Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

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.

Higher order turán inequalities for the Riemann ξ-function

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

Orbit determination using GPS including perturbations due to geopotential coefficients of high degree and order and solar radiation pressure

The main target here is to determine the orbit of an artificial satellite, using signals of the GPS constellation and least squares algorithms implemented through sequential Givens rotations as a method of estimation, with the aim of improving the performance of the orbit estimation process and, at the same time, minimizing the computational procedure cost. Geopotential perturbations up to high order and direct solar radiation pressure were taken into account. It was also considered the position of the GPS antenna on the satellite body that, lately, consists of the influence of the satellite attitude motion in the orbit determination process. An application has been done, using real data from the Topex/Poseidon satellite, whose ephemeris is available at Internet. The best accuracy obtained in position was smaller than 5 meters for short period (2 hours) and smaller than 28 meters for long period (24 hours) orbit determination. In both cases, the perturbations mentioned before were taken into consideration and the analysis occurred without selective availability on the signals measurements.

Connection coefficients and zeros of orthogonal polynomials

We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.

The Q-D algorithm for transforming series expansions into a corresponding continued fraction: an extension to cope with zero coefficients

An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

The hierarchical model of branch planning with random coefficients

We consider the management branch model where the random resources of the subsystem are given by the exponential distributions. The determinate equivalent is a block structure problem of quadratic programming. It is solved effectively by means of the decomposition method, which is based on iterative aggregation. The aggregation problem of the upper level is resolved analytically. This overcomes all difficulties concerning the large dimension of the main problem.

Osmotic dehydration of apples in sugar/salt solutions: Concentration profiles and effective diffusion coefficients

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

Friction factors, convective heat transfer coefficients and the Colburn analogy for industrial sugarcane juices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effective diffusion coefficients behavior in osmotic dehydration of apple slices considering shrinking and local concentration dependence

The mass transfer during osmotic dehydration of apple slices immersed in 40, 50 and 60% (w/w) aqueous sucrose solutions was investigated to evaluate the influence of solution concentration on diffusivities. In the mathematical model, the diffusion coefficients were functions of the local water and sucrose concentration. The mass transfer equations were, simultaneously, solved for water and sucrose using an implicit numerical method. Material coordinates following the shrinkage of the solid were used. The predicted concentration profiles were integrated and compared to experimental data, showing a reasonable agreement with the measured data. on average, the effective diffusion coefficients for water and sucrose decreased as the osmotic solution concentration increased; that is the behavior of the binary coefficients in water-sucrose solutions. However, the diffusivities expressed as a function of the local concentration in the slices varied between the treatments. Water diffusion coefficients showed a remarkable variation throughout the slice and unusual behavior, which was associated to the cellular structure changes observed in tissue immersed in osmotic solutions. Cell structure changes occurred in different ways: moderate plasmolysis at 40%, accentuated plasmolysis at 50% and generalized damage of the cells at 60%. Intact vacuoles were observed after a long time of exposure (30 h) to 40 and 50% solutions. Effects of the concentration on tissue changes make it difficult to generalize the behavior of diffusion coefficients.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Antimony orthophosphate glasses with large nonlinear refractive indices, low two-photon absorption coefficients, and ultrafast response

Antimony glasses based on the composition Sb2O3-SbPO4 were prepared and characterized. The samples present high refractive index, good transmission from 380 to 2000 nm, and high thermal stability. The nonlinear refractive index, n(2), of the samples was studied using the optical Kerr shutter technique at 800 nm. The third-order correlation signals between pump and probe pulses indicate ultrafast response (<100 fs) for all compositions. Enhancement of n(2) was observed by adding lead oxide to the Sb2O3-SbPO4 composition. Large values of n(2)approximate to10(-14) cm(2)/W and negligible two-photon absorption coefficients (smaller than 0.01 cm/GW) were determined for all samples. The glass compositions studied present appropriate figure-of-merit for all-optical switching applications. (C) 2005 American Institute of Physics.