Um estudo sobre a função exponencial

Pós-graduação em Matemática em Rede Nacional - IBILCE

GeoGebra e o método de Briot & Bouquet para a resolução gráfica de equações cúbicas

In the mid-nineteenth century, french mathematicians Briot and Bouquet have proposed an intriguing graphical method for solving cubic equations "depressed" - the third degree equations that do not have the quadratic term. The proposal is simple geometric construction, though based on an ingenious algebra. We propose here the verification and testing graphical method through an instructional sequence using the software GeoGebra also present the ingenious algebraic development that resulted in this graphic method for determination of real roots of a cubic equation of the type x³ + px + q = 0 where p and q are real numbers. The method states that these solutions are summarized in the abscissas of the points of intersection of the circumference containing the origin and the center C (-q/2, 1-p/2) with the parable y = x².

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Conhecimentos presentes na disciplina de análise nos cursos de licenciatura em Matemática no Brasil

Pós-graduação em Educação Matemática - IGCE

The Effect of a Supragingival Plaque-Control Regimen on the Subgingival Microbiota in Smokers and Never-Smokers: Evaluation by Real-Time Polymerase Chain Reaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Real orthogonal polynomials in frequency analysis

We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

Periodontal status in smokers and never-smokers: Clinical findings and real-time polymerase chain reaction quantification of putative periodontal pathogens

Background: Smoking is a well-known risk factor for destructive periodontal disease, but its relationship with periodontal status and subgingival microbiota remains unclear. Inherent limitations of microbiological methods previously used may partly explain these mixed results, and real-time polymerase chain reaction (PCR) has been presented as a valid alternative. The aim of the present study was to investigate the clinical condition and microbiological profile of patients with chronic periodontitis as related to the habit of smoking.Methods: Fifty patients (33 to 59 years old), 25 smokers and 25 never-smokers, constituted the sample. The visible plaque index (VPI), gingival bleeding index (GBI), bleeding on probing (BOP), periodontal probing depth (PD), clinical attachment loss (CAL), and gingival crevicular fluid (GCF) volume were recorded. Real-time PCR quantified Porphyromonas gingivalis, Micromonas micros, Dialister pneumosintes, Actinobacillus actinomycetemcomitans and total bacteria in subgingival samples.Results: Smokers and never-smokers showed similar values for VPI, GBI, and BOP. Smokers had deeper PD in buccal/lingual sites and higher CAL independently of the tooth surface. The GCF volume was smaller in smokers, independent of the PD. Similar amounts of total bacteria and P. gingivalis were observed for both groups. Significantly higher numbers of D. pneumosintes and M. micros were present in smokers and associated with moderate and deep pockets. When heavy smokers were considered, higher counts of total bacteria, M. micros, and D. pneumosintes were observed.Conclusions: Smoking seems to have a detrimental impact on the periodontal status and microbiological profile of patients with periodontitis. Compared to never-smokers, smokers had deeper pockets, greater periodontal destruction, and higher counts of some putative periodontal pathogens.

A recursive approach to space resection using straight lines

An approach using straight lines as features to solve the photogrammetric space resection problem is presented. An explicit mathematical model relating straight lines, in both object and image space, is used. Based on this model, Kalman Filtering is applied to solve the space resection problem. The recursive property of the filter is used in an iterative process which uses the sequentially estimated camera location parameters to feedback to the feature extraction process in the image. This feedback process leads to a gradual reduction of the image space for feature searching, and consequently eliminates the bottleneck due to the high computational cost of the image segmentation phase. It also enables feature extraction and the determination of feature correspondence in image and object space in an automatic way, i.e., without operator interference. Results obtained from simulated and real data show that highly accurate space resection parameters are obtained as well as a progressive processing time reduction. The obtained accuracy, the automatic correspondence process, and the short related processing time show that the proposed approach can be used in many real-time machine vision systems, making possible the implementation of applications not feasible until now.

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.