The study of formal power series is an area of interest that spans many areas of mathematics. We begin by looking at single-variable formal power series with coefficients from a field. By restricting to those series which are invertible with respect to formal composition we form a group. Our focus on this group focuses on the classification of elements having finite order. The notion of a semi-cyclic group comes up in this context, leading to several interesting results about torsion subgroups of the group. We then expand our focus to the composition of multivariate formal power series, looking at similar questions about classifying elements of finite order. We end by defining a natural automorphism on this group induced by a group action of the symmetric group.

Session ID: FR-G2-2 / Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, September 17-21, 2008, Nagoya University, Nagoya, Japan

The possible benefits of employing inerters in automotive suspensions are explored for passenger comfort and handling. Different suspension strut designs in terms of the relative arrangement of springs, dampers and inerters have been considered and their performance compared with that of a conventional system. An alternate method of electrically realizing complex mechanical circuits by using a linear motor (or a rotary motor with an appropriate mechanism) and a shunt circuit is then proposed and evaluated for performance. However, the performance improvement is shown from simulations to be significant only for very stiff suspensions, unlike those in passenger vehicles. Hence, the concept is not taken up for prototyping. Variable damping can be implemented in suspension systems in various ways, for example, using magneto-rheological (MR) fluids, proportional valves, or variable shunt resistance with a linear electromagnetic motor. Hence for a generic variable damping system, a control algorithm is developed which can provide more comfort and better handling simultaneously compared to a passive system. After establishing through simulations that the proposed adaptive control algorithm can demonstrate a performance better than some controllers in prior-art, it is implemented on an actual vehicle (Cadillac STS) which is equipped with MR dampers and several sensors. In order to maintain the controller economical so that it is practically viable, an estimator is developed for variables which require expensive sensors to measure. The characteristic of the MR damper installed in the vehicle is obtained through tests as a 3-dimensional map relating suspension speed, input current and damping force and then used as a look-up table in the controller. Experiments to compare the performance of different controllers are carried out on smooth and rough roads and over speed bumps.

Radiation treatment planning is a process through which a certain plan is devised in order to irradiate tumors or lesions to a prescribed dose without posing surrounding organs to the risk of receiving radiation. A plan comprises a series of shots at di erent positions with di erent shapes. The inverse planning approach which we propose utilizes certain optimization techniques and builds mathematical models to come up with the right location and shape, for each shot, automating the whole process. The models which we developed for PerfexionTM unit (Elekta, Stockholm, Sweden), in essence, have come to the assistance of oncologists in automatically locating isocentres and de ning sector durations. Sector duration optimization (SDO) and sector duration and isocentre location optimization (SDIO) are the two classes of these models. The SDO models, which are, in fact, variations of equivalent uniform dose optimization model, are solved by two nonlinear optimization techniques, namely Gradient Projection and our home-developed Interior Point Constraint Generation. In order to solve SDIO model, a commercial optimization solver has been employed. This study undertakes to solve the isocentre selection and sector duration optimization. Moreover, inverse planning is evaluated, using clinical data, throughout the study. The results show that automated inverse planning contributes to the quality of radiation treatment planning in an unprecedentedly optimal fashion, and signi cantly reduces computation time and treatment time.

国立情報学研究所で電子化したコンテンツを使用している。

Proefschrift Universiteit van Amsterdam. / Met bibliogr., lit. opg. - Met samenvatting in het Spaans en Nederlands.

Th.--Sci. phys.--Nancy--I.N.P.L., 1981.

