Neste trabalho são estudados os parâmetros de verificação do estado limite de deformações excessivas (a relação flecha-altura-a/H) e da estabilidade global (o parâmetro &#945 e o coeficiente &#947z) das estruturas de edifícios. Através da utilização de exemplos de estruturas de trinta (30) edifícios usuais de concreto armado, estabelece-se uma relação entre esses parâmetros, objetivando propiciar ao projetista de estruturas condições de avaliar a eficiência e o grau de confiabilidade de cada um deles. São também discutidos e comparados alguns dos procedimentos usuais para realizar uma análise global de segunda ordem das estruturas. Nesta análise deve-se levar em conta tanto a não-linearidade física (NLF) quanto a geométrica (NLG) e, para tanto, são adotados métodos rigorosos e aproximados. Quer-se com isso, principalmente, analisar o processo simplificado como suficiente para se obter os esforços finais de segunda ordem, uma vez que se pretende incluir tal procedimento na norma brasileira NB-1, atualmente em fase de revisão. / In this work, a servicebility pararneter (displacement-height ratio - a/H) is studied, as well as the global stability parameters of building structures (&#945 and &#947z stability coefficients). By analyzing thirty (30) actual reinforced concrete building structures, a relationship among these parameters (&#945, &#947z and a/H) is achieved aiming to demonstrate to the building structure designers their level of efficiency and reliability for practical purposes. Some standard procedures for global second order structure analysis are also discussed with comparison among them. In this analysis, the material and the geometric non-linearities have to be considered and for that one can adopt approximated and accureted methods. Mainly, the interest is to verify the possibility of using the simplified method as a proper tool to compute the final second order efforts of buildings, once this procedure could be included into the Brazilian Code, NB-1, which is being revised.

Neste trabalho são estudados os parâmetros de verificação do estado limite de deformações excessivas (a relação flecha-altura-a/H) e da estabilidade global (o parâmetro &#945 e o coeficiente &#947z) das estruturas de edifícios. Através da utilização de exemplos de estruturas de trinta (30) edifícios usuais de concreto armado, estabelece-se uma relação entre esses parâmetros, objetivando propiciar ao projetista de estruturas condições de avaliar a eficiência e o grau de confiabilidade de cada um deles. São também discutidos e comparados alguns dos procedimentos usuais para realizar uma análise global de segunda ordem das estruturas. Nesta análise deve-se levar em conta tanto a não-linearidade física (NLF) quanto a geométrica (NLG) e, para tanto, são adotados métodos rigorosos e aproximados. Quer-se com isso, principalmente, analisar o processo simplificado como suficiente para se obter os esforços finais de segunda ordem, uma vez que se pretende incluir tal procedimento na norma brasileira NB-1, atualmente em fase de revisão. / In this work, a servicebility pararneter (displacement-height ratio - a/H) is studied, as well as the global stability parameters of building structures (&#945 and &#947z stability coefficients). By analyzing thirty (30) actual reinforced concrete building structures, a relationship among these parameters (&#945, &#947z and a/H) is achieved aiming to demonstrate to the building structure designers their level of efficiency and reliability for practical purposes. Some standard procedures for global second order structure analysis are also discussed with comparison among them. In this analysis, the material and the geometric non-linearities have to be considered and for that one can adopt approximated and accureted methods. Mainly, the interest is to verify the possibility of using the simplified method as a proper tool to compute the final second order efforts of buildings, once this procedure could be included into the Brazilian Code, NB-1, which is being revised.

