Semi-infinite programming problems is a class of optimization problems in finite dimensional variables which are subject to infinitely many inequality constraints. If the infinite index of inequality constraints depends on the decision variable, then the problem is called generalized semi-infinite programming problem (GSIP). If the infinite index set is fixed, then the problem is called standard semi-infinite programming problem (SIP). In this thesis, convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems is investigated. In this method, using nonlinear complementarity problem functions the upper and lower level Karush-Kuhn-Tucker conditions of the optimization problem are reformulated as a semismooth system of equations. A possible violation of strict complementary slackness causes nonsmoothness. In this study, we show that the standard regularity condition for convergence of the semismooth Newton method is satisfied under natural assumptions for semi-infinite programs. In fact, under the Reduction Ansatz in the lower level problem and strong stability in the reduced upper level problem this regularity condition is satisfied. In particular, we do not have to assume strict complementary slackness in the upper level. Furthermore, in this thesis we neither assume strict complementary slackness in the upper nor in the lower level. In the case of violation of strict complementary slackness in the lower level, the auxiliary functions of the locally reduced problem are not necessarily twice continuously differentiable. But still, we can show that a standard regularity condition for quadratic convergence of the semismooth Newton method holds under a natural assumption for semi-infinite programs. Numerical examples from, among others, design centering and robust optimization illustrate the performance of the method.

Randomness is an invaluable resource in theoretical computer science. However, pure random bits are hard to obtain. Quasi-randomness is a tool that has been widely used in eliminating/reducing the randomness from randomized algorithms. In this thesis, we study some aspects of quasi-randomness in graphs. Specifically, we provide an algorithm and a lower bound for two different kinds of regularity lemmas. Our algorithm for FK-regularity is derived using a spectral characterization of quasi-randomness. We also use a similar spectral connection to also answer an open question about quasi-random tournaments. We then provide a "Wowzer" type lower bound (for the number of parts required) for the strong regularity lemma. Finally, we study the derandomization of complexity classes using Turing machine simulations. 1. Connections between quasi-randomness and graph spectra. Quasi-random (or pseudo-random) objects are deterministic objects that behave almost like truly random objects. These objects have been widely studied in various settings (graphs, hypergraphs, directed graphs, set systems, etc.). In many cases, quasi-randomness is very closely related to the spectral properties of the combinatorial object that is under study. In this thesis, we discover the spectral characterizations of quasi-randomness in two different cases to solve open problems. A Deterministic Algorithm for Frieze-Kannan Regularity: The Frieze-Kannan regularity lemma asserts that any given graph of large enough size can be partitioned into a number of parts such that, across parts, the graph is quasi-random. . It was unknown if there was a deterministic algorithm that could produce a parition satisfying the conditions of the Frieze-Kannan regularity lemma in deterministic sub-cubic time. In this thesis, we answer this question by designing an O(n[superscript]w) time algorithm for constructing such a partition, where w is the exponent of fast matrix multiplication. Even Cycles and Quasi-Random Tournaments: Chung and Graham in had provided several equivalent characterizations of quasi-randomness in tournaments. One of them is about the number of "even" cycles where even is defined in the following sense. A cycle is said to be even, if when walking along it, an even number of edges point in the wrong direction. Chung and Graham showed that if close to half of the 4-cycles in a tournament T are even, then T is quasi-random. They asked if the same statement is true if instead of 4-cycles, we consider k-cycles, for an even integer k. We resolve this open question by showing that for every fixed even integer k geq 4, if close to half of the k-cycles in a tournament T are even, then T must be quasi-random. 2. A Wowzer type lower bound for the strong regularity lemma. The regularity lemma of Szemeredi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. Alon, Fischer, Krivelevich and Szegedy obtained a variant of the regularity lemma that allows one to have an arbitrary control on this measure of quasi-randomness. However, their proof only guaranteed to produce a partition where the number of parts is given by the Wowzer function, which is the iterated version of the Tower function. We show here that a bound of this type is unavoidable by constructing a graph H, with the property that even if one wants a very mild control on the quasi-randomness of a regular partition, then any such partition of H must have a number of parts given by a Wowzer-type function. 3. How fast can we deterministically simulate nondeterminism? We study an approach towards derandomizing complexity classes using Turing machine simulations. We look at the problem of deterministically counting the exact number of accepting computation paths of a given nondeterministic Turing machine. We provide a deterministic algorithm, which runs in time roughly O(sqrt(S)), where S is the size of the configuration graph. The best of the previously known methods required time linear in S. Our result implies a simulation of probabilistic time classes like PP, BPP and BQP in the same running time. This is an improvement over the currently best known simulation by van Melkebeek and Santhanam.

