THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Equifocality of a singular Riemannian foliation

A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular Riemannian foliations with sections.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

A Specialized Processor for Emulating Peripherals of the PIC Microcontroller

This paper proposes and describes an architecture that allows the both engineer and programmer for defining and quantifying which peripheral of a microcontroller will be important to the particular project. For each application, it is necessary to use different types of peripherals. In this study, we have verified the possibility for emulating the behavior of peripheral in specifically CPUs. These CPUs hold a RAM memory, where code spaces specifically written for them could represent the behavior of some target peripheral, which are loaded and executed on it. We believed that the proposed architecture will provide larger flexibility in the use of the microcontrolles since this ""dedicated hardware components"" don`t execute to a special function, but it is a hardware capable to self adapt to the needs of each project. This research had as fundament a comparative study of four current microcontrollers. Preliminary tests using VHDL and FPGAs were done.

Social behaviour of collared peccaries (Pecari tajacu) under three space allowances

Captive breeding of peccaries is on the increase in neotropical countries. Few studies, however, have reported behavioural responses of wild animals under farmed conditions. Therefore, the aim of this study was to evaluate the effects of space allowance on the occurrence of social behaviour patterns on farmed collared peccary (Pecan tajacu). We observed three herds of collared peccaries each containing eight acquainted individuals. Using a 3 x 3 Latin square design, herds were allocated, in a random order, to one of the three experimental enclosures, each with a different size. 375, 750 and 1,500 m(2) of total available area, each with three wooden shelters. We recorded all the occurrences of selected positive and agonistic behavioural patterns that occurred 90 min before and during feeding Enclosure size had a significant effect on agonistic patterns of peccaries during feeding, in that more agonistic behaviour was observed in smaller spaces We also found that shelter usage increased as space decreased Differing space allowances, however, did not have an effect on the occurrence of positive interactions that were more frequent before compared to during feeding. We concluded that enclosure size had an effect on the expression of agonistic be and the use of shelters by collared peccaries Thus, animal welfare can be improved by adopting at least 187 5 m(2) per peccary. In addition, our study also confirmed the importance of shelter areas in collared peccary husbandry.

The new research centre of the Brazilian Petroleum Company in Rio de Janeiro, Brazil: The achievements in the thermal performance of air-conditioned buildings in the tropics

The study on the thermal performance of the air-conditioned buildings of the new research centre of the Brazilian Petroleum Company, in the tropical climate of Rio de Janeiro, was part of a bigger research and consultancy, project involving environmental issues. The architectural design was the subject of a national competition in 2004, encompassing over 100,000 m(2). According to the design brief, out of the 10 buildings of the new research centre, 7 have to be either completely or partially air-conditioned, due to specific occupation requirements. The challenge for better thermal performance was related to systems` energy efficiency, to the introduction of natural ventilation and to the notion of adaptive comfort, which were verified with the support of thermal dynamic simulations. At the early stages of the assessments, the potential for natural ventilation in the working spaces considering the mixed-mode strategy achieved 30% of occupation hours. However, the development of the design project led to fully air-conditioned working spaces, due to users` references regarding the conventional culture of the office environment. Nevertheless, the overall architectural approach in accordance to the climatic conditions still showed a contribution to the buildings` energy efficiency. (C) 2008 Elsevier B.V. All rights reserved.

Interference of dexamethasone in the pulmonary cycle of Strongyloides venezuelensis in rats

The aim of this study was to investigate the interference of a daily treatment of dexamethasone in the pulmonary cycle of Strongyloides venezuelensis infection in rats. Three principal effects were found: 1) increased alveolar hemorrhagic inflammation provoked by the passage of larvae into alveolar spaces; 2) significant decrease of eosinophil and mast cell migration to the axial septum of the lungs; and 3) impaired formation of the reticular fiber network, interfering with granuloma organization. This study showed that the use of drugs with immunomodulatory actions, such as dexamethasone, in addition to interfering with the morbidity from the pulmonary cycle of S. venezuelensis infection, may contribute to showing the mechanisms involved in its pathogenesis.