Made available in DSpace on 2015-08-20T17:10:17Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-05-22. Added 1 bitstream(s) on 2015-08-20T17:25:38Z : No. of bitstreams: 1 000841360.pdf: 3682640 bytes, checksum: eaf27985d250e3c985af9a2b6f309687 (MD5) / No presente trabalho estudamos a teoria de Cálculo Variacional com o intuito de nos familiarizarmos com a teoria de Controle Ótimo. Estudamos também resultados da Teoria de Equações Diferenciais, com foco em Teoria da Medida, com o objetivo de demonstrarmos o Princípio Mínimo de Pontryagin, condição esta necessária para otimalidade de um controle. Por sua vez, condições de regularidade e existência para Controles Ótimos Lineares também foram estudadas, uma vez que são essenciais para determinação de controles ótimos. Por m, utilizamos a teoria de Controle Ótimo acima indicada para a análise de um modelo de crescimento de câncer com quimioterapia com o objetivo de minimizar a quantidade de quimioterápico aplicada no tratamento / In the worked here presented we study the theory of Optimal Control. We also studied results in Theory of Di erential Equations focusing on Measure Theory, with the goal of proving the Pontryagin Mininum Principle, a necessary condition for optimality of a control. In turn, regularity and existence conditions for Optimal Linear Controls were also studied, since they are essential for determination of optimal controls. Finally, we used the theory of Optimal Control above mentioned for an analysis of a model of tumor with chemotherapy with the goal of minimizing the quantity of chemotherapy applied in the treatment

Made available in DSpace on 2015-09-17T15:25:24Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-26. Added 1 bitstream(s) on 2015-09-17T15:48:53Z : No. of bitstreams: 1 000831631_20160226.pdf: 456086 bytes, checksum: e08fba71391f45251c1ff91038f7b50e (MD5) Bitstreams deleted on 2016-02-26T14:03:52Z: 000831631_20160226.pdf,. Added 1 bitstream(s) on 2016-02-26T14:04:47Z : No. of bitstreams: 1 000831631.pdf: 1111810 bytes, checksum: 0779e46e0c0ee233caedc7aa8be3e030 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / São apresentados resultados clássicos sobre zeros de polinômios, como também resultados mais recentes. O interesse deste trabalho é apresentar resultados que mostram o comportamento dos zeros de polinômios auto-recíprocos reais em relação ao círculo unitário. O comportamento dos zeros destes polinômios é interessante, pois se P(z) é um polinômio auto-recíproco e z0 um zero de P(z) então o inverso conjugado de z0 também será zero de P(z): São apresentados resultados conhecidos sobre condições necessárias e suficientes para que esta classe de polinômios tenha todos os seus zeros no círculo unitário, além de alguns exemplos como aplicações dos resultados para a melhor compreensão do texto. Em especial são estudadas duas classes de polinômios auto-recíprocos reais, denotadas por R( ) n (z) e S( ) n (z), apresentando suas propriedades e mostrando condições necessárias e suficientes para que todos os zeros de ambos polinômios estejam no círculo unitário / Classical results of zeros of polynomials are presented, such as more recent results. The interest of this work is to present results on the behavior of zeros of real self-reciprocal polynomial with respect to the unit circle. The behavior of zeros of these polynomials is interesting, because if P(z) is a self-reciprocal polynomial and z0 is a zero of P(z) so the inverse conjugate z0 will be zero of P(z) as well. Known results about necessary and sufficient conditions are presented in order that this class of polynomial has all its zeros on the unit circle, also examples as applications of the results for the best comprehension of the text. In particular two real self-reciprocal polynomial classes are studied, denoted by R( ) n (z) and S( ) n (z), presenting its properties and showing necessary and sufficient conditions so all zeros of both polynomials are on the unit circle

Orientador: Cristiane Nespoli Morelato França / Banca: Thais Jordão / Banca: Marcos Tadeu Oliveira Pimenta / Resumo: No presente trabalho estudamos a teoria de Cálculo Variacional com o intuito de nos familiarizarmos com a teoria de Controle Ótimo. Estudamos também resultados da Teoria de Equações Diferenciais, com foco em Teoria da Medida, com o objetivo de demonstrarmos o Princípio Mínimo de Pontryagin, condição esta necessária para otimalidade de um controle. Por sua vez, condições de regularidade e existência para Controles Ótimos Lineares também foram estudadas, uma vez que são essenciais para determinação de controles ótimos. Por m, utilizamos a teoria de Controle Ótimo acima indicada para a análise de um modelo de crescimento de câncer com quimioterapia com o objetivo de minimizar a quantidade de quimioterápico aplicada no tratamento / Abstract: In the worked here presented we study the theory of Optimal Control. We also studied results in Theory of Di erential Equations focusing on Measure Theory, with the goal of proving the Pontryagin Mininum Principle, a necessary condition for optimality of a control. In turn, regularity and existence conditions for Optimal Linear Controls were also studied, since they are essential for determination of optimal controls. Finally, we used the theory of Optimal Control above mentioned for an analysis of a model of tumor with chemotherapy with the goal of minimizing the quantity of chemotherapy applied in the treatment / Mestre