On the first part, we consider nonlinear operators I depending on a family of nonlocal linear operators [mathematical equations]. We study the solutions of the Dirichlet initial and boundary value problems [mathematical equations]. We do not assume even symmetry for the kernels. The odd part bring some sort of nonlocal drift term, which in principle competes against the regularization of the solution. Existence and uniqueness is established for viscosity solutions. Several Hölder estimates are established for u and its derivatives under special assumptions. Moreover, the estimates remain uniform as the order of the equation approaches the second order case. This allows to consider our results as an extension of the classical theory of second order fully nonlinear equations. On the second part, we study two phase problems posed over a two dimensional cone generated by a smooth curve [mathematical symbol] on the unit sphere. We show that when [mathematical equation] the free boundary avoids the vertex of the cone. When [mathematical equation]we provide examples of minimizers such that the vertex belongs to the free boundary. / text

For degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient conditions for establishing continuity have already been documented in [FP], [SW1], and [MRW], and their necessity in [R]. However, the complexity of the equations discussed in those works makes it difficult to understand the core structure of the arguments employed. Here, we present a harmonic-analytic method for establishing Hölder continuity of weak solutions in context of a simple linear equation div(Q?u) = f in a homogeneous space structure in order to showcase the form of the argument. Ad- ditionally, we correct an oversight in the adaptation of the John-Nirenberg inequality presented in [SW1], restricting it to a much smaller class of balls.

Many problems in continuum mechanics, especially in the theory of elastic materials, lead to nonlinear partial differential equations. The nonconvexity of their underlying energy potential is a challenge for mathematical analysis, since convexity plays an important role in the classical theories of existence and regularity. In the last years one main point of interest was to develop techniques to circumvent these difficulties. One approach was to use different notions of convexity like quasi-- or polyconvexity, but most of the work was done only for static (time independent) equations. In this thesis we want to make some contributions concerning existence, regularity and numerical approximation of nonconvex dynamical problems.

In this dissertation, we focus on the uncertainty quantification problems where the goal is to sample the porous media properties given integrated responses. We first introduce a reduced order model using the level set method to characterize the channelized features of permeability fields. The sampling process is completed under Bayesian framework. We hence study the regularity of posterior distributions with respect to the prior measures. The stochastic flow equations that contain both spatial and random components must be resolved in order to sample the porous media properties. Some type of upscaling or multiscale technique is needed when solving the flow and transport through heterogeneous porous media. We propose ensemble-level multiscale finite element method and ensemble-level preconditioner technique for solving the stochastic flow equations, when the permeability fields have certain topology features. These methods can be used to accelerate the forward computations in the sampling processes. Additionally, we develop analysis-of-variance-based mixed multiscale finite element method as well as a novel adaptive version. These methods are used to study the forward uncertainty propagation of input random fields. The computational cost is saved since the high dimensional problem is decomposed into lower dimensional problems. We also work on developing efficient advanced Markov Chain Monte Carlo methods. Algorithms are proposed based on the multi-stage Markov Chain Monte Carlo and Stochastic Approximation Monte Carlo methods. The new methods have the ability to search the whole sample space for optimizations. Analysis and detailed numerical results are presented for applications of all the above methods.

In the case of a natural person, conjugal community or an undivided succession domiciled in Peru which generates capital gains by transferring immovable goods, the profit generated is taxed with income tax andmay be graded as second category income –capital gain– or third category income–entrepreneurial income. From the analysis of Peruvian legislation, the author explains how the regularity in the transfer of immovable goods is configured to grade the profit made as second category income –when, over a year´s time, no more than two goods are transferred– and how, from the third transfer onward, the income will qualify as a third category income. Likewise, the author puts in evidence how the transfer of immovable goods occupied as a home is not considered as a capital gain when the seller does not generate third category income. / Tanto las personas naturales cuanto las sociedades conyugales, así como las sucesionesindivisas domiciliadas en el país y que producen ganancias de capital por la enajenación de inmuebles, generan rentas que se encuentran gravadas con el Impuesto a la Renta. Éstas califican como de segunda categoría –renta de capital–o tercera categoría –renta empresarial. A partir de la legislación vigente, el autor analiza cómo la habitualidad funciona como criterio para calificar las rentas obtenidas por enajenar inmuebles como de segunda categoría–cuando sean no más de dos enajenaciones en un mismo año– y cómo, a partir de la tercera, éstas serán calificadas como de tercera categoría. Asimismo, evidencia que no constituirá ganancia de capital la enajenación de inmuebles ocupados como casa-habitación cuando el enajenante no genere rentas de tercera categoría.

