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The problem with which this study is concerned is the development of a mathematical model and theory of teaching. The mathematical model consists of a set of abstract axioms. The fundamental elements or terms of the axioms are undefined. These primitive or undefined terms obtain their definitions only implicitly through the axioms.

This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

Made available in DSpace on 2014-06-11T19:28:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-12Bitstream added on 2014-06-13T19:37:21Z : No. of bitstreams: 1 russi_pc_me_guara.pdf: 338766 bytes, checksum: 6a00ac32d9ca90d3359a4343b50c03b0 (MD5) / O problema da modelagem da locomoção humana tem atraído a atenção de pesquisadores por muitos anos. A compreensão, análise e avaliação da marcha humana oferecem dados importantes para o uso de próteses dos membros inferiores. O objetivo deste trabalho é apresentar um modelo matemático da marcha humana, através de um modelo simplificado do corpo humano para que sirva de referência no trabalho de adaptação ao uso de próteses. O desenvolvimento da modelagem, parte da geometria dos membros inferiores num sistema de referência bidimensional e utiliza o princípio da diferença entre as energias cinética e potencial do sistema, ou seja, o método de Lagrange, introduzido na forma matricial. O modelo é representado na fase de oscilação, por dois segmentos interconectados com massas concentradas que oscila como um pêndulo duplo. Na fase de apoio é representado por três segmentos interconectados com massas concentradas que se movimenta como um pêndulo triplo invertido. Obtidas as equações que representam o modelo, os torques nas articulações do tornozelo, joelho e quadril são obtidos e a simulação numérica é realizada no programa MATLAB. Os resultados dos torques calculados apresentaram coerências com os da literatura, porém, na fase de apoio diferenças significativas foram registradas. / The problem of human locomotion modeling has been attracting the researcher attention for many years. The understanding, analysis and evaluation of the human locomotion provide important data for the use of prostheses in the inferior parts of the body. The aim of this issue is to present a mathematical model of the human locomotion through a simplified model of the human body so that it serves as reference in the adaptation for prostheses usage. The modeling was developed using the geometry of the inferior parts of the body in a system of bidimensional references and applies the principle of difference between kinetic energies and potential of the system, in other words, the method of Lagrange, introduced in the form matrix. The model is represented in the oscillation phase, for two segments interconnected with concentrated masses which oscillates as a double pendulum. In the support phase it is represented in three segments interconnected with concentrated masses which move as an inverted triple pendulum. Since the equations representing the model are provided, the torque in the articulations of the ankle, knee and hip are obtained and the numeric simulation is accomplished in the program MATLAB. The results of the calculated torque showed coherence with the one of the literature, however, in the support phase the significant differences were registered.

Orientador: Tamotsu Hirata / Banca: Mauro Pedro Peres / Banca: marcos Valério Ribeiro / Resumo: O problema da modelagem da locomoção humana tem atraído a atenção de pesquisadores por muitos anos. A compreensão, análise e avaliação da marcha humana oferecem dados importantes para o uso de próteses dos membros inferiores. O objetivo deste trabalho é apresentar um modelo matemático da marcha humana, através de um modelo simplificado do corpo humano para que sirva de referência no trabalho de adaptação ao uso de próteses. O desenvolvimento da modelagem, parte da geometria dos membros inferiores num sistema de referência bidimensional e utiliza o princípio da diferença entre as energias cinética e potencial do sistema, ou seja, o método de Lagrange, introduzido na forma matricial. O modelo é representado na fase de oscilação, por dois segmentos interconectados com massas concentradas que oscila como um pêndulo duplo. Na fase de apoio é representado por três segmentos interconectados com massas concentradas que se movimenta como um pêndulo triplo invertido. Obtidas as equações que representam o modelo, os torques nas articulações do tornozelo, joelho e quadril são obtidos e a simulação numérica é realizada no programa MATLAB. Os resultados dos torques calculados apresentaram coerências com os da literatura, porém, na fase de apoio diferenças significativas foram registradas. / Abstract: The problem of human locomotion modeling has been attracting the researcher attention for many years. The understanding, analysis and evaluation of the human locomotion provide important data for the use of prostheses in the inferior parts of the body. The aim of this issue is to present a mathematical model of the human locomotion through a simplified model of the human body so that it serves as reference in the adaptation for prostheses usage. The modeling was developed using the geometry of the inferior parts of the body in a system of bidimensional references and applies the principle of difference between kinetic energies and potential of the system, in other words, the method of Lagrange, introduced in the form matrix. The model is represented in the oscillation phase, for two segments interconnected with concentrated masses which oscillates as a double pendulum. In the support phase it is represented in three segments interconnected with concentrated masses which move as an inverted triple pendulum. Since the equations representing the model are provided, the torque in the articulations of the ankle, knee and hip are obtained and the numeric simulation is accomplished in the program MATLAB. The results of the calculated torque showed coherence with the one of the literature, however, in the support phase the significant differences were registered.

