Today the modern power system is more dynamic and its operation is a subject to a number of constraints that are reflected in various management and planning tools used by system operators. In the case of hourly generation planning, Economic Dispatch (ED) allocates the outputs of all committed generating units, which are previously identified by the solution of the Unit Commitment (UC) problem. Thus, the accurate solutions of the ED and UC problems are essential in order to operate the power system in an economic and efficient manner. A number of computation techniques have progressively been proposed to solve these critical issues. One of them is a Particle Swarm Optimisation (PSO), which belongs to the evolutionary computation techniques, and it has attracted a great attention of the research community since it has been found to be extremely effective in solving a wide range of engineering problems. The attractive characteristics of PSO include: ease of implementation, fast convergence compared with the traditional evolutionary computation techniques and stable convergence characteristic. Although the PSO algorithms can converge very quickly towards the optimal solutions for many optimisation problems, it has been observed that in problems with a large number of suboptimal areas (i.e. multi-modal problems), PSO could get trapped in those local minima, including ED and UC problems. Aiming at enhancing the diversity of the traditional PSO algorithms, this thesis proposes a method of combining the PSO algorithms with a real-valued natural mutation (RVM) operator to enhance the global search capability and investigate the performance of the proposed algorithm compared with the standard PSO algorithms and other algorithms. Prior to applying to ED and UC problems, the proposed method is tested with some selected mathematical functions where the results show that it can avoid being trapped in local minima. The proposed methodology is then applied to ED and UC problems, and the obtained results show that it can provide solutions with good accuracy and stable convergence characteristic with simple implementation and satisfactory calculation time. Furthermore, the sensitivity analysis of PSO parameters has been studied so as to investigate the response of the proposed method to the parameter variations, especially in both ED and UC problems. The outcome of this research shows that the proposed method succeeds in dealing with the PSO' s drawbacks and also shows the superiority over the traditional PSO algorithms and other methods in terms of high quality solutions, stable convergence characteristic, and robustness.

In this thesis, robust set-valued estimation is studied and its application to in-flight alignment of strapdown inertial navigation systems (SINS) with large heading uncertainty is performed. It is known that the performance of the Kalman filter is vulnerable to modeling errors. One of the estimation methods, which are robust against modeling errors, is robust set-valued estimation. In this approach, the filter calculates the set of all possible states, which are consistent with uncertainty inputs satisfying an integral quadratic constraint (IQC) for given measured system outputs. In this thesis, robust set-valued filter with deterministic input is derived. In-flight alignment of SINS with Kalman filtering using external measurements is a widely used technique to eliminate the initial errors. However, if the initial errors are large then the performance of standard Kalman filtering technique is degraded due to modeling error caused by linearization process. To solve this problem, a novel linear norm-bounded uncertain error model is proposed where the remaining second orders terms due to linearization process are considered as norm-bounded uncertainty regarding only the heading error is large. Using the uncertain error model, the robust set-valued filter is applied to in-flight alignment problem. The comparison of the Kalman filter and the robust filter is done on a simulated trajectory and a real-time data. The simulation results show that the modeling errors can be compensated to some extent in Kalman filter by increasing the process noise covariance matrix. However, for very large initial heading errors, the proposed method outperforms the Kalman filter.

