Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Factors associated with the prevalence of hypertension and control practices among elderly residents of São Paulo city, Brazil

The aim of this study was to analyze the prevalence of hypertension and control practices among the elderly. The survey analyzed data from 872 elderly people in São Paulo, Brazil, through a cluster sampling, stratified according to education and income. A Poisson multiple regression model checked for the existence of factors associated with hypertension. The prevalence of self-reported hypertension among the elderly was 46.9%. Variables associated with hypertension were self-rated health, alcohol consumption, gender, and hospitalization in the last year, regardless of age. The three most common measures taken to control hypertension, but only rarely, are oral medication, routine salt-free diet and physical activity. Lifestyle and socioeconomic status did not affect the practice of control, but knowledge about the importance of physical activity was higher among those older people with higher education and greater income. The research suggests that health policies that focus on primary care to encourage lifestyle changes among the elderly are necessary.

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of displacement and trajectory length on the variability pattern of reaching movements

The design of the present study enabled the authors to distinguish between the possible effects of movement displacement and trajectory length on the pattern of final positions of planar reaching movements. With their eyes closed, 9 subjects performed series of fast and accurate movements from different initial positions to the same target. For some series, the movements were unconstrained and were therefore performed along an approximately straight vertical line. For other series, an obstacle was positioned so that trajectory length was increased because of an increase in movement curvature. Ellipses of variability obtained by means of principal component analysis applied to the scatter of movement final positions enabled the authors to assess the pattern of movement variable errors. The results showed that the orientation of the ellipses was not affected by movement displacement or by trajectory length, whereas variable errors increased with move ment displacement. An increase in trajectory length as a consequence of increased curvature caused no change in variable error. From the perspective of current motor control theory, that finding was quite unexpected. Further studies are required so that one can distinguish among the possible effects of various kinematics, kinetics, and other variables that could affect the pattern of variable errors of reaching movements.

A história dos problemas da tautócrona e da braquistócrona

Pós-graduação em Educação Matemática - IGCE

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Seasonal variations in chemical composition and stable isotopes of farmed and wild Brazilian freshwater fish

This study examined variations in the Fulton condition factor, chemical composition, and stable isotopes of carbon and nitrogen in the Brazilian freshwater fish cachara (Pseudoplatystoma fasciatum), comparing farmed and wild fish in different seasons. Values for energy, protein, moisture, and Fulton's condition factor were higher for farmed than for wild fish in the rainy season, indicating better nutritional quality; however, these differences were not observed in the dry season. Likewise, we found significant enhancement of delta(15)N in farmed fish in the rainy season but not in the dry season, whereas enhancement of delta(13)C was observed in both seasons. The combined measurement of delta(13)C and delta(15)N provided traceability under all conditions. Our findings show that stable isotope analysis of C and N can be used to trace cachara origin, and that seasonal variations need to be considered when applying chemical and isotopic authentication of fish and fish products. (C) 2010 Elsevier Ltd. All rights reserved.

Soil attributes and efficiency of sulfentrazone on control of purple nutsedge (Cyperus rotundus L.)

Herbicidas aplicados ao solo são submetidos à adsorção, lixiviação e degradação por processos físicos, químicos e biológicos, além da absorção pelas plantas. Todos esses processos são afetados pela classe dos solos onde foram aplicados e das condições climáticas reinantes logo após a aplicação, que afetarão a eficiência dos produtos no controle de plantas daninhas. Investigaram-se as influências dos atributos de solos e condições de cultivo na eficiência do herbicida sulfentrazone no controle da planta daninha tiririca (Cyperus rotundus L.). O Latossolo Vermelho-Amarelo Distrófico (LVAd), o Latossolo Vermelho (LVd - Distrófico; LVdf - Distroférrico; LVef - Eutroférrico) e o Nitossolo Vermelho Eutrófico (NVe) foram coletados sob duas condições de cultivo, visando obter solos com teores diferenciados de argila, óxido de ferro e matéria orgânica. As amostras dos solos foram submetidas à caracterização granulométrica, química e mineralógica e, em seguida, utilizadas no bioensaio de avaliação da eficiência do sulfentrazone (1,6 L p.c. ha-1) no controle da tiririca em condições de pré-emergência. O sulfentrazone apresentou comportamento diferenciado entre as classes de solos estudados e a sua eficiência diminuiu com o aumento do teor de óxido de ferro nos solos, na seguinte ordem: LVAd, LVd, NVe, LVef e LVdf, sendo que as variações nos teores de argila (240 a 640 g kg-1) e da matéria orgânica (12 a 78 g kg-1) dos solos não interferiram na eficiência do sulfentrazone.

Control of Brachiaria decumbens and Panicum maximum by S-metolachlor as influenced by the occurrence of rain and amount of sugarcane straw on the soil

Com o objetivo de estudar o controle em pré-emergência de Brachiaria decumbens e Panicum maximum pelo herbicida S-metolachlor em função do intervalo de tempo entre a aplicação e a ocorrência de chuva e da quantidade de palha de cana-de-açúcar na superfície do solo, dois experimentos foram desenvolvidos em vasos mantidos em casa de vegetação. No primeiro, foram estudadas cinco quantidades de palha sobre o solo (0, 3, 6, 10 e 15 t ha-1) e cinco dosagens de S-metolachlor (0; 0,96; 1,44; 1,92 e 2,40 kg ha-1). No outro, foram avaliadas duas quantidades de palha sobre o solo (0 e 10 t ha-1) e sete intervalos de tempo entre a aplicação de S-metolachlor e a simulação de chuva (1 dia antes; logo após; 4, 8, 12, 16 e 20 dias após a aplicação). As dosagens de S-metolachlor não foram afetadas pelos níveis de palha na superfície do solo. Além disso, sem a manutenção de palha sobre o solo, o controle das plantas daninhas pelo herbicida S-metolachlor não foi influenciado pelos intervalos de tempo entre a aplicação e a simulação de chuva, até 20 dias. Com 10 t ha-1 de palha, o controle de B. decumbens e P. maximum pelo S-metolachlor não foi prejudicado quando choveu até 12 dias da sua aplicação ou um dia antes, mas, nesse caso apenas para P. maximum.

Nucleus isthmi and control of breathing in amphibians

Despite recent advances, the mechanisms of neurorespiratory control in amphibians are far from understood. One of the brainstem structures believed to play a key role in the ventilatory control of anuran amphibians is the nucleus isthmi (NI). This nucleus is a mesencephalic structure located between the roof of the midbrain and the cerebellum, which differentiates during metamorphosis; the period when pulmonary ventilation develops in bullfrogs. It has been recently suggested that the NI acts to inhibit hypoxic and hypercarbic drives in breathing by restricting increases in tidal volume. This data is similar to the influence of two pontine structures of mammals, the locus coeruleus and the nucleus raphe magnus. The putative mediators for this response are glutamate and nitric oxide. Microinjection of kynurenic acid (an ionotropic receptor antagonist of excitatory amino acids) and L-NAME (a non-selective NO synthase inhibitor) elicited increases in the ventilatory response to hypoxia and hypercarbia. This article reviews the available data on the role of the NI in the control of ventilation in amphibians. (C) 2004 Elsevier B.V. All rights reserved.

Efficiency of entomopathogenic fungi in the control of eggs and larvae of the horn fly Haematobia irritans (Diptera: Muscidae)

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