Szego type polynomials and para-orthogonal polynomials

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

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

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

Electronic spectra, ESR and crystal structure of tetrahedral halocuprates(II). The existence of cations (2tbpo·H+) with a very short hydrogen bond

Two compounds [2tbpo·H+)2[CuCl4]= (yellow) and (2tbpo·H+)2[CuBr4]= (dark purple) (tbpo = tribenzylphosphine oxide) have been prepared and investigated by means of crystal structure, electronic, vibrational and ESR spectra. The crystal structure of the (2tbpo·H+)2[CuCl4]= complex was determined by three-dimensional X-ray diffraction. The compound crystallizes in the space group P42/n with unit-cell dimensions a = 19.585(2), c = 9.883(1)Å, V = 3790 (1)Å3, Z = 2, Dm = 1.303 (flotation) Dx = 1.302 Mg m-3. The structure was solved by direct methods and refined by blocked full-matrix least-squares to R = 0.053 for 2583 observed reflections. Cu(II) is coordinated to four chlorides in a tetrahedral arrangement. Tribenzylphosphine oxide molecules, related by a centre of inversion, are connected by a short hydrogen bridge. Chemical analysis, electronic and vibrational spectra showed that the bromide compound is similar to the chloride one and can be formulated as (2tbpo·H+)2[CuBr4]=. The position of the dd transition bands, the charge transfer bands, the ESR and the vibrational spectra of both complexes are discussed. The results are compared with analogous complexes cited in the literature. © 1983.

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.

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

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

Hamiltonian reduction and the construction of q-deformed extensions of the Virasoro algebra

In this paper we employ the construction of the Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-Wess-Zumino-Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

Nonlinear short-wave propagation in ferrites

In this paper we discuss the propagation of nonlinear electromagnetic short waves in ferromagnetic insulators. We show that such propagation is perpendicular to an externally applied field. In the nonlinear regime we determine various possible propagation patterns: an isolated pulse, a modulated sinusoidal wave, and an asymptotic two-peak wave. The mathematical structure underlying the existence of these solutions is that of the integrable sine-Gordon equation.

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.

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.

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect

A theoretic-oriented strategy was taken to address the weak decay of uniformly accelerated protons. The decay of uniformly accelerated p+'s was analyzed using standard quantum field theory (QFT). It was shown that the FDU effect is essential to reproduce the proper decay rate in the uniformly accelerated frame.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Classes of exact wave functions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

The construction of two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions was discussed. The extension of solutions by introduction of a time-dependent mass was elaborated. The possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions was also analyzed.

Mathematical optimisation techniques applied to power system operation and planning

Nowadays, power system operation becomes more complex because of the critical operating conditions resulting from the requirements of a market-driven operation. In this context, efficient methods for optimisation of power system operation and planning become critical to satisfy the operational (technical), financial and economic demands. Therefore, the detailed analysis of modern optimisation techniques as well as their application to the power system problems represent a relevant issue from the scientific and technological points of view. This paper presents a brief overview of the developments on modern mathematical optimisation methods applied to power system operation and planning. Copyright © 2007 Inderscience Enterprises Ltd.