Orientador: Walter Alexandre Carnielli / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-23T18:22:31Z (GMT). No. of bitstreams: 1 Matulovic_Mariana_D.pdf: 1191409 bytes, checksum: 5228f60f9fdb9f3a9df31d448de09ca2 (MD5) Previous issue date: 2013 / Resumo: O presente trabalho tem por objetivo explorar, em diversas vertentes, o caráter universal de uma ferramenta poderosa de prova, apta a ser utilizada em lógicas clássicas e não clássicas, em particular em lógicas multivaloradas proposicionais (determinísticas e não-determinísticas), em lógicas paraconsistentes, em lógicas modais e na Lógica de Primeira Ordem. Trata-se do Método de Prova de Anéis de Polinômios, que também pode, em princípio, ser visto do ponto de vista da semântica algébrica, desenvolvido inicialmente em (Carnielli 2005b). O método traduz fórmulas de uma lógica específica em polinômios (em geral finitos, mas podendo ser infinitos) com coeficientes em corpos finitos, e transforma o problema de se encontrar demonstrações no correlato algébrico da busca de soluções de sistemas de equações polinomiais. Esta universalidade do método possibilita a abertura de diversas linhas de pesquisa, sendo a questão da verofuncionalidade e suas generalizações uma delas. Outras linhas de pesquisa são: possibilidades de se investigar enfoques alternativos da complexidade computacional, prova automática de teoremas, métodos heurísticos em lógica e correlações entre álgebra e lógica. Este trabalho analisa e compara sistemas de anéis de polinômios para sistemas com verofuncionalidade generalizada, como no caso das semânticas não-determinísticas, e ainda em sistemas onde a verofuncionalidade é perdida, tais como em sistemas multivalorados reduzidos a bivalorados através da conhecida redução de Suszko. O método de anéis de polinômios, além de poderoso e elegante em sua aparente simplicidade, constitui ainda um ótimo instrumento pedagógico. Em relação á lógica clássica, definimos um anel de polinômios para a Lógica de Primeira Ordem, fundamentado em um novo domínio que opera com somas e produtos infinitos, o qual se denomina domínio de séries generalizadas fechado por produtos. Finalmente, procuramos avaliar todas as potencialidades do método, principalmente no aspecto inerente á questão de se poder pensar em uma característica unificadora na medida que utiliza o mesmo viés matemático para traduzir diferentes sistemas lógicos em variedades algébricas similares. Além disso, analisamos as interrelações do método com respeito a lógica algébrica (ou álgebra da lógica), e avaliamos suas perspectivas / Abstract: This investigation aims to explore, in various aspects, the universal character of a powerful proof method, able to be used in classical and non-classical logics, in particular in propositional many-valued logics (deterministic and non- deterministic) in paraconsistent logics, in modal logics and in First Order Logic. This is the Method of Polynomial Rings, which can also be considered as an algebraic semantics, initially developed in (Carnielli 2005b). The method translates logical formulas into specific polynomials (usually finite, but sometimes infinite) with coefficients infinite fields, and transforms the problem of finding proofs in the search for solutions of systems of polynomial equations. This universality of the method enables the opening of several research lines, in particular the issue of truth-functionality and its generalizations. Other lines of research are: the possibilities of investigating alternative approaches of computational complexity, automatic theorem proving, heuristic methods in logic and correlations between algebra and logic. This study compares and analyzes the polynomial ring systems for systems with generalized truth-functionality, as in the case of non- deterministic semantic and even in systems where truth-functionality is lost, such as those many-valued systems reduced to bivalued by means of the so-called Suszko reduction. The method of polynomial rings, besides being a powerful and elegant apparatus in its apparent simplicity, is still a great teaching tool. Regarding classical logic, we define the polynomial ring for First Order Logic , based on a new domain that operates on sums and infinite products, called domain of generalized series closed under products. Finally, we evaluate the full potential of the method, especially in what concerns the question of obtaining a unifying feature that uses the same mathematical basis to translate different logical systems on similar algebraic varieties. Furthermore, we address the connections of the method with respect to algebraic logic (algebra of logic), and evaluate their perspectives / Doutorado / Filosofia / Doutora em Filosofia