Neste trabalho investigamos alguns aspectos da Lógica de Segunda Ordem, dividindo o tema em três capítulos. No primeiro capítulo discorremos sobre os conceitos básicos desta Lógica, tais como conjunto de fórmulas, sistemas dedutivos e semânticas. Fazemos também um contraste com a Lógica de Primeira Ordem, que é mais conhecida, para se ter uma espécie de modelo do qual estamos nos diferenciando. Provamos o teorema da completude para a Lógica de Segunda Ordem, devido a L. Henkin em Henkin (1950). No segundo capítulo nós procuramos entender o que acontece com a semântica da teoria de conjuntos ZF C (que é de primeira ordem) se adicionarmos alguns axiomas de segunda ordem, criando uma teoria que chamamos de ZF 2 . Mostramos um teorema devido a Zermelo (Zermelo (1930)) que diz que os modelos desta teoria são essencialmente os mesmos. Tam- bém procuramos investigar a questão da Hipótese do Contínuo com relação à de um metódo de forcing para esta teoria, mostramos que a HC ZF 2 e, através continua sem resposta. No terceiro capítulo, escrevemos sobre três temas diferentes: o primeiro é sobre a relação que existe entre a propriedade da completude, da compacidade e a semântica de Henkin. O teorema de Lindström, que provamos nesta seção, diz essencialmente que não podemos ter completude e compacidade para a Lógica de Segunda Ordem ao menos que usemos esta semântica. Na segunda seção, investigamos o número de Hanf da Lógica de Segunda Ordem com a semântica Padrão e, na terceira seção, mostramos que é possível fazer uma redução das Lógicas de ordem superior à segunda e que o conjunto das fórmulas válidas da Lógica de Segunda Ordem não é denível na estrutura dos números naturais. / In this work we investigate some aspects of Second-Order Logic, splitting the theme in three chapters. In the rst one, we discuss the basic concepts of that Logic, such as set of formulas, deductive systems and semantics. We also make a contrast with First-Order Logic, which is better know, in order to have some kind of model from wich we are dierentiating. We prove the theorem of the completeness for the Second-Order Logic, due to L. Henkin in Henkin (1950). In the second chapter we try to understand what happens with the semantics of the ZF C set theory (which is a First-Order theory) if we add some Second-Order axioms, creating a theory that we call ZF 2 . We prove a theorem due to Zermelo (Zermelo (1930)) which says that the models of this theory are essentially the same. We also investigate the question of the Continuum Hypothesis in relation to theory, we show that the HC ZF 2 and, through a method of forcing for that still has no answer. In the third chapter, we write about three dierent themes: the rst is about the relation that exists between the property of completeness, of compactness and the Henkin semantics. The Lindström\'s theorem, which we prove in this section, says essentially that we can\'t have the completeness and the compactness for the Secon-Order Logic without Henkin semantics. In the second section, we investigate the Hanf Number of Second-Order Logic and, in the third section, we show that it is possible to make a reduction of Logics of order higher than the second to the second and that the set of the Second-Order valid formulas is not denable in the structure of the natural numbers.

Under adequate conditions on $g$, we show the density in $L^2((0,\pi),(0,2\pi))$ of the set of functions $p$ for which \begin{equation*} u_{tt}(x,t)-u_{xx}(x,t)= g(u(x,t)) + p(x,t) \end{equation*} has a weak solution subject to \begin{equation*} \begin{aligned} u(x,t)&=u(x,t+2\pi)\\ u(0,t)&=u(\pi,t)=0. \end{aligned} \end{equation*} To achieve this, we prove a Saddle Point Principle by means of a refined variant of the deformation lemma of Rabinowitz. Generally, inf-sup techniques allow the characterization of critical values by taking the minimum of the maximae on some particular class of sets. In this version of the Saddle Point Principle, we introduce sufficient conditions for the existence of a saddle-structure which is not restricted to finite-dimensional subspaces.

Mixed-format tests containing both multiple-choice (MC) items and constructed-response (CR) items are used in many testing programs. The use of multiple formats presents a number of measurement challenges, one of which is how to adequately equate mixed-format tests under the common-item nonequivalent groups (CINEG) design, especially when, due to practical constraints, the common-item set contains only MC items. The purpose of this dissertation was to evaluate how equating properties were preserved for mixed-format tests under the CINEG design. Real data analyses were conducted on 22 equating linkages of 39 mixed-format tests from the Advanced Placement (AP) Examination program. Four equating methods were used: the frequency estimation (FE) method, the chained equipercentile (CE) method, item response theory (IRT) true score equating, and IRT observed score equating. In addition, cubic spline postsmoothing was used with the FE and CE methods. The factors of investigation were the correlation between MC and CR scores, the proportion of common items, the proportion of MC-item score points, and the similarity between alternate forms. Results were evaluated using three equating properties: first-order equity, second-order equity, and the same distributions property. The main findings from this dissertation were as follows: (1) Between the two IRT equating methods, true score equating better preserved first-order equity than observed score equating, and observed score equating better preserved second-order equity and the same distributions property than true score equating. (2) Between the two traditional methods, CE better preserved first-order equity than FE, but in terms of preserving second-order equity and the same distributions property, CE and FE produced similar results. (3) Smoothing helped to improve the preservation of second-order equity and the same distributions property. (4) A higher MC-CR correlation was associated with better preservation of first-order equity for both IRT methods. (5) A higher MC-CR correlation was associated with better preservation of second-order equity for IRT true score equating. (6) A higher MC-CR correlation was associated with better preservation of the same distributions property for IRT observed score equating. (7) The proportion of common items, the proportion of MC score points, and the similarity between forms were not found to be associated with the preservation of the equating properties. These results are interpreted in the context of research literature in this area and suggestions for future research are provided.

