A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Model approach for estimating potato pesticide bioconcentration factor

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

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic field processes in the mathematical modelling of damped transmission line vibrations

Wind-excited vibrations in the frequency range of 10 to 50 Hz due to vortex shedding often cause fatigue failures in the cables of overhead transmission lines. Damping devices, such as the Stockbridge dampers, have been in use for a long time for supressing these vibrations. The dampers are conveniently modelled by means of their driving point impedance, measured in the lab over the frequency range under consideration. The cables can be modelled as strings with additional small bending stiffness. The main problem in modelling the vibrations does however lay in the aerodynamic forces, which usually are approximated by the forces acting on a rigid cylinder in planar flow. In the present paper, the wind forces are represented by stochastic processes with arbitrary crosscorrelation in space; the case of a Kármán vortex street on a rigid cylinder in planar flow is contained as a limit case in this approach. The authors believe that this new view of the problem may yield useful results, particularly also concerning the reliability of the lines and the probability of fatigue damages. © 1987.

The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.

The stability of the Johnson-Mehl-Avrami equation parameters

The stability of the parameters of the Johnson-Mehl-Avrami equation was studied using two parametrizations of the sigmoidal function and its fit to some kinetic data. The results indicate that one of the forms of the function has more stable parameters and only for this form it is reasonable to use, as an approximation, the linear regression theory to analyse the parameters. © 1995 Chapman & Hall.

A recursive approach to space resection using straight lines

An approach using straight lines as features to solve the photogrammetric space resection problem is presented. An explicit mathematical model relating straight lines, in both object and image space, is used. Based on this model, Kalman Filtering is applied to solve the space resection problem. The recursive property of the filter is used in an iterative process which uses the sequentially estimated camera location parameters to feedback to the feature extraction process in the image. This feedback process leads to a gradual reduction of the image space for feature searching, and consequently eliminates the bottleneck due to the high computational cost of the image segmentation phase. It also enables feature extraction and the determination of feature correspondence in image and object space in an automatic way, i.e., without operator interference. Results obtained from simulated and real data show that highly accurate space resection parameters are obtained as well as a progressive processing time reduction. The obtained accuracy, the automatic correspondence process, and the short related processing time show that the proposed approach can be used in many real-time machine vision systems, making possible the implementation of applications not feasible until now.

Theoretical approaches to forensic entomology: II. Mathematical model of larval development

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

Global optimization approach for the H2-norm model reduction problem

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem for continuous-time linear systems, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through Linear Matrix Inequalities formulations. Examples illustrate the results.

Turning math attractive to computer science students: an application-to-model approach

This paper describes an innovative approach to develop the understanding about the relevance of mathematics to computer science. The mathematical subjects are introduced through an application-to-model scheme that lead computer science students to a better understanding of why they have to learn math and learn it effectively. Our approach consists of a single one semester course, taught at the first semester of the program, where the students are initially exposed to some typical computer applications. When they recognize the applications' complexity, the instructor gives the mathematical models supporting such applications, even before a formal introduction to the model in a math course. We applied this approach at Unesp (Brazil) and the results include a large reduction in the rate of students that abandon the college and better students in the final years of our program.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.