Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Comparison of microbial numbers in soils by using various culture media and temperatures

The influence of different media and incubation temperatures on the quantification of microbial populations in sorghum, eucalyptus and forest soils was evaluated. Microbial growth was compared by using complex (tryptone soybean agar, TSA, casein-starch, CS, and Martin) and saline (Thorton, M3, Czapeck) media and incubation temperatures of 25 and 30° C. Higher numbers of total bacterial. and fungal colony-forming units (CFU) were observed in sorghum soils, and of spore-forming and Gram-negative bacteria in forest soils than other soils. Actinomycetes counts were highest in forest soil when using CS medium at 30° C and in sorghum soil at 25° C in M3 medium. Microorganism counts were dependent on the media and incubation temperatures. The counts at temperatures of 30° C were significantly higher than at 25° C. Microbial quantification was best when using TSA medium for total. and spore-forming bacteria, Thorton for Gram-negative bacteria, M3 for actinomycetes, and Martin for fungi. © 2005 Elsevier GmbH. All rights reserved.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Distribution and insertion numbers of transposable elements in species of the Drosophila saltans group

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

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

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

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.

Chromosome numbers of some Brazilian species of diplopods (Diplopoda, Arthropoda)

The present paper presents the chromosome numbers of five brazilian species of diplopods: Plusioporus setiger (2n = 10 and 2n= 10+ lB, the distinction of the sexual pair was not possible), Pseudonannolene ophiulus (2n=12, XY), Pseudonannolene halophila (2n=16, XY), Rhinocricus sp. (2n=28, XY) and Rhinocricus padbergi (2n=20, the distinction of the sexual pair was not possible).

Critical numbers of attractive Bose-Einstein condensed atoms in asymmetric traps

A quantitative analysis of the critical number of attractive Bose-Einstein condensed atoms in asymmetric traps was studied. The Gross-Pitaevskii (GP) formalism for an atomic system with arbitrary nonspherically symmetric harmonic trap was also discussed. Characteristic limits were obtained for reductions from three to two and one dimensions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.

Border detection in digital images: An approach by fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in gray shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the gray shades making up the image, and thus calculate the appropriateness of the pixels in relation to an homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. © 2007 IEEE.

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.

Edge detection in digital images using fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in grey shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the grey shades making up the image and, thus, calculate the appropriateness of the pixels in relation to a homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. Copyright © 2009, Inderscience Publishers.