The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.

Zeros of orthogonal polynomials generated by canonical perturbations of measures

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SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

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Modificação da microbiota associada às lesões peridentárias da cara inchada em bezerros transferidos para área indene

Observations on the epizootiology of cara inchada in cattle (CI) indicated that animals affected by the disease recover spontaneously when they are transferred from the CI-prone area to CI-free pastures. In the presente study 13 young bovines with actively progressing periodontal CI-lesions were transferred to a CI-free area, in order to investigate the clinical course of the disease and the composition of the microflora in the periodontal lesions in two distinct situations: (1) in the actively progressing lesions, and (2) in the healed periodontal pouches of clinically recovered animals. The semi-quantitative and qualitative bacteriological study was undertaken in regard to the percentage of black-pigmented Bacteroides in cultures. In the actively progressing lesions of the 13 CI-diseased bovines the percentage of these bacteria was 71.3% in average. The evaluation of the composition of the microflora in the healed periodontal pouches of the clinically recovered bovines showed that bacteria of the black-pigmented Bacteroides group existed only at an average of 1.7%. The results of this investigation give further support for the infectious nature of the CI-periodontitis and the primary involvement of these bacteria.

Alocação de zeros aplicada a sistemas de controle via LMI

A systematic procedure of zero placement to design control systems is proposed. A state feedback controller with vector gain K is used to perform the pole placement. An estimator with vector gain L is also designed for output feedback control. A new systematic method of zero assignment to reduce the effect of the undesirable poles of the plant and also to increase the velocity error constant is presented. The methodology places the zeros in a specific region and it is based on Linear Matrix Inequalities (LMIs) framework, which is a new approach to solve this problem. Three examples illustrate the effectiveness of the proposed method.

Modificação no posicionamento do paciente para o procedimento para prolapso e hemorroidas (PPH): Decúbito ventral com coxim e membros inferiores afastados

Our aim is to present a modification in patient placement on surgical table for the treatment of prolapsed hemorrhoids by using PPH technique. We propose a modified jackknife position for PPH procedure where the surgeon stays between patient's legs. The modified jackknife position may provide better surgical field with better view of the dentate line which facilitates pursestring confection. In Brazil, the majority of the surgeons prefer lithotomic position for PPH technique based on Longo's first reports. In our opinion, modified jackknife position provides both better surgical field for pursestring placement and better view of the staple line after PPH firing.

Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

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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.

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.

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.

Teoria do potencial logarítmico e zeros de polinômios

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Uso de modelos inflacionados de zeros na análise de questionários de frequência alimentar

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Estudo da modificação ácido-etanólica do amido de mandioca seguida de moagem

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