Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Uses of QCD sumrules (QCDSR) from different points of view

We support the idea that the baryon, B with mass MB, couples to its current with a coupling λ2 B ∼ 0.71 M6 B from an analysis of magnetic moment sum rules. And we find a sum rule among the experimental magnetic moments which is independent of the parameters of QCDSR. © 1998 Elsevier Science B.V. All rights reserved.

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.

Health related quality of life measure in systemic pediatric rheumatic diseases and its translation to different languages: an international collaboration

Background: Rheumatic diseases in children are associated with significant morbidity and poor health-related quality of life (HRQOL). There is no health-related quality of life (HRQOL) scale available specifically for children with less common rheumatic diseases. These diseases share several features with systemic lupus erythematosus (SLE) such as their chronic episodic nature, multi-systemic involvement, and the need for immunosuppressive medications. HRQOL scale developed for pediatric SLE will likely be applicable to children with systemic inflammatory diseases.Findings: We adapted Simple Measure of Impact of Lupus Erythematosus in Youngsters (SMILEY (c)) to Simple Measure of Impact of Illness in Youngsters (SMILY (c)-Illness) and had it reviewed by pediatric rheumatologists for its appropriateness and cultural suitability. We tested SMILY (c)-Illness in patients with inflammatory rheumatic diseases and then translated it into 28 languages. Nineteen children (79% female, n= 15) and 17 parents participated. The mean age was 12 +/- 4 years, with median disease duration of 21 months (1-172 months). We translated SMILY (c)-Illness into the following 28 languages: Danish, Dutch, French (France), English (UK), German (Germany), German (Austria), German (Switzerland), Hebrew, Italian, Portuguese (Brazil), Slovene, Spanish (USA and Puerto Rico), Spanish (Spain), Spanish (Argentina), Spanish (Mexico), Spanish (Venezuela), Turkish, Afrikaans, Arabic (Saudi Arabia), Arabic (Egypt), Czech, Greek, Hindi, Hungarian, Japanese, Romanian, Serbian and Xhosa.Conclusion: SMILY (c)-Illness is a brief, easy to administer and score HRQOL scale for children with systemic rheumatic diseases. It is suitable for use across different age groups and literacy levels. SMILY (c)-Illness with its available translations may be used as useful adjuncts to clinical practice and research.

Inflection and stability points of diphasic logistic analysis of growth

Growth functions with inflection points following a diphasic model, can be adjusted by two approaches using segmented regression or the sum of two functions. In both cases, there are two functions, one for each phase, with inflection and stability points. However, when they are summed, the result is a new function and the points of inflection and stability are different from those obtained from using each function individually. A method to determine these points in a diphasic logistics sum of functions is suggested and the results obtained from fitting the models to eucalyptus growth data showed a better fit of the logistic diphasic sum as compared with segmented regression and monophasic logistic models.

Distances between critical points and midpoints of zeros of hyperbolic polynomials

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

The use of the challenge test to analyse preservative efficiency in non-sterile cosmetic and health products: applications and critical points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Concept of Matching Parallelepiped and its use in the correspondence problem

In this paper, the concept of Matching Parallelepiped (MP) is presented. It is shown that the volume of the MP can be used as an additional measure of `distance' between a pair of candidate points in a matching algorithm by Relaxation Labeling (RL). The volume of the MP is related with the Epipolar Geometry and the use of this measure works as an epipolar constraint in a RL process, decreasing the efforts in the matching algorithm since it is not necessary to explicitly determine the equations of the epipolar lines and to compute the distance of a candidate point to each epipolar line. As at the beginning of the process the Relative Orientation (RO) parameters are unknown, a initial matching based on gradient, intensities and correlation is obtained. Based on this set of labeled points the RO is determined and the epipolar constraint included in the algorithm. The obtained results shown that the proposed approach is suitable to determine feature-point matching with simultaneous estimation of camera orientation parameters even for the cases where the pair of optical axes are not parallel.

