In this paper we consider an existence of a solution for a nonlinear nonmonotone wave equation in [0,π]xR and an existence of a positive solution for a non-positone Dirichlet problem in a bounded subset of R^n.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Apresentamos uma extensÃo do Teorema de Barta devido a G. P. Bessa and J. F. Montenegro e fazemos algumas aplicaÃÃes geomÃtricas do resultado obtido. A primeira aplicaÃÃo geomÃtrica da extensÃo do Teorema de Barta à uma extensÃo do Teorema de Cheng sobre estimativas inferiores de autovalores do Laplaciano em bolas geodÃsicas normais. A segunda aplicaÃÃo geomÃtrica à uma generalizaÃÃo do Teorema de Cheng-Li-Yau de estimativas de autovalores para uma subvariedade mÃnima do espaÃo forma. / We present an extension to Barta's Theorem due to G. P. Bessa and J. F. Montenegro and we show some geometric applications of the obtained result. As first application, we extend Chang's lower eigenvalue estimates of the Laplacian in normal geodesic balls. As second application, we generalize Cheng-Li-Yau's eigenvalue estimates to a minimal submanifold of the space forms.

My thesis work started in the summer of 2005 as a three way joint project by Professor Castro and Mr. John Kwon and myself. A paper from this joint project was written and the content now forms my thesis.

Thesis (M.A.)--University of North Carolina at Greensboro, 2006. / Title from PDF title page screen. Advisor: Maya Chhetri; submitted to the Dept. of Mathematical Sciences. Includes bibliographical references (p. 39-40).

Nonparametric Bayesian models have been researched extensively in the past 10 years following the work of Escobar and West (1995) on sampling schemes for Dirichlet processes. The infinite mixture representation of the Dirichlet process makes it useful for clustering problems where the number of clusters is unknown. We develop nonparametric Bayesian models for two different clustering problems, namely functional and graphical clustering. We propose a nonparametric Bayes wavelet model for clustering of functional or longitudinal data. The wavelet modelling is aimed at the resolution of global and local features during clustering. The model also allows the elicitation of prior belief about the regularity of the functions and has the ability to adapt to a wide range of functional regularity. Posterior inference is carried out by Gibbs sampling with conjugate priors for fast computation. We use simulated as well as real datasets to illustrate the suitability of the approach over other alternatives. The functional clustering model is extended to analyze splice microarray data. New microarray technologies probe consecutive segments along genes to observe alternative splicing (AS) mechanisms that produce multiple proteins from a single gene. Clues regarding the number of splice forms can be obtained by clustering the functional expression profiles from different tissues. The analysis was carried out on the Rosetta dataset (Johnson et al., 2003) to obtain a splice variant by tissue distribution for all the 10,000 genes. We were able to identify a number of splice forms that appear to be unique to cancer. We propose a Bayesian model for partitioning graphs depicting dependencies in a collection of objects. After suitable transformations and modelling techniques, the problem of graph cutting can be approached by nonparametric Bayes clustering. We draw motivation from a recent work (Dhillon, 2001) showing the equivalence of kernel k-means clustering and certain graph cutting algorithms. It is shown that loss functions similar to the kernel k-means naturally arise in this model, and the minimization of associated posterior risk comprises an effective graph cutting strategy. We present here results from the analysis of two microarray datasets, namely the melanoma dataset (Bittner et al., 2000) and the sarcoma dataset (Nykter et al., 2006).

Thèses (Ph.D.)--Université de Sherbrooke (Canada), 1999. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.

Thesis--Copenhagen.

Thesis--Copenhagen.

Th. 3e cycle--Math. pures--Grenoble 1, 1980. N°: 87.

Thesis (M.A.)--Boston University / The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]