A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Introduction of a non-conventional solution for Amazon transmission system: Analysis of the electric aspects

This article shows an analysis of the longitudinal electric parameters of a three-phase transmission line/section using a 280-meter high steel tower. This characteristic, the height of the line conductors and distance between them, are intrinsic related to the longitudinal and transversal parameters of the line. By this means, an accurate study was carried out in order to show the electric variations between a transmission line using the new technology and a three-phase conventional 440 kV line for a wide range of frequencies and a variable soil resistivity. In addition, by using a digital line model, simulations are carried out in time domain to analyze critical overvoltage transients on the studied line. © 2011 IEEE.

Séries universelles dans CN et sur les surfaces de Riemann non compactes

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

Non-invasive user monitoring in daily tasks for cognitive rehabilitation

El uso de técnicas para la monitorización del movimiento humano generalmente permite a los investigadores analizar la cinemática y especialmente las capacidades motoras en aquellas actividades de la vida cotidiana que persiguen un objetivo concreto como pueden ser la preparación de bebidas y comida, e incluso en tareas de aseo. Adicionalmente, la evaluación del movimiento y el comportamiento humanos en el campo de la rehabilitación cognitiva es esencial para profundizar en las dificultades que algunas personas encuentran en la ejecución de actividades diarias después de accidentes cerebro-vasculares. Estas dificultades están principalmente asociadas a la realización de pasos secuenciales y al reconocimiento del uso de herramientas y objetos. La interpretación de los datos sobre la actitud de este tipo de pacientes para reconocer y determinar el nivel de éxito en la ejecución de las acciones, y para ampliar el conocimiento en las enfermedades cerebrales, sus consecuencias y severidad, depende totalmente de los dispositivos usados para la captura de esos datos y de la calidad de los mismos. Más aún, existe una necesidad real de mejorar las técnicas actuales de rehabilitación cognitiva contribuyendo al diseño de sistemas automáticos para crear una especie de terapeuta virtual que asegure una vida más independiente de estos pacientes y reduzca la carga de trabajo de los terapeutas. Con este objetivo, el uso de sensores y dispositivos para obtener datos en tiempo real de la ejecución y estado de la tarea de rehabilitación es esencial para también contribuir al diseño y entrenamiento de futuros algoritmos que pudieran reconocer errores automáticamente para informar al paciente acerca de ellos mediante distintos tipos de pistas como pueden ser imágenes, mensajes auditivos o incluso videos. La tecnología y soluciones existentes en este campo no ofrecen una manera totalmente robusta y efectiva para obtener datos en tiempo real, por un lado, porque pueden influir en el movimiento del propio paciente en caso de las plataformas basadas en el uso de marcadores que necesitan sensores pegados en la piel; y por otro lado, debido a la complejidad o alto coste de implantación lo que hace difícil pensar en la idea de instalar un sistema en el hospital o incluso en la casa del paciente. Esta tesis presenta la investigación realizada en el campo de la monitorización del movimiento de pacientes para proporcionar un paso adelante en términos de detección, seguimiento y reconocimiento del comportamiento de manos, gestos y cara mediante una manera no invasiva la cual puede mejorar la técnicas actuales de rehabilitación cognitiva para la adquisición en tiempo real de datos sobre el comportamiento del paciente y la ejecución de la tarea. Para entender la importancia del marco de esta tesis, inicialmente se presenta un resumen de las principales enfermedades cognitivas y se introducen las consecuencias que tienen en la ejecución de tareas de la vida diaria. Más aún, se investiga sobre las metodologías actuales de rehabilitación cognitiva. Teniendo en cuenta que las manos son la principal parte del cuerpo para la ejecución de tareas manuales de la vida cotidiana, también se resumen las tecnologías existentes para la captura de movimiento de manos. Una de las principales contribuciones de esta tesis está relacionada con el diseño y evaluación de una solución no invasiva para detectar y seguir las manos durante la ejecución de tareas manuales de la vida cotidiana que a su vez involucran la manipulación de objetos. Esta solución la cual no necesita marcadores adicionales y está basada en una cámara de profundidad de bajo coste, es robusta, precisa y fácil de instalar. Otra contribución presentada se centra en el reconocimiento de gestos para detectar el agarre de objetos basado en un sensor infrarrojo de última generación, y también complementado con una cámara de profundidad. Esta nueva técnica, y también no invasiva, sincroniza ambos sensores para seguir objetos específicos además de reconocer eventos concretos relacionados con tareas de aseo. Más aún, se realiza una evaluación preliminar del reconocimiento de expresiones faciales para analizar si es