We characterize invariant measures for quadratic polynomial Julia sets with no interior. We prove that besides the harmonic measure —the only one that is even and invariant—, all others are generated by a suitable odd measure. / En este artículo caracterizamos medidas invariantes sobre conjuntos de Julia sin interior asociados con polinomios cuadráticos.  Probamos que más allá de la medida armónica —la única par e invariante—, el resto son generadas por su parte impar.

In the last three decades we have witnessed a remarkable development in the area of integrated circuits. From small logic devices containing some hundred transistors to modern processors containing several tens of million transistors. However, power consumption has become a real problem and may very well be the limiting factor of future development. Designing for low power is therefore increasingly important. To accomplice an efficient low power design, accurate power estimation at early design stage is essential. The aim of this thesis was to set up a power estimation flow to estimate the power consumption at early design stage. The developed flow spans over both RTL- and gate-level incorporating Mentor Graphics Modelsim (RTL-level simulator), Cadence PKS (gate- level synthesizer) and own developed power estimation tools. The power consumption is calculated based on gate-level physical information and RTL- level toggle information. To achieve high estimation accuracy, real node annotations is used together with an own developed on-chip wire model to estimate node voltage swing. Since the power estimation may be very time consuming, the flow also includes support for low power design iteration. This gives efficient power estimation speedup when concentrating on smaller sub- parts of the design.

Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe. / In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system.

A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill-conditioned iterates may cause numerical instability. Numerical examples demonstrate the theoretical results.

The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigated. / Die Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren.

We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.

The numerical treatment of linear-quadratic regulator problems for parabolic partial differential equations (PDEs) on infinite time horizons requires the solution of large scale algebraic Riccati equations (ARE). The Newton-ADI iteration is an efficient numerical method for this task. It includes the solution of a Lyapunov equation by the alternating directions implicit (ADI) algorithm in each iteration step. On finite time intervals the solution of a large scale differential Riccati equation is required. This can be solved by a backward differentiation formula (BDF) method, which needs to solve an ARE in each time step. Here, we study the selection of shift parameters for the ADI method. This leads to a rational min-max-problem which has been considered by many authors. Since knowledge about the complete complex spectrum is crucial for computing the optimal solution, this is infeasible for the large scale systems arising from finite element discretization of PDEs. Therefore several alternatives for computing suboptimal parameters are discussed and compared for numerical examples.

The key objective of this research is to develop a generic simulation modelling methodology that can be used to model stochastic continuous systems effectively. The generic methodology renders simulation models that exhibit the following characteristics: short development and maintenance times, user-friendliness, short simulation runtimes, compact size, robustness, accuracy and a single software application. The research was initiated by the shortcomings of a simulation modelling method that is detailed in a Magister dissertation. A system description of a continuous process plant (referred to as the Synthetic Fuel plant) is developed. The decision support role of simulation modelling is considered and the shortcomings of the original method are analysed. The key objective, importance and limitations of the research are also discussed. The characteristics of stochastic continuous systems are identified and a generic methodology that accommodates these characteristics is conceptualised and developed. It consists of the following eight methods and techniques: the variables technique, the iteration time interval evaluation method, the event-driven evaluation method, the Entity-represent-module method, the Fraction-comparison method, the iterative-loop technique, the time “bottleneck” identification technique and the production lost “bottleneck” identification technique. Five high-level simulation model building blocks are developed. The generic methodology is demonstrated and validated by the development and use of two simulation models. The five high-level building blocks are used to construct identical simulation models of the Synthetic Fuel plant in two different simulation software packages, namely: Arena and Simul8. An iteration time interval and minimum sufficient sample sizes are determined and the simulation models are verified, validated, enhanced and compared. The simulation models are used to evaluate two alternative scenarios. The results of the scenarios are compared and conclusions are presented. The factors that motivated the research, the process that was followed and the generic methodology are summarised. The original method and the generic methodology are compared and the strengths and weaknesses of the generic methodology are discussed. The contribution to knowledge is explained and future developments are proposed. The possible range of application and different usage perspectives are presented. To conclude, the lessons learnt and reinforced are considered. / Thesis (PhD (Industrial Engineering))--University of Pretoria, 2004. / Industrial and Systems Engineering / unrestricted

This study investigates whether interaction design principles can be used on already existing company services in order to improve the user experience and satisfaction, and how such a process should look like, and what lessons can be learned from it. The study uses an iterative approach where prototypes are created and evaluated to further improve the prototype in the next iteration. To test this a service from the company LeoVegas mobile gaming group called Antiloop is used. Firstly a literature study is conducted to find requirements on how similar services can be designed, then an interview is conducted with employers who use Antiloop in order to find out what can be improved. Then two different prototypes are created and evaluated with the same employees to find out which one is preferred. The results of that evaluation lead to a final prototype that is evaluated together with the existing service through quantitative and qualitative methods, to see whether the new prototype has a better user experience. The results of the final evaluation showed that the new prototype is preferred over the existing version. However, because the test only had 7 participants, it might not be enough to draw a general conclusion. A list of further improvements was also presented.

Denna studie undersöker hur en applikation för mental hälsa skulle se ut om den var skapad utifrån studenternas behov med fokus på användbarhet. Syftet med denna studien var att förstå studenters behov och krav de har på en applikation som skulle kunna förbättra deras mentala hälsa och möta dessa krav genom att använda prototyper och modeller för användbarhet. Metoderna som använts i denna studie är kvalitativa intervjuer, användartester samt prototyputveckling som en metod. Intervjuerna utfördes med sex studenter och en kurator på Malmö universitet för att förstå studenters mentala hälsa och behov. Resultatet från intervjuerna implementerades i en första version av prototypen som fick namnet LUGN. LUGN fick därefter utvärderas genom användbarhetstestet som sex andra studenter deltog i, responsen från detta test resulterade i den sista versionen av LUGN. Den sista versionen av LUGN är inte komplett på det sättet att den inte kan illustrera fullt ut hur den slutgiltiga applikationen skulle se ut. Den presenterar dock ett viktigt resultat från denna studie vilket är att anpassa utefter studenters mångfald när det kommer till vad som får dem att må bra. För att få ett mer detaljerat resultat, behöver ett flertal tester och iterationer av prototypen utföras. / This study examined how a mental health application would look like if it was created together with students and focused on usability. The purpose of this study was to understand the needs and demands that students have of an application that could have the ability to improve their mental health while using prototyping and usability models to meet these demands. The methods used were qualitative interviews, usability testing and prototyping. The interviews were conducted with six students and a counselor at Malmö university to understand student’s mental health and their needs. The results from the interviews were implemented in a first version of the prototype the authors named LUGN. LUGN were evaluated through the usability test that six other students participated in, the feedback from this resulted in the final version of LUGN. The final version of LUGN is not complete in the sense that it is not an accurate portrayal of how the finished application would look like. It does however portray an important result from this study and that is to cater to student’s diversity when it comes to what makes them feel better. To achieve a more detailed result, further tests and iterations of the prototype has to be made.