The thesis presents the results of our research on symmetry for some semilinear elliptic problems and on existence of solution for quasilinear problems involving singularities. The text is composed of two parts, each of which begins with a specific introduction. The first part is devoted to symmetry and symmetry-breaking results. We study a class of partial differential equations involving radial weights on balls, annuli or $R^N$ --where these weights are unbounded--. We show in particular that on unbounded domains, focusing on symmetric functions permits to recover compactness, which implies existence of solutions. Then, we stress the fact that symmetry-breaking occurs on bounded domains, depending both on the weights and on the nonlinearity of the equation. We also show that for the considered class of problems, the multibumps-solution phenomenon appears on the annulus as well as on the ball. The second part of the thesis is devoted to partial and ordinary differential equations with singularities. Using concentration-compactness tools, we show that a rather large class of functionals is lower semi-continuous, leading to the existence of a ground state solution. We also focus on the unicity of solutions for such a class of problems.

I here develop a specific version of the deflationary theory of truth. I adopt a terminology on which deflationism holds that an exhaustive account of truth is given by the equivalence between truth-ascriptions and de-nominalised (or disquoted) sentences. An adequate truth-theory, it is argued, must be finite, non-circular, and give a unified account of all occurrences of “true”. I also argue that it must descriptively capture the ordinary meaning of “true”, which is plausibly taken to be unambiguous. Ch. 2 is a critical historical survey of deflationary theories, where notably disquotationalism is found untenable as a descriptive theory of “true”. In Ch. 3, I aim to show that deflationism cannot be finitely and non-circularly formulated by using “true”, and so must only mention it. Hence, it must be a theory specifically about the word “true” (and its foreign counterparts). To capture the ordinary notion, the theory must thus be an empirical, use-theoretic, semantic account of “true”. The task of explaining facts about truth now becomes that of showing that various sentences containing “true” are (unconditionally) assertible. In Ch. 4, I defend the claim (D) that every sentence of the form “That p is true” and the corresponding “p” are intersubstitutable (in a use-theoretic sense), and show how this claim provides a unified and simple account of a wide variety of occurrences of “true”. Disquotationalism then only has the advantage of avoiding propositions. But in Ch. 5, I note that (D) is not committed to propositions. Use-theoretic semantics is then argued to serve nominalism better than truth-theoretic ditto. In particular, it can avoid propositions while sustaining a natural syntactic treatment of “that”-clauses as singular terms and of “Everything he says is true”, as any other quantification. Finally, Horwich’s problem of deriving universal truth-claims is given a solution by recourse to an assertibilist semantics of the universal quantifier.

The preferential looking paradigm was used to investigate how toddlers integrate recently learned grammatical cues with well-established social cues in a novel word-learning scenario. To test this we examined children’s ability to decipher the referent of a novel noun using the grammatical information from a plural cue and social information from an eye-gaze cue. Experiment 1 is the first study showing that children as young as 24 months of age can rely on plural markings alone to infer the referent of a novel noun. Preliminary results of Experiment 2 suggest that when the plural cue is presented alongside contradicting information from a gaze direction cue, children still map the novel word to the grammatically cued object. Taken together, these results suggest that by the time children reach their second birthday, even newly learned grammatical information, such as plural markings, might already outweigh established social cues.

The preferential looking paradigm was used to investigate how toddlers integrate recently learned grammatical cues with well-established social cues in a novel word-learning scenario. To test this we examined children’s ability to decipher the referent of a novel noun using the grammatical information from a plural cue and social information from an eye-gaze cue. Experiment 1 is the first study showing that children as young as 24 months of age can rely on plural markings alone to infer the referent of a novel noun. Preliminary results of Experiment 2 suggest that when the plural cue is presented alongside contradicting information from a gaze direction cue, children still map the novel word to the grammatically cued object. Taken together, these results suggest that by the time children reach their second birthday, even newly learned grammatical information, such as plural markings, might already outweigh established social cues.

