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.

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A linearly tunable low-voltage CMOS transconductor with improved common-mode stability and its application to (gm)-C filters

A linearly tunable low-voltage CMOS transconductor featuring a new adaptative-bias mechanism that considerably improves the stability of the processed-signal common,mode voltage over the tuning range, critical for very-low voltage applications, is introduced. It embeds a feedback loop that holds input devices on triode region while boosting the output resistance. Analysis of the integrator frequency response gives an insight into the location of secondary poles and zeros as function of design parameters. A third-order low-pass Cauer filter employing the proposed transconductor was designed and integrated on a 0.8-mum n-well CMOS standard process. For a 1.8-V supply, filter characterization revealed f(p) = 0.93 MHz, f(s) = 1.82 MHz, A(min) = 44.08, dB, and A(max) = 0.64 dB at nominal tuning. Mined by a de voltage V-TUNE, the filter bandwidth was linearly adjusted at a rate of 11.48 kHz/mV over nearly one frequency decade. A maximum 13-mV deviation on the common-mode voltage at the filter output was measured over the interval 25 mV less than or equal to V-TUNE less than or equal to 200 mV. For V-out = 300 mV(pp) and V-TUNE = 100 mV, THD was -55.4 dB. Noise spectral density was 0.84 muV/Hz(1/2) @1 kHz and S/N = 41 dB @ V-out = 300 mV(pp) and 1-MHz bandwidth. Idle power consumption was 1.73 mW @V-TUNE = 100 mV. A tradeoff between dynamic range, bandwidth, power consumption, and chip area has then been achieved.

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.

A method for plotting the complementary root locus using the root-locus (positive gain) rules

The root-locus method is a well-known and commonly used tool in control system analysis and design. It is an important topic in introductory undergraduate engineering control disciplines. Although complementary root locus (plant with negative gain) is not as common as root locus (plant with positive gain) and in many introductory textbooks for control systems is not presented, it has been shown a valuable tool in control system design. This paper shows that complementary root locus can be plotted using only the well-known construction rules to plot root locus. It can offer for the students a better comprehension on this subject. These results present a procedure to avoid problems that appear in root-locus plots for plants with the same number of poles and zeros.

On Complementary Root Locus of Biproper Transfer Functions

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

O sobre-sinal e a resposta inversa em sistemas de controle lineares contínuos no tempo

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

DIRECT EXPRESSIONS FOR OGATA LEAD-LAG DESIGN METHOD USING ROOT LOCUS

Direct expressions for the design of a lead-lag continuous compensator using the root locus method and the procedure described in the 1970 and 1990 books by Ogata are presented. These results are useful in the Ogata design method because they avoid the geometrical determination of poles and zeros, making it easier to create a computer-based design.

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

epresentação de linhas de transmissão por meio do modelo de bergeron: inclusão do efeito da frequência nos parâmetros longitudinais

Pós-graduação em Engenharia Elétrica - FEIS

Autoregressive decomposition and pole tracking applied to vocal fold nodule signals

This letter describes a novel algorithm that is based on autoregressive decomposition and pole tracking used to recognize two patterns of speech data: normal voice and disphonic voice caused by nodules. The presented method relates the poles and the peaks of the signal spectrum which represent the periodic components of the voice. The results show that the perturbation contained in the signal is clearly depicted by pole's positions. Their variability is related to jitter and shimmer. The pole dispersion for pathological voices is about 20% higher than for normal voices, therefore, the proposed approach is a more trustworthy measure than the classical ones. © 2007.

Posição e densidade dos zeros de Yang-Lee do modelo de Blume-Emery-Griffiths unidimensional sobre anéis conexos e desconexos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relacoes entre a concentracao espacial dos ramos industriais 'motrizes' e o desenvolvimento regional: o caso do Estado de Sao Paulo.

This paper, having its conceptual basis in the Theory of Growth Poles, by F.Perroux, tests the effective existence of correlation between the spatial incidence and concentration of the 'propulsive' industrial groups and the industrial growth as a whole and the demographic increase. The selected case study was the state of Sao Paulo and data used was the 1970 census. As consequence of the techniques applied a industrial regionalization of the 'paulista' space was obtained, showing few areas of intense industrial concentration, especially of 'propulsive' groups, with multiple growth poles, and large areas with industrial rarefaction, with little or no poles.-after English summary

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Planejamento e projeto de circuitos secundários de distribuição de energia elétrica por meio de algoritmo busca tabu

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)