Dans cette thèse, nous nous intéressons à des inclusions de la forme 0∈ f( x) + F(x), où f est une application univoque et F est une application multivoque à graphe fermé. Ces dernières années, diverses méthodes de résolutions d'inclusions de ce type ont été développées par les chercheurs et, après un bref rappel sur quelques notions d'analyse (univoque et multivoque) nous en présentons quelques unes utilisant l'hypothèse de régularité métrique sur l'application multivoque. Dans la suite de notre travail, plutôt que d'utiliser cette hypothèse de régularité métrique, nous lui préférons des hypothèses directement liées à la solution qui sont la semistabilité et l'hemistabilité. Notons que la semistabilité d'une solution x̅ de l'inclusion 0∈G(x) est en fait équivalente à la sous-régularité métrique forte de l'application multivoque G en x̅ pour 0. Après avoir présenté des méthodes utilisant la semistabilité et l'hemistabilité, nous exposons les nouveaux résultats auxquels nous avons abouti qui consistent essentiellement en des améliorations des méthodes présentées. Ce que nous entendons par améliorations se décline en deux points principaux : soit nous obtenons un meilleur taux de convergence, soit nous utilisons des hypothèses plus faibles qui nous permettent d'obtenir des taux de convergence similaires. / In this thesis, we focus on inclusions in the form of 0∈ f( x) + F(x), where f is a single-valued function and F is a set-valued map with closed graph. In the last few years, various methods to solve such inclusions have been developed; after having recalled some notions in analysis (single-valued and set-valued) we present some of them using metric regularity on the set-valued map. Then, instead of considering this metric regularity assumption, we prefer assumptions which are directly connected to the solution, that are semistability and hemistability. One can note that semistabily of a solution x̅ of the inclusion 0∈G(x) is actually equivalent strong metric subregularity on the set-valued map G at x̅ for 0. After having presented some methods using semistability and hemistability, we show the new results we obtained, most of them being improvement of the presented methods. What we mean by improvement is mainly a better convergence rate on the one hand, and weaker assumptions that lead to similar convergence rate, on the other.

L’intérêt des différents langages de la famille des diagrammes de décisionvalués (VDD) est qu’ils admettent des algorithmes en temps polynomialpour des traitements (comme l’optimisation, la cohérence inverse globale,l’inférence) qui ne sont pas polynomiaux (sous l’hypothèse P 6= NP), si ilssont effectués sur le problème dans sa forme originale tel que les réseaux decontraintes ou les réseaux bayésiens.Dans cette thèse, nous nous intéressons au problème de configuration deproduit, et plus spécifiquement, la configuration en ligne avec fonction de valuationassociée (typiquement, un prix). Ici, la présence d’un utilisateur enligne nous impose une réponse rapide à ses requêtes, rapidité rendant impossiblel’utilisation de langages n’admettant pas d’algorithmes en temps polynomialpour ces requêtes. La solution proposée est de compiler hors-ligneces problèmes vers des langages satisfaisant ces requêtes, afin de diminuer letemps de réponse pour l’utilisateur.Une première partie de cette thèse est consacrée à l’étude théorique desVDD, et plus particulièrement les trois langages Algebraic Decision Diagrams,Semi ring Labelled Decision Diagrams et Affine Algebraic Decision Diagrams(ADD, SLDD et AADD). Nous y remanions le cadre de définition des SLDD,proposons des procédures de traductions entre ces langages, et étudions la compacitéthéorique de ces langages. Nous établissons dans une deuxième partie lacarte de compilation de ces langages, dans laquelle nous déterminons la complexitéalgorithmique d’un ensemble de requêtes et transformations correspondantà nos besoins. Nous proposons également un algorithme de compilationà approche ascendante, ainsi que plusieurs heuristiques d’ordonnancement devariables et contraintes visant à minimiser la taille de la représentation aprèscompilation ainsi que le temps de compilation. Enfin la dernière partie estconsacrée à l’étude expérimentale de la compilation et de l’utilisation de formescompilées pour la configuration de produit. Ces expérimentations confirmentl’intérêt de notre approche pour la configuration en ligne de produit.Nous avons implémenté au cours de cette thèse un compilateur (le compilateurSALADD) pleinement fonctionnel, réalisant la compilation de réseauxde contraintes et de réseaux bayésiens, et avons développés un ensemble defonctions adaptées à la configuration de produit. Le bon fonctionnement etles bonnes performances de ce compilateur ont été validés via un protocole devalidation commun à plusieurs solveurs. / The different languages from the valued decision diagrams (VDD) family benefitfrom polynomial-time algorithms for some tasks of interest (such as optimization,global inverse consistency, inference) for which no polynomial-timealgorithm exists (unless P = NP) when the input is a constraint network ora Bayesian network considered at start.In this thesis, we focus on configuration product problems, and more specificallyon-line configuration with an associated valuation function (typically, aprice). In this case, the existence of an on-line user forces us to quickly answerto his requests, making impossible the use of languages that does not admitpolynomial-time algorithm for this requests. Therefore, our solution consistsin an off-line compilation of these problems into languages that admit suchpolynomial-time algorithms, and thus decreasing the latency for the user.The first part of this thesis is dedicated to the theoretical study of VDDs,an more specifically Algebraic Decision Diagrams (ADDs), Semi ring LabelledDecision Diagrams (SLDDs) and Affine Algebraic Decision Diagrams(AADDs). We revisit the SLDD framework, propose translation proceduresbetween these languages and study the succinctness of these languages. In asecond part, we establish a knowledge compilation map of these languages,in which we determine the complexity of requests and transformations correspondingto our needs. We also propose a bottom-up compilation algorithmand several variables and constraints ordering heuristics whose aim is to reducethe size of the compiled form, and the compilation time. The last partis an experimental study of the compilation and the use of the compiled formin product configuration. These experimentations confirm the interest of ourapproach for on-line product configuration.We also implemented a fully functional bottom-up compiler (the SALADDcompiler), which is capable of compiling constraints network and Bayesian networkinto SLDDs. We also developed a set of functions dedicated to productconfiguration. The proper functioning and good performances of this programwas validated by a validation protocol common to several solvers.

Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.

The main object of this thesis is to review financial situation of the company Grammer CZ by using financial analysis method. The thesis contains theoretical and practical parts. The theoretical module includes determination of the theoretic-methodological data, which serve as basis of processing financial analysIs of selected company. The practical module includes horizontal and vertical analysis of financial reports, analysis of basic ratio indicators and analysis of economic value added (EVA) of the company. The final values are compared with averages in branch, in which the selected company is working.

<p>Proučeno je oscilatorno kretanje i disipacija energije stuba napravljenog<br />od nekoliko krutih blokova, koji pri horizontalnom seizmičkom dejstvu<br />mogu da klize jedan po drugom. Pored međusobnog kontakta sa trenjem, koje je<br />modelirano neglatkom viševrednosnom funkcijom, veze između blokova<br />sadrže i viskoelastične elemente, čije konstitutivne relacije uključuju<br />frakcione izvode, kao i ograničenja na koeficijente koja slede iz<br />Klauzius-Dijemove nejednakosti. Postavljeni Košijev problem predstavlja<br />uopštenje klasičnog problema ponašanja konstrukcija pod dejstvom<br />seizmičkog opterećenja, jer objedinjuje izvode proizvoljnog realnog reda<br />sa teorijom neglatkih viševrednosnih funkcija. Predložena je numerička<br />procedura za rešavanje postavljenog problema.</p> / <p> Seismic response and energy dissipation of a column made of several rigid<br /> blocks, which can slide along each other, was considered. Besides friction<br /> contact, which was modeled by a set valued function, viscoelastic elements<br /> whose constitutive equations include fractional derivatives as well as restrictions<br /> on the coefficients that follow from Clausius-Duhem inequality are present in<br /> connections between blocks. The posed Caushy problem represents the<br /> generalization of a classical problem of seismic response because it merges<br /> fractional derivatives with the theory of set valued functions. The numerical<br /> procedure for solving the problem was suggested.</p>

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Ramanujan introduced his now celebrated mock theta functions in 1920, grouping them into families parameterized by an integer called the order. In 2010 Bringmann and Ono discovered generalizations of Ramanujan's mock theta functions for any order relatively prime to 6; this result was later strengthened by Garvan in 2016. It was also shown that by adding suitable nonholomorphic completion terms to the mock theta functions the family of mock theta functions corresponding to a given order constitute a complex vector space which is closed under the action of the modular group. We strengthen the Bringmann, Ono, and Garvan result by constructing a vector-valued modular form of weight 1/2 transforming according the Weil representation for orders greater than 3 by introducing an algorithm which simultaneously numerically constructs the form and proves its transformation laws. We also explicitly construct the 7th order form and prove analytically that it has the proper modular transformations. It is conjectured the same method will apply for other orders.