y sus cruces en sistemas de cría extensiva en el estado de São Paulo

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

Radial basis function networks with quantized parameters

A RBFN implemented with quantized parameters is proposed and the relative or limited approximation property is presented. Simulation results for sinusoidal function approximation with various quantization levels are shown. The results indicate that the network presents good approximation capability even with severe quantization. The parameter quantization decreases the memory size and circuit complexity required to store the network parameters leading to compact mixed-signal circuits proper for low-power applications. ©2008 IEEE.

Calibration uncertainty estimation for internal aerodynamic balance

Aerodynamic balances are employed in wind tunnels to estimate the forces and moments acting on the model under test. This paper proposes a methodology for the assessment of uncertainty in the calibration of an internal multi-component aerodynamic balance. In order to obtain a suitable model to provide aerodynamic loads from the balance sensor responses, a calibration is performed prior to the tests by applying known weights to the balance. A multivariate polynomial fitting by the least squares method is used to interpolate the calibration data points. The uncertainties of both the applied loads and the readings of the sensors are considered in the regression. The data reduction includes the estimation of the calibration coefficients, the predicted values of the load components and their corresponding uncertainties, as well as the goodness of fit.

Testes de vigor para avaliação da qualidade fisiológica de sementesde Sebastiania commersoniana (Baill.) Smith & Downs.

The objective of this work was to evaluate the efficiency of different vigor tests to assess S. commersoniana seeds physiological quality during storage. Therefore, seeds were stored in cloth bags, plastic bags and glass containers for 531 days, both at room temperature and in a cold chamber. Periodically samples were taken and the following tests were conducted: standard germination, germination speed index, first count after germination, seedlings fresh and dry matter, electrical conductivity (imbibitions for 2 and 24 hours) and accelerated aging, in order to monitoring the seeds physiologic quality. Data were submitted to polynomial regression analysis, for each of the combination of packaging/storage condition. The results obtained led to the following considerations: a) the speed germination index and the accelerated aging test permitted a good evaluation of the seed-lots quality; b) the first count of germination did not allow any prediction about seed lots vigor; c) seedling fresh and dry matter did not discriminate among seed lots; d) electrical conductivity test after 2 h imbibitions was not adequate to evaluate the seed lots vigor and e) the electric conductivity test with 24 h imbibitions was more adequate to differentiate among seed lots, but with little efficiency to discriminate among seed lots with intermediate vigor or with low quality differences.

L(+) Lactic acid production by new Lactobacillus rhamnosus B 103

L(+) Lactic acid fermentation was studied by Lactobacillus rhamnosus sp. under the effects of pH control and a lowcost nutritional medium (sugarcane juice and corn steep liquor-CSL). Central composite design (CCD) was employed to determine maximum lactic acid production at optimum values for process variables and a satisfactory fit model was realized. Statistical analysis of the results showed that the linear and quadratic terms of two variables (sugarcane juice and pH) had significant effects. The interactions between the three variables were found to contribute to the response at a significant level. A second-order polynomial regression model estimated that the maximum lactic acid production of 86.36 g/L was obtained when the optimum values of sucrose, CSL and pH were 112.65 g/L, 29.88 g/L and 6.2, respectively. Verification of the optimization showed that L(+) lactic acid production was of 85.06 g/L. Under these conditions, Y P/S and Q P values of 0.85 g/g and 1.77 g/Lh, respectively, were obtained after 48 h fermentation, with a maximal productivity of 2.2 g/L h at 30 h of process. © 2010 de Lima CJB, et al.