Orientador: Vanessa Avansini Botta Pirani / Banca: Messias Meneguette Júnior / Banca: Cleonice Fatima Bracciali / Resumo: São apresentados resultados clássicos sobre zeros de polinômios, como também resultados mais recentes. O interesse deste trabalho é apresentar resultados que mostram o comportamento dos zeros de polinômios auto-recíprocos reais em relação ao círculo unitário. O comportamento dos zeros destes polinômios é interessante, pois se P(z) é um polinômio auto-recíproco e z0 um zero de P(z) então o inverso conjugado de z0 também será zero de P(z): São apresentados resultados conhecidos sobre condições necessárias e suficientes para que esta classe de polinômios tenha todos os seus zeros no círculo unitário, além de alguns exemplos como aplicações dos resultados para a melhor compreensão do texto. Em especial são estudadas duas classes de polinômios auto-recíprocos reais, denotadas por R( ) n (z) e S( ) n (z), apresentando suas propriedades e mostrando condições necessárias e suficientes para que todos os zeros de ambos polinômios estejam no círculo unitário / Abstract: Classical results of zeros of polynomials are presented, such as more recent results. The interest of this work is to present results on the behavior of zeros of real self-reciprocal polynomial with respect to the unit circle. The behavior of zeros of these polynomials is interesting, because if P(z) is a self-reciprocal polynomial and z0 is a zero of P(z) so the inverse conjugate z0 will be zero of P(z) as well. Known results about necessary and sufficient conditions are presented in order that this class of polynomial has all its zeros on the unit circle, also examples as applications of the results for the best comprehension of the text. In particular two real self-reciprocal polynomial classes are studied, denoted by R( ) n (z) and S( ) n (z), presenting its properties and showing necessary and sufficient conditions so all zeros of both polynomials are on the unit circle / Mestre

The popularity of personal computing devices (e.g. smart cards) exposes users to risks, notably identity theft, and creates new requirements for secure communication. A recently proposed approach to creating secure communication is to use human trust and human interactions. These approaches potentially eliminate the need for passwords as in Bluetooth, shared secrets or trusted parties, which are often too complex and expensive to use in portable devices. In this new technology, handheld devices exchange data (e.g. payment, heart rates or public keys) over some medium (e.g. WiFi) and then display a short and non-secret digest of the protocol's run that the devices' human owners manually compare to ensure they agree on the same data, i.e. human interactions are used to prevent fraud. In this thesis, we present several new protocols of this type which are designed to optimise the work required of humans to achieve a given level of security. We discover that the design of these protocols is influenced by several principles, including the ideas of commitment without knowledge and separation of security concerns, where random and cryptographic attacks should be tackled separately. Underpinning the technology is a new cryptographic function, termed a keyed digest function, which produces a short number for humans to compare. This is similar to the notion of a universal hash function, but its output length is shorter (e.g. 16 bits). Hence, it should be faster to compute. We propose several digest constructions using Toeplitz matrices, integer multiplication and pseudorandom numbers. The application of digest functions leads us to develop more efficient alternatives to standard digital signatures. Our protocol security analysis leads to a new bound on the key length for an almost universal hash function, which can be derived by the pigeon-hole principle. The new bound turns out to be tighter than another similar bound derived from the combination of the Singleton bound in coding theory and an equivalence between error-correcting codes and almost universal hash functions.

Please read the abstract in the section 00front of this document / Dissertation (MSc (Computer Science))--University of Pretoria, 2006. / Computer Science / unrestricted

Orientador: Messias Meneguette Junior / Banca: Simone de Almeida Delphim / Banca: Carlos Alberto Dutra Fraga Filho / Resumo: O estudo dos métodos sem malha tem sido muito atrativo nos últimos anos, devido a suas capacidades de melhor resolver deficiências enfrentadas pelos métodos tradicionais que usam malha. O SPH é um dos primeiros métodos sem malha, por isso vários estudos têm sido feitos para seu melhor desenvolvimento. Uma das aplicações clássicas em dinâmica dos fluidos é a ruptura de barragens. Uma das problemáticas enfrentadas na aplicação da ruptura de barragem é a recuperação do campo de velocidades e de pressão. O objetivo deste trabalho é analisar as correções aplicadas ao SPH a m de suavizar as oscilações dos campos de velocidades e do campo de pressões, usando a viscosidade artificial e as correções dos filtros de densidade Shepard e MLS, por meio do software SPHysics. Além disso, foi feita uma comparação dos resultados simulados com resultados de laboratório. As correções aplicadas se mostraram eficientes na recuperação dos campos propostos. Quando comparados os resultados simulados para o escoamento do fluido com os resultados laboratoriais, foram obtidas boas aproximações, com diferenças percentuais baixas. / Abstract: The study of the meshless methods have been very attractive in recent years due to their ability to better address shortcomings faced by traditional mesh based methods. SPH is one of the first meshless methods, so several studies have been done for its best development. One of the classic applications in fluid dynamics is the dam break problem, which has been the subject of much research using the SPH method. One of the difficulties faced in the application of dam break is the recovery of velocity and pressure fields. The objective of this work is to analyze the corrections applied to SPH in order to smooth and better recover the velocity and pressure fields, using artificial viscosity and the corrections of the Shepard and MLS density filters, through the SPHysics software. In addition, a comparison between simulated and available experimental results is made in order to validate the study. The applied corrections were efficient for recovering the mentioned fields. The comparisons showed very good agreement, that is, very low percentage differences. / Mestre

