The scope of this research concerns the passive damping of structural vibrations by the use of viscoelastic layers. It is motivated by the need for efficient numerical tools to deal with the medium frequency behaviour of industrial viscoelastic sandwich products. The sandwich modelling technique is based on the use of an interface element: the two deformable plates are modelled by special plate elements while the intermediate dissipative layer is modelled with interface elements. This interface element is based on the first-order shear deformation theory and assume constant peel and shear stresses in the polymer thickness. This element couples the lower and upper layers without additional degrees of freedom. The partition of unity finite element method (PUFEM) is applied to the development of enriched Mindlin plate elements. The element shape functions are obtained as the product of partition of unity functions with arbitrary chosen enrichment functions. Polynomial enrichment leads to the generation of high-order polynomial shape functions and is therefore similar to a p-FEM technique. Numerical examples illustrate the use of both PUFEM Mindlin plate elements and interface elements for the simulation of viscoelastic sandwich structures.

The first chapter provides some basic definitions and results from the theory of convex analysis and nonlinear mappings related to our work. Some sufficient conditions for the existence of a solution of problem (GVIP) are also recalled. In the second chapter, we first illustrate the scope of the auxiliary problem procedure designed to solve problems like (GVIP) by examining some well-known methods included in that framework. Then, we review the most representative convergence results for that class of methods that can be found in the literature in the case where F is singlevalued as well as in the multivalued case. Finally, we somewhat discuss the particular case of projection methods to solve affine variational inequalities. The third chapter introduces the variational convergence notion of Mosco and combines it with the auxiliary problem principle. Then, we recall the convergence conditions existing for the resulting perturbed scheme before our own contribution and we comment them. Finally, we introduce and illustrate the rate of convergence condition that we impose on the perturbations to obtain better convergence results. Chapter 4 presents global and local convergence results for the family of perturbed methods in the case where F is singlevalued. We also discuss how our results extend or improve the previous ones. Chapter 5 studies the multivalued case. First, we present convergence results generalizing those obtained when there is no perturbations. Then, we relax the scheme by means of a notion of enlargement of an operator and we provide convergence conditions for this inexact scheme. In Chapter 6, we build a bundle algorithm to solve problem (GVIP) and we study its convergence.

In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch project, a computer-based initiative designed to improve the mathematical skills of children from grades 5-8 in the Southwest. A sample of 86 students (26 ELs and 60 EPs), clustered in four different classes, was used for this project. A Generalized Linear Mixed Model (GLMM) approach with the GLIMMIX procedure in SAS 9.3 showed that students from the classes that had a higher percentage of EL students performed better than those in the classes where the EL concentration was lower. Classes with more EL males were better at learning mathematics than classes with more EP females. The results also indicated: (a) a positive correlation between the students' ability to solve algebra word problems on their first attempt and their success ratio in solving all problems, and (b) a negative correlation between the percentage of problems solved correctly and those considered too hard from the very beginning. I conclude my dissertation by making specific recommendations for further research.

存活分析主要在研究事件的發生時間；傳統的存活分析並不考慮治癒者(或免疫者)的存在。若以失敗為事件，且造成失敗的可能原因不止一種，但它們不會同時發生，則這些失敗原因就是失敗事件的競爭風險。競爭風險可分為有參數的競爭風險與無母數的競爭風險。本文同時考慮了有治癒與有參數的混合廣義Gamma分配，並將預估計的位置參數與失敗機率有關的參數與解釋變數結合，代入Choi及Zhou(2002)提出的最大概似估計量的大樣本性質。並考慮在治癒情況下，利用電腦模擬來估計在型一設限及無訊息(non-informative)的隨機設限(random censoring)下之一個失敗原因與兩個失敗原因下的參數平均數與標準差。 / The purpose of survival analysis is aiming to analyze the timeline of events. The typically method of survival analysis don’t take account of the curer (or the immune). If the event is related to failure and there are more than one possible reason causing the failure but are not happening at the same time, we called the possible reasons a competing risk for failed occurrence. competing risk can be categorized as parameter and non-parameter. This research has considered the generalized gamma distribution over both cure and parameter aspects. In addition, it combines anticipated parameter with covariate which affected to the possibilities of failure. Follow by the previous data, it is then substituted by the large-sample property of the maximum likelihood estimator which is presented by Choi and Zhou in 2002. With considering the possibilities of cure, it uses computer modeling to investigate that under the condition of type-1 censoring and non-informatively random censoring, we will find out the parameter mean and standard error that is resulted by one and two reason causes failure.

