In my thesis, I explore William Blake's technique of combining word and image in his practice of engraving. The unity of text and image is deeply related to his unique mythology and concept of infinity. Blake's artistic theories and practices, such as his emphasis on the line as the most essential artistic element, are reflective of his understanding of art in relation to human perception and imagination. The interaction of his words and images provides a space of imaginative engagement for the reader, which opens the doors of perception and creates the possibility of revealing infinity.

La présente étude est une analyse et une reconstruction interprétative de la centurie de Calliste Cataphygiotès, intitulée De l'union avec Dieu et de la vie contemplative, chapitres syllogistiques et hauts. Notre approche à ce texte pluridisciplinaire est prioritairement philosophique. Dans le but de mettre en valeur l'intérêt philosophique qu'il représente, nous avons concentré notre analyse sur les problèmes liés au rapport de l'intellect avec l'Un, sur l'étude du concept de l'infini, sur son rôle dans la contemplation et sur la méthode dialectique dont Calliste Cataphygiotès s'en sert. Nous avons reconstruit la doctrine de la contemplation, implicite au texte de Calliste et nous avons tenté une reconstruction globale de la centurie qui permettra au lecteur d'apprécier les qualités spéculatives et l'esprit synthétique de ce mystique byzantin presque inconnu. / The present study is an analysis and an interpretative reconstruction of Callistus Cataphygiotes's syllogistic chapters, entitled The union with God and the contemplative life. Our approach to this multidisciplinary text is primarily philosophical. In order to emphasize the philosophical aspect of the text we focused our analysis on issues related to the concept of infinity, its role in contemplation, the relation of the intellect with the One, as well as the dialectical method used by Callistus Cataphygiotes. We rebuilt the doctrine of contemplation, implied in the text of Callistus and we tried to do a complete reconstruction of the text that will allow the reader to appreciate the speculative and the synthetic spirit of this almost unknown Byzantine mystic.

Esta dissertação versa sobre o ensino de Sequências e Séries na educação básica. A questão é entender em que medida o uso da Teoria dos Registros de Representação Semiótica se mostra favorável à criação de atividades que sejam propícias à aprendizagem dos alunos. Foram elaboradas dez atividades sobre Sequências e Séries e foi feita uma aplicação de quatro destas atividades com alunos de 1a série do ensino médio. Com esta aplicação, procurou-se buscar evidências de que o uso de diversos registros de representação semiótica favorecem a aprendizagem dos alunos em Matemática. Como escopo secundário, buscamos também investigar a concepção de infinito que os alunos manifestaram durante a aplicação das atividades. Antes, porém, buscamos na história da Matemática diferentes maneiras de como filósofos e matemáticos concebiam e utilizavam o infinito. Visto que Sequências e Séries também são assunto tratados no ensino superior, foram abordadas algumas dificuldades de transição ensino básico/ensino superior tendo em vista diferenças culturais entre os dois níveis de ensino. Concluímos que o uso de materiais concretos para representação de objetos matemáticos se mostrou favorável à compreensão dos alunos e a concepção de infinito dos alunos está predominantemente ligada a ideia de infinito potencial. / The subject of this research is about teaching and learning sequences and series in primary education. The research question is to understand how favorable is the use of the theory of semiotic representation registers to create activities that help students to learn. Were created ten activities about sequences and series and four of these were chosen to be used in a classroom with 1st year students of a secondary school. By observing these activities being used in classroom, evidences were searched to evaluate if including different semiotic representation registers facilitates student\'s learning on mathematics. As a secondary aim, the student\'s infinity conception is investigated in the classroom. We also researched mathematics\' history to find different conceptions adopted by philosophers and mathematicians on infinity. As sequences and series are also studied in college, some transition difficulties (from High School to College) were discussed considering cultural differences between the two educational levels. It was concluded that concrete teaching materials to the students\' comprehension and the students\' concept of infinity is mainly linked to potential infinity.

<p>In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.</p><p>The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities.</p><p>To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.</p><p>The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.</p>

<p>Dynamiken för en starkt accelerande robot har modellerats. Modellen linjäriseras så att roboten beskrivs som ett linjärt tidsvariabelt system. Denna representation beskriver roboten väl då robotens anblåsningsvinkel, vilket är vinkeln mellan robotkroppen och robotens hastighet, är liten. Eftersom det ej är möjligt att mäta alla robotens tillstånd har en observatör tagits fram i form av ett Kalmanfilter. Problematik vid framtagandet av observatören diskuteras i rapporten. Den linjära tidsvariabla modellen har använts till att ta fram två regulatorer. En LQ-regulator och en H_∞-regulator. Hur dessa tas fram och vilka problem som finns diskuteras i rapporten. För att kunna se fördelar och nackdelar beträffande prestanda och robusthet har en mängd tester gjort. Testerna visar på olika fördelar hos de olika reglersystemen. Till exempel är det lättare att få bra prestanda med LQ-regulatorn än H_∞-regulatorn om systemet som styrs stämmer bra överens med systemet som använts vid reglerdesignen. H_∞-regulatorn har bättre förmåga att anpassa sig till modellförändringar givet att observatören gör bra skattningar. Det är dock svårt att utnämna en generell vinnare.</p>

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 135-140).

We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo ‘lower order terms’) by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y 0, the (operator-valued) edge symbol of ‘first generation’, cf. [15]. The novelty here is the edge symbol σ^ of ‘second generation’, parametrised by (z, Ϛ) 2 T*Z 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.

In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low. The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities. To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems. The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.

This thesis is divided in to two different parts. The first part includes examination of the measurementsystem of an industrial robot using a resolver sensor. The main focus is on methods for suppressing noise in the angularvelocity signal without increasing timedelay. Five different methods are investigated. Three of these are based on oversampling: burstsamplingmethod, meanvaluemethod and correlationmethod. The meanvaluemethod and the correlationmethod have given good results. The two other methods are: extended kalmanfiltering and computation of the angular velocity without using numeric method to compute the angle. Extended kalmanfilter gives the overall best result. In part two the control structure design of an industrial robot has been studied and how different sampling times and motorinertias affect the disturbance rejection and stability of the control loop. Different control structure designs have also been studied with the aim to suppress disturbances. Mainly H-infinity and GIMC designs have been compared with an ordinary PID controller. Here it can be shown that both the H-infinity and the GIMC controller yields good disturbance rejection. But both the methods lack in the robustness of model uncertainty.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.