Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Assessment of surface water in two Amazonian rivers impacted by industrial wastewater, Barcarena City, Pará State (Brazil)

No ano de 2007, águas superficiais foram coletadas a partir de 21 pontos de amostragem na cidade de Barcarena, Região Norte, Brasil: um ponto de amostragem localizado em um pequeno córrego que recebe descarga de resíduos a partir da indústria de beneficiamento do caulim e deságua no Rio Curuperê, três pontos de amostragens localizados próximos de fontes que emergem na margem esquerda e deságuam no Rio Curuperê, nove pontos de amostragem no Rio Curuperê, que deságua no Rio Dendê, e oito no Rio Dendê, afluente da margem esquerda do Rio Pará. Para todas as amostras de água foram quantificadas 14 variáveis físico-químicas e níveis de 12 metais. Os resultados nos pontos próximos das fontes do Rio Curuperê apresentaram perfil físico-químico e níveis de metais típicos para águas superficiais e esses valores foram utilizados como referência para comparar e identificar possíveis alterações nas características químicas para os demais pontos de amostragem. Quando os resultados das fontes do rio Curuperê foram comparados com os resultados do ponto próximo a descarga de resíduos industriais foram observadas fortes alterações nos valores de 6 variáveis físico-químicas (pH, condutividade elétrica (EC), total de sólidos suspensos (TDS), nitrogênio amoniacal (N-NH4), sulfato (SO4) e salinidade) e aumento em magnitude dos níveis de quatro metais (Al, Fe, Mn e Zn), caracterizando que esses resíduos eram descarregados no ambiente sem tratamentos adequados. Os resultados nos demais pontos de amostragem demonstraram que estas condições anômalas também foram encontradas ao longo dos Rios Curuperê e Dendê, principalmente durante a maré baixa. A partir desta caracterização química das águas foram identificadas condições prejudiciais aos ecossistemas aquáticos e potencial risco à saúde da população local que usa os rios para consumo, recreação e transporte.

Lipid profile and cardiovascular risk in two Amazonian populations

OBJETIVO: Comparar o perfil lipídico e risco coronariano de uma população ribeirinha (Vigia) ao de uma população urbana (Belém). MÉTODOS: Foram avaliados 50 indivíduos de cada região, controlados por idade e sexo, examinando-se os principais fatores de risco para a doença coronariana. RESULTADOS: Segundo o Programa Nacional de Educação sobre o Colesterol (NCEP III) e determinando-se o escore de Framingham, ambas as populações expressaram o mesmo risco absoluto de eventos (Vigia 5,4 ± 1 vs. Belém 5,7 ± 1), a despeito da população de Vigia apresentar menor consumo de gordura saturada (p<0,0001), maior de mono e poliinsaturada (p<0,03), além de menores valores do índice de massa corpórea (25,4±0,6 vs. 27,6±0,7kg/m², p<0,02), da prega biceptal (18,6±1,1 vs. 27,5±1,3mm, p<0,0001) e triceptal (28,7±1,2 vs. 37,3±1,7mm, p<0,002), de colesterol total (205±5 vs. 223±6mg/dL, p< 0,03) e triglicérides (119 ± 9 vs. 177±18mg/dL, p<0,005), não diferindo no HDL-c (46±1 vs. 46±1mg/dL), LDL-c (135 ± 4 vs. 144 ± 5mg/dL) e pressão arterial (PAS 124 ± 3 vs. 128 ± 3mmHg; PAD 80 ± 2 vs. 82 ± 2mmHg). CONCLUSÃO: A população ribeirinha e urbana da Amazônia apresentaram risco cardiovascular semelhante. Entretanto, a marcante diferença entre as variáveis estudadas sugere que devam ser aplicadas diferentes estratégias de prevenção.