While magnetohydrodynamic (MHD) instabilities are considered one of the intriguing topics in tokamak physics, a feasibility study was conducted in the Saskatchewan Torus-Modified (STOR-M) tokamak to investigate the global MHD activities during the normal (L-mode) and improved (H-mode) confinement regimes. The experimental setup consists of 32 discrete Mirnov coils arranged into four poloidal arrays and mounted on STOR-M at even toroidal distances. The perturbed magnetic field fluctuations during STOR-M discharges were acquired and processed by the Fourier transform (FT), the wavelet analysis and the singular value decomposition (SVD) techniques. In L-mode discharges, the poloidal MHD mode numbers varied from 2 to 4 with peak frequencies in the range 20-40 kHz. The dominant toroidal modes were reported between 1 and 2 oscillating at frequencies 15-35 kHz. In another experiment, a noticeable MHD suppression was observed during the H-mode-like phase induced by the compact torus (CT) injection into STOR-M. However, a burst-like mode called the gong mode was triggered prior to the H-L transition, followed by coherent Mirnov oscillations. Mirnov oscillations with strong amplitude modulations were observed in the STOR-M tokamak. Correlations between Mirnov signals and soft x-ray (SXR) signals were found.

The thesis parts from the view that statistics starts with data, and starts by introducing the data sets studied: marine benthic species counts and chemical measurements made at a set of sites in the Norwegian Ekofisk oil field, with replicates and annually repeated. An introductory chapter details the sampling procedure and shows with reliability calculations that the (transformed) chemical variables have excellent reliability, whereas the biological variables have poor reliability, except for a small subset of abundant species. Transformed chemical variables are shown to be approximately normal. Bootstrap methods are used to assess whether the biological variables follow a Poisson distribution, and lead to the conclusion that the Poisson distribution must be rejected, except for rare species. A separate chapter details more work on the distribution of the species variables: truncated and zero-inflated Poisson distributions as well as Poisson mixtures are used in order to account for sparseness and overdispersion. Species are thought to respond to environmental variables, and regressions of the abundance of a few selected species onto chemical variables are reported. For rare species, logistic regression and Poisson regression are the tools considered, though there are problems of overdispersion. For abundant species, random coefficient models are needed in order to cope with intraclass correlation. The environmental variables, mainly heavy metals, are highly correlated, leading to multicollinearity problems. The next chapters use a multivariate approach, where all species data is now treated simultaneously. The theory of correspondence analysis is reviewed, and some theoretical results on this method are reported (bounds for singular values, centring matrices). An applied chapter discusses the correspondence analysis of the species data in detail, detects outliers, addresses stability issues, and considers different ways of stacking data matrices to obtain an integrated analysis of several years of data, and to decompose variation into a within-sites and between-sites component. More than 40 % of the total inertia is due to variation within stations. Principal components analysis is used to analyse the set of chemical variables. Attempts are made to integrate the analysis of the biological and chemical variables. A detailed theoretical development shows how continuous variables can be mapped in an optimal manner as supplementary vectors into a correspondence analysis biplot. Geometrical properties are worked out in detail, and measures for the quality of the display are given, whereas artificial data and data from the monitoring survey are used to illustrate the theory developed. The theory of display of supplementary variables in biplots is also worked out in detail for principal component analysis, with attention for the different types of scaling, and optimality of displayed correlations. A theoretical chapter follows that gives an in depth theoretical treatment of canonical correspondence analysis, (linearly constrained correspondence analysis, CCA for short) detailing many mathematical properties and aspects of this multivariate method, such as geometrical properties, biplots, use of generalized inverses, relationships with other methods, etc. Some applications of CCA to the survey data are dealt with in a separate chapter, with their interpretation and indication of the quality of the display of the different matrices involved in the analysis. Weighted principal component analysis of weighted averages is proposed as an alternative for CCA. This leads to a better display of the weighted averages of the species, and in the cases so far studied, also leads to biplots with a higher amount of explained variance for the environmental data. The thesis closes with a bibliography and outlines some suggestions for further research, such as a the generalization of canonical correlation analysis for working with singular covariance matrices, the use partial least squares methods to account for the excess of predictors, and data fusion problems to estimate missing biological data.