An integral quadratic form is said to be strictly regular if it primitively represents all integers that are primitively represented by its genus. The goal of this dissertation is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception for that form. So, the strictly regular forms are those forms for which there are no primitive exceptions. Our computations of primitive exceptions for each of the 119 positive definite regular ternary forms which lie in multiple-class genera, and of the companion forms in their genera, show that there are 45 inequivalent such forms that are candidates for strict regularity. We provide a proof of the strict regularity of one of these candidates, bringing the total number of forms for which such proofs are known to 15, and prove partial results on the integers primitively represented by the other form in its genus. The theory of primitive spinor exceptional integers is used to analyze the primitive exceptions for the forms in two other genera known to contain a regular ternary form. In these cases, results are obtained relating the primitive representation of certain integers c by a given form in one of these genera to the primitive representation of the integers 4c and 9c by the forms in the genus.

Made available in DSpace on 2016-08-03T12:29:39Z (GMT). No. of bitstreams: 1 Marcos Paulo da Silva_2013.pdf: 4473442 bytes, checksum: fc5d5786af305d357f4fb43bbf661ccf (MD5) Previous issue date: 2013-01-30 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This dissertation is an eminently qualitative theoretical-conceptual discussion about the cultural construction of the newsworthiness criteria inside the journalism practice. Its central proposal is to insert the issue of newsworthiness that is, the debate around the responsible parameters for characterizing certain events as newsworthy events over others inside a wider cultural reflection that targets to dimensionate the news narrative as one of the most consistent elements of the modern everyday experience. The specific research goals are: 1) the theoretical discussion about some of the most significant conceptual approaches that the newsworthiness criteria have historically in the social sciences; 2) the presentation of an alternative group of theoretical conceptions that articulated can explain the complexity of the news selection process; and 3) a proposal of a theoretical-conceptual systematization for these articulations so that this dissertation could be synchronized with the state of art in the field of journalism theory. The debate will arrive, finally, in the creation of an explicative pendulum model that consolidates itself as a possible metaphor for the relation between the journalism practice, the everyday paradoxes and the symbolic parameters that characterize the everyday regularity as a cultural pattern of the modern sociability. / A tese constitui uma discussão teórico-conceitual de natureza eminentemente qualitativa sobre a construção cultural dos chamados critérios de noticiabilidade no jornalismo. Sua proposta central é inserir a problemática da noticiabilidade isto é, a discussão em torno dos parâmetros que levam determinados acontecimentos a receber a valoração de notícia em detrimento de outros no interior de uma reflexão mais ampla, de ordem culturalista, que objetiva dimensionar a narrativa noticiosa como um dos elementos estético-expressivos mais consistentes na sustentação da experiência cotidiana moderna. Como objetivos específicos, busca-se: 1) a discussão teórica de algumas das mais significativas abordagens conceituais que os critérios de noticiabilidade recebem historicamente nas ciências sociais; 2) a apresentação de um conjunto alternativo de concepções teóricas que, articuladas, possam explicitar a complexidade do processo de seleção noticiosa; e 3) a proposição de uma sistematização teórico-conceitual para tais articulações de modo a sintonizar a tese com o estado da arte no campo da teoria do jornalismo. Aporta-se, ao fim, na elaboração de um modelo explicativo pendular que se institui como metáfora possível para a relação entre o jornalismo, os paradoxos cotidianos e os parâmetros simbólicos que caracterizam a regularidade cotidiana como padrão cultural da sociabilidade moderna.