adecuado para el reconocimiento del estado de ánimo durante la tarea. Por su parte, todos los componentes y algoritmos desarrollados son integrados en un prototipo simple para ser usado como plataforma de monitorización. Se realiza una evaluación técnica del funcionamiento de cada dispositivo para analizar si es adecuada para adquirir datos en tiempo real durante la ejecución de tareas cotidianas reales. Finalmente, se estudia la interacción con pacientes reales para obtener información del nivel de usabilidad del prototipo. Dicha información es esencial y útil para considerar una rehabilitación cognitiva basada en la idea de instalación del sistema en la propia casa del paciente al igual que en el hospital correspondiente. ABSTRACT The use of human motion monitoring techniques usually let researchers to analyse kinematics, especially in motor strategies for goal-oriented activities of daily living, such as the preparation of drinks and food, and even grooming tasks. Additionally, the evaluation of human movements and behaviour in the field of cognitive rehabilitation is essential to deep into the difficulties some people find in common activities after stroke. This difficulties are mainly associated with sequence actions and the recognition of tools usage. The interpretation of attitude data of this kind of patients in order to recognize and determine the level of success of the execution of actions, and to broaden the knowledge in brain diseases, consequences and severity, depends totally on the devices used for the capture of that data and the quality of it. Moreover, there is a real need of improving the current cognitive rehabilitation techniques by contributing to the design of automatic systems to create a kind of virtual therapist for the improvement of the independent life of these stroke patients and to reduce the workload of the occupational therapists currently in charge of them. For this purpose, the use of sensors and devices to obtain real time data of the execution and state of the rehabilitation task is essential to also contribute to the design and training of future smart algorithms which may recognise errors to automatically provide multimodal feedback through different types of cues such as still images, auditory messages or even videos. The technology and solutions currently adopted in the field don't offer a totally robust and effective way for obtaining real time data, on the one hand, because they may influence the patient's movement in case of marker-based platforms which need sensors attached to the skin; and on the other hand, because of the complexity or high cost of implementation, which make difficult the idea of installing a system at the hospital or even patient's home. This thesis presents the research done in the field of user monitoring to provide a step forward in terms of detection, tracking and recognition of hand movements, gestures and face via a non-invasive way which could improve current techniques for cognitive rehabilitation for real time data acquisition of patient's behaviour and execution of the task. In order to understand the importance of the scope of the thesis, initially, a summary of the main cognitive diseases that require for rehabilitation and an introduction of the consequences on the execution of daily tasks are presented. Moreover, research is done about the actual methodology to provide cognitive rehabilitation. Considering that the main body members involved in the completion of a handmade daily task are the hands, the current technologies for human hands movements capture are also highlighted. One of the main contributions of this thesis is related to the design and evaluation of a non-invasive approach to detect and track user's hands during the execution of handmade activities of daily living which involve the manipulation of objects. This approach does not need the inclusion of any additional markers. In addition, it is only based on a low-cost depth camera, it is robust, accurate and easy to install. Another contribution presented is focused on the hand gesture recognition for detecting object grasping based on a brand new infrared sensor, and also complemented with a depth camera. This new, and also non-invasive, solution which synchronizes both sensors to track specific tools as well as recognize specific events related to grooming is evaluated. Moreover, a preliminary assessment of the recognition of facial expressions is carried out to analyse if it is adequate for recognizing mood during the execution of task. Meanwhile, all the corresponding hardware and software developed are integrated in a simple prototype with the purpose of being used as a platform for monitoring the execution of the rehabilitation task. Technical evaluation of the performance of each device is carried out in order to analyze its suitability to acquire real time data during the execution of real daily tasks. Finally, a kind of healthcare evaluation is also presented to obtain feedback about the usability of the system proposed paying special attention to the interaction with real users and stroke patients. This feedback is quite useful to consider the idea of a home-based cognitive rehabilitation as well as a possible hospital installation of the prototype.

