Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the N-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the N-body problem is reduced to N one-body problems.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Ex vivo biocompatibility tests of regular and white forms of mineral trioxide aggregate

Aim: To examine the genotoxicity and cytotoxicity of regular and white mineral trioxide aggregate (MTA) ex vivo by the single-cell gel (comet) assay and trypan blue exclusion test, respectively. Methodology: Aliquots of 1 × 10 4 Chinese hamster ovary cells were incubated at 37°C for 3 h with grey and white forms of MTA at final concentrations ranging from 1 to 1000 μg mL -1. The negative control group was treated with vehicle control phosphate buffer solution for 3 h at 37°C and the positive control group was treated with methyl metasulfonate (at 1 μg mL -1) for 1 h at 37°C. After incubation, the cells were centrifuged at 180 g for 5 min and washed twice with fresh medium and resuspended with fresh medium. Each individual treatment was repeated three times consecutively to ensure reproducibility. Parameters from single-cell gel (comet) and cytotoxicity assays were assessed by the Kruskal-Wallis nonparametric test. Results: Neither compounds produced genotoxic effects with respect to the single-cell gel (comet) assay in all concentrations evaluated. In the same way, the dose-response relationships of all compounds tested at concentrations ranging from 1 to 1000 μg mL -1 on cell viability assessed by the trypan blue assay displayed no statistically significant differences (P > 0.05) for either endodontic material. Conclusions: Regular (grey) and white MTA are not genotoxins and do not induce cellular death. © 2006 International Endodontic Journal.

Genotoxicity in primary human peripheral lymphocytes after exposure to regular and white mineral trioxide aggregate

Objective: Taking into consideration that DNA damage plays an important role in carcinogenesis, the purpose of this study was to evaluate whether regular and white mineral trioxide aggregate (MTA) are able to induce genetic damage in primary human cells. Study design: Human peripheral lymphocytes obtained from 10 healthy volunteers were exposed to 2 presentation forms of MTA at final concentrations ranging from 1 to 1000 μg/mL for 1 hour at 37°C. The negative control group was treated with vehicle control (phosphate buffer solution, PBS) for 1 hour at 37°C and the positive control group was treated with hydrogen peroxide (at 100 μM) for 5 minutes on ice. Results were analyzed by the Friedman nonparametric test. Results: The results pointed out that either regular or white MTA in all concentrations tested did not induce DNA breakage in human peripheral lymphocytes as depicted by the mean tail moment. Conclusion: In summary, our results indicate that exposure to MTA may not be a factor that increases the level of DNA lesions in human peripheral lymphocytes as detected by single cell gel (comet) assay. © 2006 Mosby, Inc. All rights reserved.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

Fluoride intake from regular and low fluoride dentifrices by 2-3-year-old children: Influence of the dentifrice flavor

This study evaluated the fluoride intake from dentifrices with different fluoride concentrations ([F]) by children aged 24-36 months, as well as the influence of the dentifrice flavor in the amount of fluoride ingested during toothbrushing. Thirty-three children were randomly divided into 3 groups, according to the [F] in the dentifrices: G-A (523 μgF/g), G-B (1,062 μgF/g) and G-C (1,373 μgF/g). Dentifrices A and B are marketed for children, while dentifrice C is a regular product. The amount of F ingested was indirectly obtained, subtracting the amount expelled and the amount left on the toothbrush from the amount initially loaded onto the brush. The results were analyzed by ANOVA, Tukey's test and linear regression analysis (p < 0.05). Children ingested around 60% of the dentifrice loaded onto the brush, but no significant differences were seen among the groups (p > 0.05). Mean daily fluoride intake from dentifrice for G-A, G-B and G-C was 0.022 a, 0.032 a and 0.061 b mg F/kg body weight, respectively (p < 0.01). There was a strong positive correlation (r = 0.86, p < 0.0001) between the amount of dentifrice used and the amount of fluoride ingested during toothbrushing. The results indicate the need for instructing children's parents and care givers to use a small amount of dentifrice (< 0.3 g) to avoid excessive ingestion of fluoride. The use of low-[F] dentifrices by children younger than 6 years also seems to be a good alternative to minimize fluoride intake. Dentifrice flavor did not influence the percentage of fluoride intake.

As características dos alunos são determinantes para o adoecimento de professores - um estudo comparativo sobre a incidência de Burnout em professores do ensino regular e especial

The practice of teaching is permeated by adverse working conditions, low wages, inadequacy of material and teaching resources, overcrowded classrooms, tension in relationships with the students, excessive work load, lack of safety in the school environment, insignificant participation in institutional planning and in institutional politics. The objective of the present study was to compare burnout among three groups of teachers who work in elementary grades: a) 20 teachers who teach in regular school classrooms without the inclusion of students with special educational needs - RSI Group; b) 20 teachers who teach in the regular classroom with special needs students - RCI Group; c) 20 teachers who teach in resource classrooms (SR Group). The instruments used for data collection were the Maslach Burnout Inventory -MBI. The data was analyzed by SPSS version 13.0 and Kruskal-Wallis test for comparison of the three groups. The results were organized in the form of figures and tables. In general, the results demonstrated that the groups presented relative similarity. The teachers from the SR Group obtained the best results in the evaluation of the three burnout scales when compared to the RSI Group and RCI Group, that is, there was a prevalence of answers in the lower levels of emotional exhaustion, high level of low personal accomplishment and low level for depersonalization. It is hoped that these results contribute to a better understanding of burnout in teachers from regular classrooms with or without students with educational special needs and/or to indicate new directions for investigation.

Quenching in a non-ideal mechanical system and the Averaging Method

In this paper, for the first time, a quenching result in a non-ideal system is rigorously obtained. In order to do this a new mechanical hypothesis is assumed, it means that the moment of inertia of the rotating parts of the energy source is big. From this is possible to use the Averaging Method. © 2012 American Institute of Physics.

Ideas of four-fermion operators in hadron physics

Four-fermion operators have been utilized in the past to link the quarkexchange processes in the interaction of hadrons with the effective mesonexchange amplitudes. In this paper, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes.

Ideas of four-fermion operators in electromagnetic form factor calculations

Four-fermion operators have been used in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this paper, we apply the similar idea of a Fierz rearrangement to the self-energy and electromagnetic processes and focus on the electromagnetic form factors of the nucleon and the electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes. © 2013 American Physical Society.