While magnetohydrodynamic (MHD) instabilities are considered one of the intriguing topics in tokamak physics, a feasibility study was conducted in the Saskatchewan Torus-Modified (STOR-M) tokamak to investigate the global MHD activities during the normal (L-mode) and improved (H-mode) confinement regimes. The experimental setup consists of 32 discrete Mirnov coils arranged into four poloidal arrays and mounted on STOR-M at even toroidal distances. The perturbed magnetic field fluctuations during STOR-M discharges were acquired and processed by the Fourier transform (FT), the wavelet analysis and the singular value decomposition (SVD) techniques. In L-mode discharges, the poloidal MHD mode numbers varied from 2 to 4 with peak frequencies in the range 20-40 kHz. The dominant toroidal modes were reported between 1 and 2 oscillating at frequencies 15-35 kHz. In another experiment, a noticeable MHD suppression was observed during the H-mode-like phase induced by the compact torus (CT) injection into STOR-M. However, a burst-like mode called the gong mode was triggered prior to the H-L transition, followed by coherent Mirnov oscillations. Mirnov oscillations with strong amplitude modulations were observed in the STOR-M tokamak. Correlations between Mirnov signals and soft x-ray (SXR) signals were found.

In this study, it is aimed to investigate the mixed-mode fracture behavior of orthotropic functionally graded material (FGM) coatings bonded to a homogeneous substrate through a homogeneous bond-coat. Analytical and computational methods are used to solve the embedded cracking problems under mechanical or thermal loading conditions. It is assumed that the material property gradation of the FGM coating is in the thickness direction and cracks are parallel to the boundaries. The principal axes of orthotropy are parallel and perpendicular to the boundaries. A single embedded crack in the orthotropic FGM coating is investigated analytically assuming that crack surfaces are subjected to either uniform normal or uniform shear stresses. Using Fourier transformations, the problem is reduced to a couple of singular integral equations that are solved numerically to obtain the mixed-mode stress intensity factors, energy release rate and crack opening displacements. To investigate the analytically untractable problems without restrictive assumptions, a computational approach is employed. The adopted computational approach is based on finite element method and displacement correlation technique. Using the computational approach, fracture parameters are obtained considering single and periodic embedded cracking conditions in the orthotropic FGM coatings under mechanical or thermal loads. The results obtained in this study show the effects of material nonhomogeneity, material orthotropy and geometric variables on the fracture behavior of the structure.

Data analysis has become a very important area for both companies and researchers as a consequence of the technological developments in recent years. Companies are trying to increase their profit by analyzing the existing data about their customers and making decisions for the future according to the results of these analyses. Parallel to the need of companies, researchers are investigating different methodologies to analyze data more accurately with high performance. Recommender systems are one of the most popular and widespread data analysis tools. A recommender system applies knowledge discovery techniques to the existing data and makes personalized product recommendations during live customer interaction. However, the huge growth of customers and products especially on the internet, poses some challenges for recommender systems, producing high quality recommendations and performing millions of recommendations per second. In order to improve the performance of recommender systems, researchers have proposed many different methods. Singular Value Decomposition (SVD) technique based on dimension reduction is one of these methods which produces high quality recommendations, but has to undergo very expensive matrix calculations. In this thesis, we propose and experimentally validate some contributions to SVD technique which are based on the user and the item categorization. Besides, we adopt tags to classical 2D (User-Item) SVD technique and report the results of experiments. Results are promising to make more accurate and scalable recommender systems.

This study considers the elastostatic contact problem of a semi-infinite cylinder. The cylinder is compressed against a layer lying on a rigid foundation. There is a sharp-edged circular hole in the middle of the foundation. It is assumed that all the contacting surfaces are frictionless and only compressive normal tractions can be transmitted through the interfaces. The contact along interfaces of the elastic layer and the rigid foundation forms a circular area of which outer diameter is unknown. The problem is converted into the singular integral equations of the second kind by means of Hankel and Fourier integral transform techniques. The singular integral equations are then reduced to a system of linear algebraic equations by using Gauss-Lobatto and Gauss-Jacobi integration formulas. This system is then solved numerically. In this study, firstly, the extent of the contact area between the layer and foundation are evaluated. Secondly, contact pressure between the cylinder and layer and contact pressure between the layer and foundation are calculated for various material pairs. Finally, stress intensity factor on the edge of the cylinder and in the end of the sharp-edged hole are calculated.