In this dissertation group theory, being the standard mathematical tool for describing symmetry, is used to characterize the symmetries of bodies and features, especially the symmetries relevant to contact between bodies. Such a characterization reveals the necessity of intersecting subgroups of the proper Euclidean group ${\cal E}\sp{+}$. The central theoretical results of this dissertation are to establish this necessity mathematically and to provide a compact representation for the subgroups of ${\cal E}\sp{+}$ that leads an efficient group intersection algorithm. I define a geometric representation in terms of characteristic invariants for an important family of subgroups of ${\cal E}\sp{+}$. Each member of this family is called a $TR$ group since it is a semidirect product of a translation group $T$ and a rotation group $R$. I prove that there is a one-to-one correspondence between $TR$ groups and their characteristic invariants. I also prove that the intersection of $TR$ groups is closed and can be efficiently calculated from their characteristic invariants. A practical issue addressed in this dissertation is the linkage between mechanical design and robotic task-level planning. The formal treatment of $TR$ symmetry groups has been embedded into the implementation of an assembly planning system ${\cal KA}$3, which takes as input the geometric boundary models of assembly components provided by an off-the-shelf geometric solid modeller PADL2, and a set of instructions in the form of 'body A fits body B'. ${\cal KA}$3 finds a set of detailed robotic assembly task specifications in three steps: Step one: ${\cal KA}$3 finds mating features from the boundary models of assembly components using a salient feature library and the symmetry group intersection algorithm. Step two: ${\cal KA}$3 applies techniques used in constraint satisfaction problems (CSP) to satisfy kinematic and spatial constraints for each candidate assembly configuration. Step three: ${\cal KA}$3 generates a partially ordered sequence of contact states for assembly components through an analysis of disassembly via translational motion. The interaction between algebra and geometry within a group theoretic framework and the interaction between CSP techniques and heuristic search strategies provide us with a unified computational treatment of reasoning about how parts with multiple contacting features fit together.

Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In the first part of this dissertation we consider two such restricted specification logics on words: linear temporal logic (LTL) and two-variable first-order logic (FO2). LTL is more expressive but FO2 can be more succinct, and hence it is not clear which should be easier to verify. We take a comprehensive look at the issue, giving a comparison of verification problems for FO2, LTL, and various sublogics thereof across a wide range of models. In particular, we look at unary temporal logic (UTL), a subset of LTL that is expressively equivalent to FO2. We give three logic-to-automata translations which can be used to give upper bounds for FO2 and UTL and various sublogics. We apply these to get new bounds for model checking both non-deterministic systems (hierarchical and recursive state machines, games) and for probabilistic systems (Markov chains, recursive Markov chains, and Markov decision processes). Our results give a unified approach to understanding the behaviour of FO2, LTL, and their sublogics. We further consider the problem of computing maximal probabilities for interval Markov chains (and recursive interval Markov chains, stochastic context-free grammars) to satisfy LTL specifications. Using again our automata constructions we describe an expectation-maximisation algorithm to solve this problem in practice. Our algorithm can be seen as a variant of the classical Baum-Welch algorithm on hidden Markov models. We also introduce a publicly available on-line tool Tulip to perform such analysis. Finally, we investigate the extension of our techniques from words to trees. We show that the parallel between the complexity of FO2 satisfiability on general and on restricted structures breaks down as we move from words to trees, since trees allow one to encode alternating exponential time computation.

A system is data independent in a type T if the only operations allowed on variables of type T are input, output, assignment and equality testing. This property can be exploited to give procedures for the automatic verification of such systems independently of the instance of the type T. Alloy is an extension of first-order logic for modelling software systems. Alloy has a fully automatic analyzer which attempts to refute Alloy formulas by searching for counterexamples within a finite scope. However, failure to find a counterexample does not prove the formula correct. A small model theorem is a theorem which shows that if a formula has a model then it has a model within some finite scope. The contribution of this thesis is to give a small model theorem which applies when modelling data-independent systems in Alloy. The theorem allows one to detect automatically whether an Alloy formula is data independent in some type T and then calculate a threshold scope for T, thereby completing the analysis of the automatic analyzer with respect to the type T. We derive the small model theorem using a model-theoretic approach. We build on the standard semantics of the Alloy language and introduce a more abstract interpretation of formulas, by way of a Galois insertion. This more abstract interpretation gives the same truth value as the original interpretation for many formulas. Indeed we show that this property holds for any formula built with a limited set of language constructors which we call data-independent constructors. The more abstract interpretation is designed so that it often lies within a finite scope and we can calculate whether this is the case and exactly how big the finite scope need be from the types of the free variables in the formula. In this way we can show that if a formula has any instance or counterexample at all then it has one within a threshold scope, the size of which we can calculate.