Two methods of analyzing multi-dimensional frequency data are detailed. The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴi's and ϴj's. The ϴi's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴij are not zero, then the ϴi's are analogous to a main effect in a 2m factorial analysis, (m = number of factors or classifications). The ϴif's may be interpreted as a measure and direction of the two factor relationships. These ϴij are analogous to partial or adjusted phi-coefficients. The second method discussed assumes a multinomial distribution and the statistics are developed from an Information Theoretic Approach. Each hypothesis is tested using twice the minimum discrimination information statistic (m.d.i.s), 2I. From the null hypothesis it is possible to estimate unique cell probabilities by an iterative metod. Then 2 is equal to 2 (sample frequencies) log (sample frequencies) - 2 (expected frequencies) log (expected frequencies). (141 pages)

<p>For random waves the free surface elevation can be described by a number of individual wave parameters. The main objective of this work has been to study the statistical properties of individual parameters in successive waves; the wave crest height, the wave height and the wave period.</p><p>In severe sea states the wave crest heights exhibit a nonlinear behavior, which must be reflected in the models. An existing marginal distribution that uses second order Stokes-type nonlinearity is transformed to a two-dimensional distribution by use of the two–dimensional Rayleigh distribution. This model only includes sum frequency effects. A two-dimensional distribution is also established by transforming a second order model including both sum and different frequency effects. Both models are based on the narrow-band assumption, and the effect of finite water depth is included. A parametric wave crest height distribution proposed by Forristall (2000) has been extended to two dimensions by transformation of the two-dimensional Weibull distribution. </p><p>Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregression model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. </p><p>Successive wave periods are modeled with the Nataf transformation by using a two-parameter Weibull distribution and a generalized Gamma distribution as the initial distribution, where the latter is in best agreement with data. Results for the marginal and two-dimensional distributions are compared with existing models. In practical applications, it is often of interest to consider successive wave periods with corresponding wave heights exceeding a certain threshold. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights can be approximated by a multivariate Gaussian distribution. When comparing the results with data, a long time series is needed in order to obtain enough data cases. Results for three successive wave periods are also presented. </p><p>The models are compared with field data from the Draupner field and the Japan Sea, and with laboratory data from experiments at HR Wallingford. In addition, data from numerical simulations based on second order wave theory, including both sum and frequency effects, are included.</p>

<p>Participation in the European Parliament Election has steadily declined since the start in 1979. In 2004 less than half (47.8%) of the voting-age population of the European Union used their right to vote. This has actualized questions asking if the European Parliament is a good representation of the European citizens. The paradigm when it comes to explaining the electoral turnout in the European Parliament Election is the second-order theory. Though the theory explains the low voter participation, it does not explain why the European Parliament Election has become a second-order election. Thus, in this thesis will search for the underlying variable explaining why the European Parliament Election is a second-order election. Through our research we find that distances are important in the European Union, and they create centres and peripheries within the European Union. By looking at Rokkan and Urwin‟s horizontal and vertical types of peripheries, where the vertical type consists of Rokkan and Urwin‟s three domain of social life, our research concludes that centre-periphery structures within the European Union are the underlying variable, explaining why the European Parliament Election is a second-order election.</p>

The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : Rn → R, as well the constraint case: minimize p(x) on a semialgebraic set K, i.e., a set defined by polynomial equalities and inequalities. We also summarize some questions that we are currently considering. / Singapore-MIT Alliance (SMA)

Many optimization problems can be formulated as second order cone programming (SOCP) problems. Theoretical results show that applying interior-point method (IPM) to SOCP has global polynomial convergence. However, various stability issues arise in the implementation of IPM. The standard normal equation based implementation of IPM encounters stability problems in the computation of search direction. In this paper, an augmented system approach is proposed to overcome the stability problems. Numerical experiments show that the new approach can improve the stability. / Singapore-MIT Alliance (SMA)