Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Characterization of generalized Bessel polynomials in terms of polynomial inequalities

Generalized Bessel polynomials (GBPs) are characterized as the extremal polynomials in certain inequalities in L-2 norm of Markov type. (C) 1998 Academic Press.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of detector motion in Bell inequalities with entangled fermions

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

Behavioral and biological correlates of medicine use in type 2 diabetic patients attended by Brazilian public healthcare system

A relação entre atividade física e consumo de medicamentos não é clara. Assim, o objetivo do estudo foi investigar a relação entre nível de atividade física e uso de medicamentosem diabéticos tipo 2 atendidos pelo Sistema Único de Saúde. A amostra foi composta por 121 diabéticos do tipo 2 de ambos os sexos atendidos pelos sistema público de saúde. Gordura corporal (antropometria e bioimpedância elétrica), atividade física (Questionário de Baecke) e uso de medicamentos (15 dias prévios a avaliação) foram avaliados. Houve relação entre uso de medicamentos e sexo (r = 0.18; p = 0.045), índice de massa corporal (r = 0.22; p = 0.012), circunferência de cintura (r = 0.19; p = 0.029), percentual de gordura (r = 0.21; p = 0.016), idade (r = 0.23; p = 0.009) e atividade física (r = -0.22; p = 0.012). A regressão linear incluiu no modelo apenas idade (β = 0.718; p = 0.057), IMC BMI (β = 0.057; p = 0.022) e atividade física (β = -0.176; p = 0.044) no modelo multivariado. Conclui-se que a prática de atividade física diminui uso de medicamentos independente da idade e obesidade.

Hipertensão arterial em idosos: prevalência, fatores associados e práticas de controle no Município de Campinas, São Paulo, Brasil

Este estudo teve como objetivo avaliar a prevalência da hipertensão arterial referida em idosos de Campinas, São Paulo, Brasil, identificando os fatores associados, o uso de serviços de saúde e o conhecimento e as práticas quanto às opções do tratamento. Trata-se de estudo transversal, de base populacional, com amostra de conglomerados, estratificada e em múltiplos estágios. A análise dos dados referentes aos 426 indivíduos (sessenta anos e mais) levou em conta o desenho amostral e o efeito do delineamento. A prevalência de hipertensão foi de 51,8% (46,4% nos homens e 55,9% nas mulheres) e mostrou-se mais elevada em idosos: com menor escolaridade (55,9%), migrantes de outros estados (60,2%) e com sobrepeso ou obesidade (57,2%). Os resultados indicam que os serviços de saúde estão garantindo o acesso ao atendimento médico (71,6% visitam o médico regularmente) e aos medicamentos (86,7% tomam medicamento de rotina), sem distinção de nível sócio-econômico. Persistem, no entanto, desigualdades sociais quanto ao conhecimento e utilização de outras práticas de controle da pressão arterial, como dieta adequada e atividade física, que são insuficientemente utilizadas também pelos segmentos socialmente mais favorecidos.

Fatores associados à realização dos exames de rastreamento para o câncer de próstata: um estudo de base populacional

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

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

Surveillance Programme for Healthcare Associated Infections in the State of São Paulo, Brazil. Implementation and the first three years' results

Governmental programmes should be developed to collect and analyse data on healthcare associated infections (HAIs). This study describes the healthcare setting and both the implementation and preliminary results of the Programme for Surveillance of Healthcare Associated Infections in the State of São Paulo (PSHAISP), Brazil, from 2004 to 2006. Characterisation of the healthcare settings was carried out using a national database. The PSHAISP was implemented using components for acute care hospitals (ACH) or long term care facilities (LTCF). The components for surveillance in ACHs were surgical unit, intensive care unit and high risk nursery. The infections included in the surveillance were surgical site infection in clean surgery, pneumonia, urinary tract infection and device-associated bloodstream infections. Regarding the LTCF component, pneumonia, scabies and gastroenteritis in all inpatients were reported. In the first year of the programme there were 457 participating healthcare settings, representing 51.1% of the hospitals registered in the national database. Data obtained in this study are the initial results and have already been used for education in both surveillance and the prevention of HAI. The results of the PSHAISP show that it is feasible to collect data from a large number of hospitals. This will assist the State of São Paulo in assessing the impact of interventions and in resource allocation. (C) 2010 The Hospital Infection Society. Published by Elsevier Ltd. All rights reserved.

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.

Bell inequalities for entangled pairs of neutral kaons

We extend the use of Bell inequalities to Φ → K0K̄0 decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a CP-violating Hamiltonian. © 1999 The American Physical Society.

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.

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.

Robust control to parametric uncertainties in smart structures using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft and aerospace structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.