A história dos problemas da tautócrona e da braquistócrona

Pós-graduação em Educação Matemática - IGCE

Work and Inter-subjectivity: a theoretical reflection on its dialectics in the field of health and nursing

This theoretical reflection intends to show the inter-subjective relationship that takes place in health and nursing practices under the following theoretical perspectives: Institutional Analysis, Psychodynamics of Labor and the Theory of Communicative Action, with an emphasis on the latter. Linking these concepts to the Marxist approach to work in the field of health emerges from recognizing the need for its continuous reconstruction-in this case, with a view to understand the interaction and communication intrinsic to work in action. The theory of Communicative Action seeks to consider these two inextricable dimensions: work as productive action and as interaction. The first corresponds to instrumental action based on technical rules with a production-guided rationale. The second refers to the interaction that takes place as communicative action and seeks understanding among subjects. We assume that adopting this theoretical perspective in the analysis of health and nursing practices opens new possibilities for clarifying its social and historical process and inter-subjective connections.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Thermographic imaging: assessment of drought and heat tolerance in Spanish germplasm of Brachypodium distachyon.

The annual grass Brachypodium distachyon has been recently recognized as the model plant for functional genomics of temperate grasses, including cereals of economic relevance like wheat and barley. Sixty-two lines of B. distachyon were assessed for response to drought stress and heat tolerance. All these lines, except the reference genotype BD21, derive from specimens collected in 32 distinct locations of the Iberian Peninsula, covering a wide range of geo- climatic conditions. Sixteen lines of Brachypodium hybridum, an allotetraploid closely related to B. distachyon were used as reference of abiotic-stress well-adapted genotypes. Drought tolerance was assessed in a green-house trial. At the rosette-stage, no irrigation was applied to treated plants whereas their replicates at the control were maintained well watered during all the experiment. Thermographic images of treated and control plants were taken after 2 and 3 weeks of drought treatment, when stressed plants showed medium and extreme wilting symptoms. The mean leaf temperature of stressed (LTs) and control (LTc) plants was estimated based upon thermographic records from selected pixels (183 per image) that strictly correspond to leaf tissue. The response to drought was based on the analysis of two parameters: LTs and the thermal difference (TD) between stressed and control plants (LTs – LTc). The response to heat stress was based on LTc. Comparison of the mean values of these parameters showed that: 1) Genotypes better adapted to drought (B. hybridum lines) presented a higher LTs and TD than B. distachyon lines. 2) Under high temperature conditions, watered plants of B. hybridum lines maintained lower LTc than those of B. distachyon. Those results suggest that in these species adaptation to drought is linked to a more efficient stomata regulation: under water stress stomata are closed, increasing foliar temperature but also water use efficiency by reducing transpiration. With high temperature and water availability the results are less definite, but still seems that opening stomata allow plants to increase transpiration and therefore to diminish foliar temperature.

The dynamics of power and resistance in police interview discourse

This is a study of police interviewing using an integrated approach, drawing on CA, CDA and pragmatics. The study focuses on the balance of power and control, finding that in particular the institutional status of the participants, the discursive roles assigned to them by the context, and their relative knowledge, are significant factors affecting the dynamics of the discourse. Four discursive features are identified as particularly significant, and a detailed analysis of the complex interplay of these features shows that power and control are constantly under negotiation, and are always open to challenge and resistance. Further it is shown that discursive dominance is not necessarily advantageous to participants, due to the specific goals and purposes of the police interview context. A wider consideration of the context illustrates the contribution that linguistics can make to the use of police interview data as evidence in the UK criminal justice system.

Critical earthquake input power spectral density function models for engineering structures

The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

Efficient control of an autonomous underwater vehicle while accounting for thruster failure

This paper is concerned with the design and implementation of control strategies onto a test-bed vehicle with six degrees-of-freedom. We design our trajectories to be efficient in time and in power consumption. Moreover, we also consider cases when actuator failure can arise and discuss alternate control strategies in this situation. Our calculations are supplemented by experimental results.

Design and implementation of time efficient trajectories for an underwater vehicle

This paper discusses control strategies adapted for practical implementation and efficient motion of underwater vehicles. These trajectories are piecewise constant thrust arcs with few actuator switchings. We provide the numerical algorithm which computes the time efficient trajectories parameterized by the switching times. We discuss both the theoretical analysis and experimental implementation results.

Optimal-stopping control for airborne collision avoidance and return-to-course flight

This paper considers an aircraft collision avoidance design problem that also incorporates design of the aircraft’s return-to-course flight. This control design problem is formulated as a non-linear optimal-stopping control problem; a formulation that does not require a prior knowledge of time taken to perform the avoidance and return-to-course manoeuvre. A dynamic programming solution to the avoidance and return-to-course problem is presented, before a Markov chain numerical approximation technique is described. Simulation results are presented that illustrate the proposed collision avoidance and return-to-course flight approach.

Reducing Actuator Switchings for Motion Control of Autonomous Underwater Vehicles

A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle. Indeed, due to the vehicles' design and the actuation modes usually under consideration for underwater plateforms the number of actuator switchings must be kept to a small value to insure feasibility and precision. This is the main objective of the algorithm presented in this paper. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six-degrees-of freedom and one is minimally actuated with control motions in the vertical plane only.