Risk factors for perinatal death in two different levels of care: a case-control study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The relationship between leaf nitrogen, nitrogen metabolites and herbivory in two species of Nyctaginaceae from the Brazilian Cerrado

Guapira graciliflora and Neea theifera are taxonomically related species of the tribe Pisoneae. Both species are found in the same environment, the Brazilian Cerrado, and therefore, are subjected to similar selective pressures. These species occur in oligotrophic environments, yet contain high concentrations of nitrogen in their leaves. The present study was carried out to investigate the ecological role of nitrogen in herbivory on these species. The differences in the N content, compositions of secondary N-metabolites, mechanical resistance, and water content between their leaves indicate that these species have different adaptations as defense mechanisms. In both species, their high nitrogen content seems to promote herbivory. The presence of secondary nitrogen metabolites does not prevent the species from suffering intense damage by herbivores on their early leaves. The herbivory rates observed were lower for mature leaves of both species than for young leaves. In G. graciliflora, nutritional content and leaf hardness are the most important variables correlated with reduction of herbivory rates, whereas in N. theifera, N compounds are also correlated with herbivory rates. Despite the differences in the strategies of these two species, they exhibit a similar efficiency of protection against natural enemies because their total herbivory rates are similar. The difference in their N defense allocation may imply benefits for survival under Cerrado conditions. We briefly discuss the oligotrophic habitat conditions of the studied plants and possible advantages of their strategies of N accumulation and metabolic uses. (C) 2011 Elsevier B.V. All rights reserved.

Surface-acoustic-wave counterflow micropumps for on-chip liquid motion control in two-dimensional microchannel arrays

Fully controlled liquid injection and flow in hydrophobic polydimethylsiloxane (PDMS) two-dimensional microchannel arrays based on on-chip integrated, low-voltage-driven micropumps are demonstrated. Our architecture exploits the surface-acoustic-wave (SAW) induced counterflow mechanism and the effect of nebulization anisotropies at crossing areas owing to lateral propagating SAWs. We show that by selectively exciting single or multiple SAWs, fluids can be drawn from their reservoirs and moved towards selected positions of a microchannel grid. Splitting of the main liquid flow is also demonstrated by exploiting multiple SAW beams. As a demonstrator, we show simultaneous filling of two orthogonal microchannels. The present results show that SAW micropumps are good candidates for truly integrated on-chip fluidic networks allowing liquid control in arbitrarily shaped two-dimensional microchannel arrays.

Proposal of an Alternative Model for Speed-Flow Relationship in Two-Lane Highways

A research has been carried out in two-lanehighways in the Madrid Region to propose an alternativemodel for the speed-flowrelationship using regular loop data. The model is different in shape and, in some cases, slopes with respect to the contents of Highway Capacity Manual (HCM). A model is proposed for a mountainous area road, something for which the HCM does not provide explicitly a solution. The problem of a mountain road with high flows to access a popular recreational area is discussed, and some solutions are proposed. Up to 7 one-way sections of two-lanehighways have been selected, aiming at covering a significant number of different characteristics, to verify the proposed method the different classes of highways on which the Manual classifies them. In order to enunciate the model and to verify the basic variables of these types of roads a high number of data have been used. The counts were collected in the same way that the Madrid Region Highway Agency performs their counts. A total of 1.471 hours have been collected, in periods of 5 minutes. The models have been verified by means of specific statistical test (R2, T-Student, Durbin-Watson, ANOVA, etc.) and with the diagnostics of the contrast of assumptions (normality, linearity, homoscedasticity and independence). The model proposed for this type of highways with base conditions, can explain the different behaviors as traffic volumes increase, and follows a polynomial multiple regression model of order 3, S shaped. As secondary results of this research, the levels of service and the capacities of this road have been measured with the 2000 HCM methodology, and the results discussed. © 2011 Published by Elsevier Ltd.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Numerical quadrature over a rectangular domain in two or more dimensions /

"This work was supported in part by the Office of Naval Research under Contract Nonr-1834(27)."