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

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

As diferentes “personalidades” do número racional trabalhadas através da resolução de problemas

We address the different "personalities" of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number - rational point, quotient, fraction, ratio, and operator - are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different "personalities" of the rational number. In general, these "personalities" are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these "personalities", the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics.

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).

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

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.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Rational use of residential digesters for sewage treatment with Carbon Credits

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of anatomical location on CT numbers in cone beam computed tomography

Objective: To assess the influence of anatomical location on computed tomography (CT) numbers in mid- and full field of view (FOV) cone beam computed tomography (CBCT) scans. Study Design: Polypropylene tubes with varying concentrations of dipotassium hydrogen phosphate (K2HPO4) solutions (50-1200 mg/mL) were imaged within the incisor, premolar, and molar dental sockets of a human skull phantom. CBCT scans were acquired using the NewTom 3G and NewTom 5G units. The CT numbers of the K2HPO 4 phantoms were measured, and the relationship between CT numbers and K2HPO4 concentration was examined. The measured CT numbers of the K2HPO4 phantoms were compared between anatomical sites. Results: At all six anatomical locations, there was a strong linear relationship between CT numbers and K2HPO4 concentration (R 2 > 0.93). However, the absolute CT numbers varied considerably with the anatomical location. Conclusion: The relationship between CT numbers and object density is not uniform through the dental arch on CBCT scans. © 2013 Elsevier Inc.