Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤aorthogonal polynomials with respect to the strong positive measure ψ. The purpose of this manuscript is to consider some properties of the kernel polynomials associated with these L-orthogonal polynomials. As applications, we consider the quadrature rules associated with these kernel polynomials. Associated eigenvalue problems and numerical evaluation of the nodes and weights of such quadrature rules are also considered. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

Tri-state Space Vector Modulation for Three-phase integrated inverters

The aim of this work is to present a modified Space Vector Modulation (SVM) suitable for Tri-state Three-phase inverters. A standard SVM algorithm and the Tri-state PWM (Pulse Width Modulation) are presented and their concept are mixed into the novel SVM. The proposed SVM is applied to a three-phase tri-state integrated Boost inverter, intended to Photovoltaic Energy Applications. The main features for this novel SVM are validated through simulations and also by experimental tests. The obtained results prove the feasibility of the proposal. © 2011 IEEE.

Integrated single-stage converters with Tri-state modulation suitable for photovoltaic systems

The aim of this work is to present two topological simplified converters named Tri-state Boost and Tri-state Buck-Boost integrated single-phase inverters. An important operation capability can be achieved for these converters using a Tri-state Modulation control scheme. This is the inductive power decoupling and the independent input output control. These features are directly related with the photovoltaic micro-converter needs, improving efficiency, cost and mainly lifetime. These features for the proposed modulation are confirmed through experimental results. © 2011 IEEE.

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Myenteric denervation in gastric carcinogenesis: Differential modulation of nitric oxide and annexin-A1

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

Strain- and electric field-induced band gap modulation in nitride nanomembranes

The hexagonal nanomembranes of the group III-nitrides are a subject of interest due to their novel technological applications. In this paper, we investigate the strain- and electric field-induced modulation of their band gaps in the framework of density functional theory. For AlN, the field-dependent modulation of the bandgap is found to be significant whereas the strain-induced semiconductor-metal transition is predicted for GaN. A relatively flat conduction band in AlN and GaN nanomembranes leads to an enhancement of their electronic mobility compared to that of their bulk counterparts. © 2013 IOP Publishing Ltd.

A fast cholinergic modulation of the primary acoustic startle circuit in rats

Cochlear root neurons (CRNs) are the first brainstem neurons which initiate and participate in the full expression of the acoustic startle reflex. Although it has been suggested that a cholinergic pathway from the ventral nucleus of the trapezoid body (VNTB) conveys auditory prepulses to the CRNs, the neuronal origin of the VNTB-CRNs projection and the role it may play in the cochlear root nucleus remain uncertain. To determine the VNTB neuronal type which projects to CRNs, we performed tract-tracing experiments combined with mechanical lesions, and morphometric analyses. Our results indicate that a subpopulation of non-olivocochlear neurons projects directly and bilaterally to CRNs via the trapezoid body. We also performed a gene expression analysis of muscarinic and nicotinic receptors which indicates that CRNs contain a cholinergic receptor profile sufficient to mediate the modulation of CRN responses. Consequently, we investigated the effects of auditory prepulses on the neuronal activity of CRNs using extracellular recordings in vivo. Our results show that CRN responses are strongly inhibited by auditory prepulses. Unlike other neurons of the cochlear nucleus, the CRNs exhibited inhibition that depended on parameters of the auditory prepulse such as intensity and interstimulus interval, showing their strongest inhibition at short interstimulus intervals. In sum, our study supports the idea that CRNs are involved in the auditory prepulse inhibition of the acoustic startle reflex, and confirms the existence of multiple cholinergic pathways that modulate the primary acoustic startle circuit. © 2013 Springer-Verlag Berlin Heidelberg.

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.

Simvastatin treatment increases nitrite levels in obese women: Modulation by T-786C polymorphism of eNOS

Objective and Subjects: Evidence indicates an impairment of nitric oxide (NO) in obesity. Statins present pleiotropic effects independently of cholesterol-lowering, including increasing of eNOS expression and antioxidant effects. We evaluated the effects of simvastatin treatment at 45 days on circulating nitrite (NO marker) and TBARS-MDA levels in obese women without comorbidities (hypertension, diabetes and dyslipidemia). Moreover, we verified whether obese women carrying the C variant of T-786C polymorphism located in eNOS may have increased levels of nitrite after treatment compared to TT genotype. Results: After simvastatin treatment, while the plasma nitrite levels increased 42% (P = 0.0008), the TBARS-MDA levels reduced 58% (P = 0.0069). We observed increased levels of nitrite in both groups of genotypes (TT vs. TC + CC); however, rise in C-allele carriers was 60% comparing with 44% in TT. Conclusion: Our results demonstrated a restoration of nitrite levels in obese women treated with simvastatin, which is modulated by T-786C polymorphism. © 2013 Elsevier Inc. All rights reserved.

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.

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.

Modulation of nociceptive-like behavior in zebrafish (Danio rerio) by environmental stressors

Zebrafish have been demonstrated to react consistently to noxious chemical stimuli and present reliable phenotypes of stress, fear, and anxiety. In this article, we describe the modulation of nociceptive-like responses of zebrafish to fear-, stress-, and anxiety-eliciting situations. Animals were exposed to an alarm substance, confinement stress, or a novel environment before being injected with 1% acetic acid in the tail. The alarm substance and confinement stress reduced the display of erratic movements and tail-beating behavior elicited by acetic acid. The novelty of the environment, in contrast, increased the frequency of tail-beating behavior. The results suggest that descending modulatory control of nociception exists in zebrafish, with apparent fear- and stress-induced analgesia and anxiety-induced hyperalgesia.