Polar Multiplicities and Euler obstruction of the stable types in weighted homogeneous map germs from C-n to C-3 n >= 3

In this article we show that for corank 1, quasi-homogeneous and finitely determined map germs f : (C-n, 0)-> (C-3, 0), n >= 3 one can obtain formulae for the polar multiplicities defined on the following stable types of f, f(Delta(f) and f(Sigma(n-2,1)(f), in terms of the weights and degrees of f. As a consequence we show how to compute the Euler obstruction of such stable types, also in terms of the weights and degrees of f.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chromosome numbers and their taxonomic implications for eight Brazilian andropogons (Poaceae: Andropogoneae)

Eleven chromosome counts are reported for Brazilian populations of eight species of Andropogon. Counts for five of the species are first reports for the species. Four of these species, A. arenarius, A. glaziovii, A. lateralis, and A. lindmanii, are hexaploids (n=30) and belong to a group of about a dozen species informally referred to as the Andropogon lateralis complex. Two other species of this complex, A. bicornis and A. hypogynus, we also found to be hexaploids, in agreement with previous reports. Diploid counts (n=10) for A. macrothrix (a first report) and A. virgatus (the same as two previous reports) support the morphological affinities of these two species to other species complexes within Andropogon. © 1986 the New York Botanical Garden.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

Comparative study of LMI-based output feedback spr synthesis for plants with different numbers of inputs and outputs

New Linear Matrix Inequalities (LMI) conditions are proposed for the following problem, called Strictly Positive Real (SPR) synthesis: given a linear time-invariant plant, find a constant output feedback matrix Ko and a constant output tandem matrix F for the controlled system to be SPR. It is assumed that the plant has the number of outputs greater than the number of inputs. Some sufficient conditions for the solution of the problem are presented and compared. These results can be directly applied in the LMI-based design of Variable Structure Control (VSC) of uncertain plants. ©2008 IEEE.

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.

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.

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.

Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Palindromic and perturbed polynomials: zeros location

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

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Assessment of CT numbers in limited and medium field-of-view scans taken using Accuitomo 170 and Veraviewepocs 3De cone-beam computed tomography scanners

To assess the influence of anatomic location on the relationship between computed tomography (CT) number and X-ray attenuation in limited and medium field-of-view (FOV) scans. Materials and Methods Tubes containing solutions with different concentrations of K2HPO4 were placed in the tooth sockets of a human head phantom. Cone-beam computed tomography (CBCT) scans were acquired, and CT numbers of the K2HPO4 solutions were measured. The relationship between CT number and K2HPO4 concentration was examined by linear regression analyses. Then, the variation in CT number according to anatomic location was examined. Results The relationship between K2HPO4 concentration and CT number was strongly linear. The slopes of the linear regressions for the limited FOVs were almost 2-fold lower than those for the medium FOVs. The absolute CT number differed between imaging protocols and anatomic locations. Conclusion There is a strong linear relationship between X-ray attenuation and CT number. The specific imaging protocol and anatomic location of the object strongly influence this relationship.