In this dissertation we investigate Lagrange interpolation. Our first result will deal with a hierarchy of interpolation schemes. Specifically, we will show that given a triangular array of points in a regular compact set K, such that the corresponding Lebesgue constants are subexponential, one always has the uniform convergence of Ln(f) to f for all functions analytic on K. We will then show that uniform convergence of Ln(f) to f for all analytic functions f is equivalent to the fact that the probability measures γn = 1/n Σn j=1 δzn,j , which are associated with our triangular array, converge weak star to the equilibrium distribution for K. Motivated by our hierarchy, we will then come to our main result, namely that the Lebesgue constants associated with Leja sequences on fairly general compact sets are subexponential. More generally, considering Newton interpolation on a sequence of points, we will show that the weak star convergence of their corresponding probability measures to the equilibrium distribution, together with a certain distancing rule, implies that their corresponding Lebesgue constants are sub-exponential.

No description available.

The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular nodal distributions, namely Lobatto distribution and Fekete distribution, are compared in terms of accuracy and implementation complexity. Accuracies provided by triangular and quadrilateral grids of equal computational size are compared. Adaptive mesh refinement studies are conducted using three different error indicators, including a novel one based on elemental mass loss. Effect of modifying the least-squares functional by multiplying the continuity equation by a weight factor is investigated in regards to mass conservation.

The present thesis focuses on the representations of gays in Czech and Slovak contemporary theater plays. Its aim is to analyze the queer and campy aspects of the representations of gays in the mainstream plays and uncover the principles of creation of the gay character in the structure of dramatic Arts. The results of analysis explain the integrative mode of representation of gays in Czech and Slovak contemporary plays.