Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Propriedades e convergência de certas fórmulas de quadratura interpolatórias

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Differential orthogonality: Laguerre and Hermite cases with applications

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

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Palindromic and perturbed polynomials: zeros location

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

On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Quantitative assessment of total and Gram-positive aerobic bacteria in fresh and ambient-temperature-stored sub-tropical marine fish

The current study was undertaken to enumerate Gram-positive bacteria in fresh sub-tropical marine fish and determine the effect of ambient storage (25°C) on the Gram-positive bacterial count. Total and Gram-positive bacteria were enumerated in the muscles, gills and gut of fresh and stored Pseudocaranx dentex, Pagrus auratus and Mugil cephalus on tryptone soya agar (TSA) and TSA with 0.25% phenylethyl alcohol (PEA), respectively. Initial studies indicated that PEA significantly reduced total aerobic bacterial count (TABC) whereas control Gram-positive bacteria were not affected by 0.25% PEA. TABC significantly increased in all fish body parts, whereas Gram-positive aerobic bacterial count (GABC) significantly increased only in the muscles and gills during ambient storage for 15 h. The TABC of the fish species increased from 4.00, 6.13 and 4.58 log cfu g-1, respectively in the muscles, gills, and gut to 6.31, 7.31 and 7.23 log cfu g-1 by the end of storage. GABC increased from 2.00, 3.52 and 2.20 log cfu g-1 to 4.70, 5.85 and 3.36 log cfu g-1. Within each species, TABC were significantly higher in the gills compared to that of muscles and gut; however, no significant differences were found in GABC between muscles and gills. This study demonstrated the potential importance of Gram-positive bacteria in sub-tropical marine fish and their spoilage.

Weakening of the Gram-negative bacterial outer membrane - A tool for increasing microbiological safety

Gram-negative bacteria are harmful in various surroundings. In the food industy their metabolites are potential cause of spoilage and this group also includes many severe or potential pathogens, such as Salmonella. Due to their ability to produce biofilms Gram-negative bacteria also cause problems in many industrial processes as well as in clinical surroundings. Control of Gram-negative bacteria is hampered by the outer membrane (OM) in the outermost layer of the cells. This layer is an intrinsic barrier for many hydrophobic agents and macromolecules. Permeabilizers are compounds that weaken OM and can thus increase the activity of antimicrobials by facililating entry of hydrophobic compounds and macromolecules into the cell where they can reach their target sites and inhibit or destroy cellular functions. The work described in this thesis shows that lactic acid acts as a permeabilizer and destabilizes the OM of Gram-negative bacteria. In addition, organic acids present in berriers, i.e. malic, sorbic and benzoic acid, were shown to weaken the OM of Gram-negative bacteria. Organic acids can poteniate the antimicrobial activity of other compounds. Microbial colonic degradation products of plant-derived phenolic compounds (3,4-dihydroxyphenylacetic acid, 3-hydroxyphenylacetic acid, 3,4-dihydroxyphenylpropionic acid, 4-hydroxyphenylpropionic acid, 3-phenylpropionic acid and 3-hydroxyphenylpropionic acid) efficiently destabilized OM of Salmonella. The studies increase our understanding of the mechanism of action of the classical chelator, ethylenediaminetetra-acetic acid (EDTA). In addition, the results indicate that the biocidic activity of benzalkonium chloride against Pseudomonas can be increased by combined use with polyethylenimine (PEI). In addition to PEI, several other potential permeabilizers, such as succimer, were shown to destabilize the OM of Gram-negative bacteria. Furthermore, combination of the results obtained from various permeability assays (e.g. uptake of a hydrophobic probe, sensitization to hydrophobic antibiotics and detergents, release of lipopolysaccharide (LPS) and LPS-specific fatty acids) with atomic force microscopy (AFM) image results increases our knowledge of the action of permeabilizers.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.