El diseño, la construcción y el control de robots antropomórficos móviles es un desafío aún no resuelto en el ámbito de la robótica móvil. Los robots más avanzados en la actualidad no son capaces de caminar en dos pies de una forma comparable a los seres humanos: tienen problemas al caminar en superficies irregulares, gastan una gran cantidad de energía para desplazarse, caminan de una forma poco natural desde el punto de vista humano, no pueden correr, saltar, ni mucho menos, hacer algún tipo de acrobacia. Existe un compromiso entre la eficiencia energética y la versatilidad de los robots móviles que aún no ha sido resuelto. Clasificando los robots pasivos según su nivel de actuación se obtienen dos grupos de robots: los robots pasivos, que son eficientes energéticamente, pero muy poco versátiles, y los robots activos, que son versátiles, pero muy ineficientes energéticamente. La existencia de estas dos clases de robots con características complementarias dependiendo del enfoque utilizado en su diseño, plantea el desafío de encontrar una solución intermedia que combine las características positivas de ambos enfoques. Este trabajo de tesis propone el diseño de un robot semi-pasivo, consistente en un robot activo, que al momento de ser diseñado, considera las condiciones sobre sus parámetros que permiten la existencia de un ciclo de caminata pasiva. Para lograr el diseño y construcción de este robot semi-pasivo se propone una nueva clase de articulaciones de rigidez variable basadas en el principio de torcer cuerdas para obtener un desplazamiento lineal, simple en su construcción y que permite que la dinámica intrínseca del robot fluya naturalmente. La articulación propuesta es construida y validada, obteniendo buenos resultados según lo esperado para su aplicación en un robot bípedo semi-pasivo. También se propone una nueva metodología que permite encontrar las condiciones sobre los parámetros de un modelo arbitrario de robot de dinámica pasiva que permiten la existencia de un ciclo de caminata pasivo. Esta metodología implementa un proceso de búsqueda que permite encontrar subespacios estables en el espacio de parámetros (regiones con combinaciones de parámetros que producen ciclos de caminata estables) simulando la dinámica del robot para diferentes combinaciones de parámetros. Después de que se seleccionan aleatoriamente las condiciones iniciales, la dinámica del robot se modela paso a paso, verificando la existencia de ciclos de caminata en la sección de Poincaré. La metodología incluye la definición de un algoritmo de búsqueda para explorar el espacio de parámetros, un método para la partición del espacio en hipercubos y su manejo eficiente usando las estructuras de datos apropiadas, y el uso de las denominadas funciones de valor que cuantifican la factibilidad de los parámetros resultantes. La metodología es independiente del robot (puede ser usada con cualquier modelo de caminata de dinámica pasiva, sin importar su complejidad), y es robusta (los subespacios estables incorporan un indicador del margen de estabilidad que se encarga de las diferencias entre el modelo del robot y su realización física). Esta metodología es validada en el diseño de un robot semi-pasivo, el que en simulaciones mediante un software externo presenta un ciclo de caminata de dinámica pasiva según lo predicho por los resultados de la aplicación de la metodología.