O processo civil precisa de ordem, simplicidade e eficiência para atingir o seu escopo de prestação de uma tutela jurisdicional adequada, justa e célere. Para tanto, o ordenamento processual tem sofrido relevantes modificações com o objetivo de se adaptar às novas exigências sociais e jurídicas, em que o formalismo deve servir para proteger, e não para derrubar. Além disso, variadas técnicas processuais têm sido utilizadas para conferir mais efetividade à tutela jurisdicional, sem prejuízo da necessária segurança jurídica. Nesse contexto se insere a ordem pública processual, que embora possa ter uma interessante abordagem principiológica, atua no processo como técnica de controle da regularidade de atos e do procedimento. Por sua vez, o papel do magistrado na gestão dessa técnica se mostra fundamental para ela atinja seu objetivo, que é eliminar do processo os defeitos capazes de macular a sua integridade, bem como a legitimidade da tutela judicial. O controle adequado e tempestivo da regularidade dos atos e do procedimento é um dever do juiz e também uma garantia das partes. Dessa forma, a tese busca identificar as questões processuais passíveis de controle, de acordo com o grau de interesse público que cada uma revela, sendo certo que a lei, a doutrina e a jurisprudência servem de fonte e ainda podem modular a relevância da matéria conforme tempo e espaço em que se observam. Por sua vez, a importância da avaliação do interesse público de cada questão processual reflete no regime jurídico que será estabelecido e as consequências que se estabelecem para os eventuais defeitos com base nas particularidades do caso concreto. Ademais, identificada a irregularidade, o processo civil oferece variadas técnicas de superação, convalidação e flexibilização do vício antes de se declarar a nulidade de atos processuais ou de se inadmitir o procedimento adotado pela parte, numa forma de preservar ao máximo o processo. Já no âmbito recursal, embora haja requisitos específicos de admissibilidade, os vícios detectados em primeiro grau de jurisdição perdem força em segundo grau e perante os Tribunais Superiores, haja vista a necessidade casa vez maior de se proporcionar ao jurisdicionado a entrega da prestação jurisdicional completa, ou seja, com o exame do mérito. Registre-se, ainda, a possibilidade de controle judicial nos meios alternativos de resolução de conflitos, uma vez que também devem se submeter a certos requisitos, para que sejam chancelados e legitimados. Como se observa, a abrangência do tema da ordem pública processual faz com que o ele seja extenso e complexo, o que normalmente assusta os operadores do direito. Portanto, o intento deste estudo é não só descrever o assunto, mas também adotar uma linguagem diferenciada, proporcionando uma nova forma de abordar e sistematizar o que ainda parece ser um dogma em nosso sistema processual. / Civil procedure requires order, simplicity, and efficiency in order to attain its scope of providing adequate jurisdictional adjudication that is fair and expeditious. To do so, the procedural system has endured relevant modifications in furtherance of adapting itself to new social and legal requirements, in which formalism should serve to protect and not to overturn. Furthermore, various technical procedures have been used to grant more effectiveness to jurisdictional adjudication, without damage to necessary juridical certainty. In this context, is contained the procedural public policy, which might possess an interesting approach for the principle, that engages the procedure as a technical means to control the regularity of the acts and the proceedings. In turn, the role of the magistrate in the management of this technique shows itself to be essential in order for it to accomplish its objective, which is to eliminate from the procedure, the defects capable of blotting its integrity, as well as the legitimacy of judicial adjudication. Appropriate and timely control of the regularity of the acts and the proceedings is a duty of the judge and also a guaranty to the parties. In this sense, the thesis seeks to identify procedural issues that could be controlled according to the degree of public interest wherein each one is revealed, being certain that the law, doctrine, and jurisprudence are the source and can still modulate the relevant matter according to the time and space in which they are observed, contextualized, or inserted. In turn, the importance of evaluating the public interest of each procedural matter reflects the legal regime to be established and the consequences established for any eventual defects on the basis of the particulars of the recorded case. Additionally, in identifying the irregularity, civil procedure offers various techniques for overcoming, confirming, and easing of a defect before declaring the nullity of the procedural acts or the inadmissibility of the procedure adopted by the party, in a way to preserve most of the procedure. Already in the appellate context, although there are specific requirements of admissibility, the defects detected at the first level of jurisdiction lose strength at the second level and before the Superior courts, giving each time a greater need to provide jurisdiction and the delivery of full jurisdictional performance, that is, with an examination on the merits. Registering still, the possibility of judicial control as an alternative means of dispute resolution, it also must undergo certain requirements, so as to be approved and legitimized. As noted, the range of the theme of procedural public policy causes it to be extensive and complex, which usually alarms jurists. Therefore, the intent of this study will not only be to describe the subject, but also to adopt a differentiated language, providing a new way to approach and systematize what still seems to be dogma in our procedural system.