Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.

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.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

A dimension formula for reduced plethysms

The boson calculus formalism is used to construct realizations of basis states of irreducible representations of unitary groups taking as a paradigm the interacting boson models of atomic nuclei. These realizations, together with a theorem on plethysms for obtaining branching rules, allowed us to obtain a dimension formula for reduced plethysms. © 2005 IOP Publishing Ltd.

PID 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 plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. © 2005 IEEE.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Evaluating residues and integrals through negative dimensional integration method (NDIM)

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

Developing new radiotherapy techniques using linac based gamma radiation sources

A major challenge in cancer radiotherapy is to deliver a lethal dose of radiation to the target volume while minimizing damage to the surrounding normal tissue. We have proposed a model on how treatment efficacy might be improved by interfering with biological responses to DNA damage using exogenous electric fields as a strategy to drastically reduce radiation doses in cancer therapy. This approach is demonstrated at this Laboratory through case studies with prokaryotes (bacteria) and eukaryotes (yeast) cells, in which cellkilling rates induced by both gamma radiation and exogenous electric fields were measured. It was found that when cells exposed to gamma radiation are immediately submitted to a weak electric field, cell death increases more than an order of magnitude compared to the effect of radiation alone. This finding suggests, although does not prove, that DNA damage sites are reached and recognized by means of long-range electric DNA-protein interaction, and that exogenous electric fields could destructively interfere with this process. As a consequence, DNA repair is avoided leading to massive cell death. Here we are proposing the use this new technique for the design and construction of novel radiotherapy facilities associated with linac generated gamma beams under controlled conditions of dose and beam intensity.

A Influência da Referência de Tensão na Avaliação de Indicadores de Qualidade de Energia

This paper discusses the importance of the voltage referential for power quality monitoring and power systempsilas instrumentation. Considering the operating conditions of simple power circuits, it will be demonstrated that an incorrect choice of the voltages referential may result in erroneous quantification of some power quality indices, especially in three-phase four wire circuits. The use of a virtual reference point and the neutral conductor as reference have been considered and the simulation results confirm the influence of the voltage reference selection in the evaluation of total harmonic distortion, unbalance factors and voltage sags. Finally a way of linking both methods will be discussed by means of Blakesleypsilas theorem. © Copyright 2010 IEEE - All Rights Reserved.