Development of a prototype for measuring plantar forces

Studies on the distribution of plantar pressure between the sole of the foot and the ground were developed before the 19th century. Currently, the most often employed plantar pressure measurement systems are Pedar® and FScan®, which have restrictions such as operational difficulty and high cost. In the present study, a device was constructed from two pressure plates capable of measuring plantar forces in discreet areas of the feet at a low cost, using strain-gages attached to sixteen strategic points of the mechanical elements. Sixteen prismatic beams were soldered to each frame, for which the free extremity of each beam represented a specific point of the foot. Two strain gauges were attached to each beam - one near the upper fixed extremity and the other near the lower fixed extremity. Using a Wheatstone bridge electric circuit, the gauges were used to measure the force acting on the extremity of the beam. Precision and accuracy of the prototype was about 10%. In some measurements, accuracy was 2%. The low precision and accuracy were mainly due to the restrictions of the available equipment, which only permitted four measurements at a time. Thus, it was necessary for participants to stand on the plates four separate times, which signified possible changes in the position of the feet on the pressure plates. Despite some limitations, the aim was achieved. The prototype has been used in some studies and represents a contribution to biomechanics, demonstrating the viability of using strain gauges.

Coupling rate measurement of a novel multi-actuated piezoelectric device using optical interferometry

The class of piezoelectric actuators considered in this paper consists of a multi-flexible structure actuated by two or more piezoceramic devices that must generate different output displacements and forces at different specified points of the domain and in different directions. The devices were modeled by finite element using the software ANSYS and the topology optimization method. The following XY actuators were build to achieve maximum displacement in the X and Y directions with a minimum crosstalk between them. The actuator prototypes are composed of an aluminum structure, manufactured by using a wire Electrical Discharge Machining, which are bonded to rectangular PZT5A piezoceramic blocks by using epoxy resin. Multi-actuator piezoelectric device displacements can be measured by using optical interferometry, since it allows dynamic measurements in the kHz range, which is of the order of the first resonance frequency of these piezomechanisms. A Michelson-type interferometer, with a He-Ne laser source, is used to measure the displacement amplitudes in nanometric range. A new optical phase demodulation technique is applied, based on the properties of the triangular waveform drive voltage applied to the XY piezoelectric nanopositioner. This is a low-phase-modulation-depth-like technique that allows the rapid interferometer auto-calibration. The measurements were performed at 100 Hz frequency, and revealed that the device is linear voltage range utilized in this work. The ratio between the generated and coupled output displacements and the drive voltages is equal to 10.97 nm/V and 1.76 nm/V, respectively, which corresponds to a 16% coupling rate. © 2010 IEEE.

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants.

Extensive computation of albedo contrast between martian dust devil tracks and their neighboring regions

We have developed a method to compute the albedo contrast between dust devil tracks and their surrounding regions on Mars. It is mainly based on Mathematical Morphology operators and uses all the points of the edges of the tracks to compute the values of the albedo contrast. It permits the extraction of more accurate and complete information, when compared to traditional point sampling, not only providing better statistics but also permitting the analysis of local variations along the entirety of the tracks. This measure of contrast, based on relative quantities, is much more adequate to establish comparisons at regional scales and in multi-temporal basis using imagery acquired in rather different environmental and operational conditions. Also, the substantial increase in the details extracted may permit quantifying differential depositions of dust by computing local temporal fading of the tracks with consequences on a better estimation of the thickness of the top most layer of dust and the minimum value needed to create dust devils tracks. The developed tool is tested on 110 HiRISE images depicting regions in the Aeolis, Argyre, Eridania, Noachis and Hellas quadrangles. As a complementary evaluation, we also performed a temporal analysis of the albedo in a region of Russell crater, where high seasonal dust devil activity was already observed before, comprising the years 2007-2012. The mean albedo of the Russell crater is in this case indicative of dust devil tracks presence and, therefore, can be used to quantify dust devil activity. (C) 2014 Elsevier Inc. All rights reserved.

Evaluation of the double agar gel immunodiffusion test and of the enzyme-linked immunosorbent assay in the diagnosis and follow-up of patients with chronic pulmonary aspergillosis

Coordenação de Aperfeiçoamento do Pessoal de Nível Superior (CAPES)