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This thesis is concerned, loosely, with time series analysis. It is also, loosely, concerned with smoothers and Generalized Additive Models. And, finally, it is also concerned with the estimation of health risk due to air pollution. In the field of time series analysis, we develop two data-driven interpolation algorithms for interpolation of mixed time series data; that is, data which has a stationary or “almost” stationary background with embedded deterministic trend and sinusoidal components. These interpolators are developed to deal with the problem of estimating power spectra under the condition that some observations of the series are unavailable. We examine the structure of time-based cubic regression spline smoothers in Generalized Additive Models and demonstrate several interpretation problems with the resultant models. We propose, implement, and test a replacement smoother and show dramatic improvement. We further demonstrate a new, spectrally motivated way of examining residuals in Generalized Additive Models which drives many of the findings of this thesis. Finally, we create and analyze a large-scale Canadian air pollution and mortality database. In the course of analyzing the data we rebuild the standard risk estimation model and demonstrate several improvements. We conclude with a comparison of the original model and the updated model and show that the new model gives consistently more positive risk estimates. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-10-26 14:32:00.678

Major Depression (MD) and Generalized Anxiety Disorder (GAD) are psychiatric disorders that arise from dysfunction of the core human capacities for emotion. Sapience is inextricably bound up with the potential for feelings of regret, worry and concern. When these emotions lead to clinically significant impairment or distress, they may result in one or both of the disorders of MD and GAD. The occurrence of MD and GAD in the same person, known as comorbidity, is remarkably high; substantially higher than would be expected by chance. MD and GAD have been studied since the mid-20th century, resulting in a substantial body of literature. The personality trait of neuroticism is also known to correlate highly with these disorders. This project was designed to compare the etiological structure of MD and GAD using a range of psychosocial and genetic methods in three datasets, while also assessing the correlated trait of neuroticism. Results are used to inform theoretical formulation of an approximate model of comorbidity for the two disorders. Psychosocial findings suggest that MD and GAD have similar relationships with most risk factors, and that neuroticism displays results consistent with it composing a portion of the liability to MD and GAD. Efforts to detect specific genetic loci involved in the etiology of MD and GAD are modestly successful. Two genome-wide significant variants were found for MD (one already identified in the literature); two for GAD, and one for neuroticism. There were also a number of significant genomic regions for each outcome. The use of aggregate genetic methods to estimate heritability based on genotypes was less successful. Estimation was only successful in one sample of the three, and produced modest estimates of heritability (0.2-0.25) for MD and comorbid MD+GAD. Genetic correlation was estimated to be very high between neuroticism and MD. Models of comorbidity are evaluated in light of these results, and a model comprising multiple liability distributions, one shared entirely by MD and GAD, and two additional correlated ones for the two disorders, with reciprocal phenotypic causation, is deemed most consistent with observed evidence.

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As flexible and accurate model for the logarithmic returns we use the $t$-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric quality of the triangles in the constrained Delaunay triangulation of the polygon. This characterization is sharp in the sense that families of polygons with poor quality triangles in their constrained Delaunay triangulations are shown to produce large error when interpolating a basic quadratic function. Non-convex polygons exhibit a similar limitation: large constrained Delaunay triangles caused by vertices approaching a non-adjacent edge also lead to large interpolation error. While this relationship is generalized to convex polyhedra in three dimensions, the possibility of sliver tetrahedra in the constrained Delaunay triangulation prevent the analogous estimate from sharply reflecting the actual interpolation error. Non-convex polyhedra are shown to be fundamentally different through an example of a family of polyhedra containing vertices which are arbitrarily close to non-adjacent faces yet the interpolation error remains bounded.

The most general AdS$_5 imes Y$ solutions of type IIB string theory that are AdS/CFT dual to superconformal field theories in four dimensions can be fruitfully described in the language of generalized geometry, a powerful hybrid of complex and symplectic geometry. We show that the cone over the compact five-manifold $Y$ is generalized Calabi-Yau and carries a generalized holomorphic Killing vector field $xi$, dual to the R-symmetry. Remarkably, this cone always admits a symplectic structure, which descends to a contact structure on $Y$, with $xi$ as Reeb vector field. Moreover, the contact volumes of $Y$, which can be computed by localization, encode essential properties of the dual CFT, such as the central charge and the conformal dimensions of BPS operators corresponding to wrapped D3-branes. We then define a notion of ``generalized Sasakian geometry'', which can be characterized by a simple differential system of three symplectic forms on a four-dimensional transverse space. The correct Reeb vector field for an AdS$_5$ solution within a given family of generalized Sasakian manifolds can be determined---without the need of the explicit metric---by a variational procedure. The relevant functional to minimize is the type IIB supergravity action restricted to the space of generalized Sasakian manifolds, which turns out to be just the contact volume. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of the dual superconformal field theory. The power of this volume minimization is illustrated by the calculation of the contact volumes for a new infinite family of solutions, in perfect agreement with the results of $a$-maximization in the dual mass-deformed generalized conifold theories.