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Determination of viscosity of some Australian honeys based on composition

Rheological properties of four unprocessed unifloral Australian honeys (heath, tea tree, yapunya, and yellow box) and an artificial honey were analysed at 20degreesC. A model previously used to describe viscosity data of various sugar and sugar mixtures was used to describe the concentration dependence of the viscosity of honey samples with varying moisture contents. The model successfully described the sugar concentration dependence of the unadulterated and medium moisture (70-85% solids) range honey samples.

Subsidies as Optimal Fiscal Stimuli

In the theoretical macroeconomics literature, fiscal policy is almost uniformly taken to mean taxing and spending by a ‘benevolent government’ that exploits the potential aggregate demand externalities inherent in the imperfectly competitive nature of goods markets. Whilst shown to raise aggregate output and employment, these policies crowd-out private consumption and hence typically reduce welfare. In this paper we consider the use of ‘tax-and-subsidise’ instead of ‘taxand- spend’ policies on account of their widespread use by governments, even in the recent recession, to stimulate economic activity. Within a static general equilibrium macro-model with imperfectly competitive good markets we examine the effect of wage and output subsidies and show that, for a small open economy, positive tax and subsidy rates exist which maximise welfare, rendering no intervention as a suboptimal state. We also show that, within a two-country setting, a Nash non-cooperative symmetric equilibrium with positive tax and subsidy rates exists, and that cooperation between trading partners in setting these rates is more expansionary and leads to an improvement upon the non-cooperative solution.

Environmental data mining and modeling based on machine learning algorithms and geostatistics

The paper presents some contemporary approaches to spatial environmental data analysis. The main topics are concentrated on the decision-oriented problems of environmental spatial data mining and modeling: valorization and representativity of data with the help of exploratory data analysis, spatial predictions, probabilistic and risk mapping, development and application of conditional stochastic simulation models. The innovative part of the paper presents integrated/hybrid model-machine learning (ML) residuals sequential simulations-MLRSS. The models are based on multilayer perceptron and support vector regression ML algorithms used for modeling long-range spatial trends and sequential simulations of the residuals. NIL algorithms deliver non-linear solution for the spatial non-stationary problems, which are difficult for geostatistical approach. Geostatistical tools (variography) are used to characterize performance of ML algorithms, by analyzing quality and quantity of the spatially structured information extracted from data with ML algorithms. Sequential simulations provide efficient assessment of uncertainty and spatial variability. Case study from the Chernobyl fallouts illustrates the performance of the proposed model. It is shown that probability mapping, provided by the combination of ML data driven and geostatistical model based approaches, can be efficiently used in decision-making process. (C) 2003 Elsevier Ltd. All rights reserved.

Consistency and the core of multi-sided assignment markets

[cat] En aquest treball es demostra que en el domini dels jocs d’assignació equilibrats multisectorials (Quint, 1991), el core és l’única solució no buida que satisfà derived consistency i projection consistency. També es caracteritza el core en tota la classe dels jocs d’assignació multisectorials amb els axiomes de singleness best, individual antimonotonicity i derived consistency. Com a casos particulars, s’obtenen dues noves axiomàtiques del core per als jocs d’assignació bilaterals (Shapley and Shubik, 1972).