Numerical Weather Prediction (NWP) and climate models parametrize the effects of boundary-layer turbulence as a diffusive process, dependent on a diffusion coefficient, which appears as nonlinear terms in the governing equations. In the advection dominated zone of the boundary layer and in the free atmosphere, the air flow supports different wave motions, with the fastest being the sound waves. Time integrations of these terms, in both zones, need to be implicit otherwise they impractically restrict the stable time step sizes. At the same time, implicit schemes may lose accuracy compared to explicit schemes in the same level, which is due to dispersion error associated with these schemes. Furthermore, the implicit schemes need iterative approaches like the Newton-Raphson method. Therefore, the combination of implicit and explicit methods, called IMEX or semi-implicit, has extensively attracted attention. In the combined method, the linear part of the equation as well as the fast wave terms are treated by the implicit part and the rest is calculated by the explicit scheme. Meanwhile, minimizing the dissipation and dispersion errors can enhance the performance of time integration schemes, since the stability and accuracy will be restricted by these inevitable errors. Hence, the target of this thesis is to increase the stability range, while obtaining accurate solutions by using IMEX and semi-implicit time integration methods. Therefore, a comprehensive effort has been made toward minimizing the numerical errors to develop new Runge-Kutta schemes, in IMEX and semi-implicit forms, to temporally integrate the governing equations in the atmospheric field so that the stability is extended and accuracy is improved, compared to the previous schemes. At the first step, the A-stability and the Strong Stability Preserving (SSP) optimized properties were compared as two essential properties of the time integration schemes. It was shown that both properties attempt to minimize the dissipation and dispersion errors, but in two different aspects. The SSP optimized property focuses on minimizing the errors to increase the accuracy limits, while the A-stability property tries to extend the range of stability. It was shown that the combination of both properties is essential in the field of interest. Moreover, the A-stability property was found as an essential property to accelerate the steady state solutions. Afterward, the dissipation and dispersion errors, generated by three-stage second order IMEX Runge-Kutta scheme were minimized, while the proposed scheme, so called IMEX-SSP2(2,3,2) enjoys the A-stability and SSP properties. A practical governing equation set in the atmospheric field, so called compressible Boussinesq equations set, was calculated using the new IMEX scheme and the results were compared to one well-known IMEX scheme in the literature, i.e. ARK2(2,3,2), which is an abbreviation of Additive Runge-Kutta. Note that, the ARK2(2,3,2) was compared to various types of IMEX Runge-Kutta schemes and it was found as the more efficient scheme in the atmospheric fields (Weller et al., 2013). It was shown that the IMEX-SSP2(2,3,2) could improve the accuracy and extend the range of stable time step sizes as well. Through the van der Pol test case, it was shown that the ARK2(2,3,2) with L-stability property may decline to the first order in the calculation of stiff limit, while IMEX-SSP2(2,3,2), with A-stability property, is able to retain the assigned second order of accuracy. Therefore, it was concluded that the L-stability property, due to restrictive conditions associated with, may weaken the time integration’s performance, compared to the A-stability property. The ability of the IMEX-SSP2(2,3,2) was proved in solving different case, which is the inviscid Burger equation in spherical coordinate system by using a realistic initial condition dataset. In the next step, it was attempted to maximize the non-negativity property associated with the numerical stability function of three-stage third order Diagonally Implicit Runge-Kutta (DIRK) schemes. It was shown that the non-negativity has direct relation with non-oscillatory behaviors. Two new DIRK schemes with A- and L-stability properties, respectively, were developed and compared to the SSP(3,3), which obtains the SSP optimized property in the same class of DIRK schemes. The SSP optimized property was found to be more beneficial for the inviscid (advection dominated) flows, since in the von Neumann stability analysis, the SSP optimized property provides more nonnegative region for the imaginary component of the stability function. However, in most practical cases, i.e. the viscous (advection diffusion) flows, the nonnegative property is needed for both real and imaginary components of the stability function. Therefore, the SSP optimized property, individually, is not helpful, unless mixed with the A-stability property. Meanwhile, the A- and L-stability properties were compared as well. The intention is to find how these properties influence the DIRK schemes’ performances. The A-stability property was found as preserving the SSP property more than the L-stability property. Moreover, the proposed A-stable scheme tolerates larger Courant Friedrichs Lewy (CFL) number, while preserving the accuracy and non-oscillatory computations. This fact was proved in calculating different test cases, including compressible Euler and nonlinear viscous Burger equations. Finally, the time integration of the boundary layer flows was investigated as well. The nonlinearity associated with the diffusion coefficient makes the implicit scheme impractical, while the explicit scheme inefficiently limits the stable time step sizes. By using the DIRK scheme, a new semi-implicit approach was proposed, in which the diffusion coefficient at each internal stage is calculated by a weight-averaged combination of the solutions at current internal stage and previous time step, in which the time integration can benefit from both explicit and implicit advantages. As shown, the accuracy was improved, which is due to engaging the explicit solutions and the stability was extended due to taking advantages of implicit scheme. It was found that the nominated semi-implicit method results in less dissipation error, more accurate solutions and less CPU time usage, compared to the implicit schemes, and it enjoys larger range of stable time steps than other semi-implicit approaches in the literature.

Dans l’optique de développer de nouveaux système RF les plus intégrés possibles, les technologies above-IC compatibles avec les technologies silicium ouvrent des perspectives prometteuses sur un plan économique pour l’industrie du semi-conducteur. En effet, a contrario des résonateurs SAW et céramiques, les résonateurs à ondes acoustiques de volume (BAW) peuvent être fabriqués en utilisant des matériaux compatible CMOS VLSI pour des performances électriques comparables, voir supérieures dans certains cas en termes de fréquence et de puissance. Les travaux de cette thèse ont connus deux grandes partie ; la première a été focalisée sur le développement d’une nouvelle topologie de filtre BAW accordable pour des applications de quatrième génération de téléphone mobile (4G). La seconde partie a été orientée vers une étude de faisabilité d’un filtre BAW-SMR autour d’une fréquence de travail à 7GHz pour une application spatiale. / Abstract