Expert systems technology is a discipline of artificial intelligence that has recently emerged from the research environment and is currently making significant inroads into business and industry. The proponents of expert systems make many attractive claims. Two of the claims are that expert systems can capture the knowledge of the experts and can be programmed by non-programmers. To date, most uses of this technology in the process industry are in off-line applications, that is, applications that are not directly tied to operating environments. Moreover, those that are used in on-line environments are used as advisors and only suggest changes, human operators are required to close-the-loop to the process. This technology should be applicable to operating environments and should the claims of its proponents be valid, then it should also be better than existing tools currently in use. In an operating environment it could use the knowledge of experienced operators as an intelligent controller and apply it directly to a process without the intervention of human operators. In this thesis the prospect of using an expert system as an intelligent controller is investigated. The thesis offers background to expert systems, how expert systems are related to artificial intelligence and what the generic components of an expert system are. As a test of the technology an expert system was developed as an intelligent controller in a mineral processing application. The prototype expert system was developed as a supervisory controller in the copper flotation circuit in the concentrator at Brenda Mines Ltd.. The expert system operated on-line and controlled the process in real-time. It read sensor data and using the operating experience of Brenda's flotation operators, manipulated regulatory controller setpoints as deemed necessary. The expert system was able to manipulate directly reagent flowrates and process air flowrates. Also, it suggested changes to other process variables not directly under its control. The manipulated variables were collector and frother reagent flowrates, the air flowrate to a bank of scavenger flotation cells and the air flowrate to four flotation columns. The operators were allowed to, and sometimes required to, intervene in instances of large process upsets. Results of a month long trial period in the flotation circuit indicated the success of the application. The expert system was indeed able to maintain metallurgical performance at a level approximating that of the operating experts, however, no direct comparison between the performance of the circuit under expert system control, versus performance under operator control, was possible. A rudimentary comparison was made between the circuit's performance under expert system control and its historic performance. The results were favourable. A less tangible measure, though as important, were the attitudes of the operators toward the system. Almost unanimously, the operators felt the system eased the task of circuit operation and was responsible for better circuit performance. / Applied Science, Faculty of / Mining Engineering, Keevil Institute of / Graduate

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This thesis has been performed in the university context for Master thesis 30 credits,which is a compulsory exercise in order to gain a degree in electrical engineering. The thesis main objectives were to investigate how the damping and the stiffness of ahydroelectric generator changed depending on different parameter values, and to testa new mathematical model to calculate the damping and stiffness constants Kd and Ks.The work has been performed at the request of VG Power, but has been performedat the division for electricity at Uppsala University. The reason for undertaking thisthesis was to ensure that generators are robust. But also when building future modelsfor generators, to have a system that can be used to compute robustness. During this thesis a power cabinet has also been constructed to be able to test thesimulated model on a real generator. Under the first five weeks a power cabinet wasconstructed in the laboratory at the division for electricity. The tests were thenperformed at a generator with a rated power of 75 kVA.

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