No description available.

In this thesis, we analyze theoretical properties of the discontinuous Galerkin method (DGM) and propose novel approaches to implementation with the aim to increase its efficiency. First, we derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin spatial discretization applied to the linear advection equation. We show that the eigenvalues are related to the subdiagonal [p/p+1] Pade approximation of exp(-z) when the p-th degree basis functions are used. Then, we extend the analysis to nonuniform meshes where both the size of elements and the composition of the mesh influence the spectrum. We show that the spectrum depends on the ratio of the size of the largest to the smallest cell as well as the number of cells of different types. We find that the spectrum grows linearly as a function of the proportion of small cells present in the mesh when the size of small cells is greater than some critical value. When the smallest cells are smaller than this critical value, the corresponding eigenvalues lie outside of the main spectral curve. Numerical examples on nonuniform meshes are presented to show the improvement on the time step restriction. In particular, this result can be used to improve the time step restriction on Cartesian grids. Finally, we present a discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries. Cutting an embedded geometry out of the Cartesian grid creates cut cells, which are difficult to deal with for two reasons. One is the restrictive CFL number and the other is the integration on irregularly shaped cells. We use explicit time integration employing cell merging to avoid restrictively small time steps. We provide an algorithm for splitting complex cells into triangles and use standard quadrature rules on these for numerical integration. To avoid the loss of accuracy due to straight sided grids, we employ the curvature boundary conditions. We show that the proposed method is robust and high-order accurate.

This thesis deals with Martin Heideggers critique of the Cartesian problem of scepticism in Being and Time. In addition to the critique itself, Heideggers position with regards to the sense and task of phenomenological research, as well as fundamental ontology, is discussed as a necessary underpinning of his critique. Finally, the objection to Heideggers critique that is raised by Charles Guignon in his book, Heidegger and the Problem of Knowledge, (namely, that it suffers from the problem of reflexivity) is evaluated.

No description available.

vii, 99 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We investigate Cesàro summability of the Fourier orthogonal expansion of functions on B d × I m , where B d is the closed unit ball in [Special characters omitted] and I m is the m -fold Cartesian product of the interval [-1, 1], in terms of orthogonal polynomials with respect to the weight functions (1 - z ) α (1 + z ) β (1 - |x| 2 ) λ-1/2 , with z ∈ I m and x ∈ B d . In addition, we study a discretized Fourier orthogonal expansion on the cylinder B 2 × [-1, 1], which uses a finite number of Radon projections. The Lebesgue constant of this operator is obtained, and the proof utilizes generating functions for associated orthogonal series. / Committee in charge: Yuan Xu, Chairperson, Mathematics; Huaxin Lin, Member, Mathematics Jonathan Brundan, Member, Mathematics; Marcin Bownik, Member, Mathematics; Jun Li, Outside Member, Computer & Information Science

The aim of this diploma thesis is using cartesian genetic programming on design image filters and creating basic structure for implement diferent type of problems. Genetic programming is rapidly growing method, which often using for solve dificult problems. This thesis analyze basic principle, way of application and implementing this method to design filters. Result of this thesis is program realize design filters define by specific parameters, overview of implementig method and achieve summary from this sphere.

The aim of this dissertation is to provide a critique of the idea that skepticism was the driving force in the development of early modern thought. Historian of philosophy Richard Popkin introduced this thesis in the 1950s and elaborated on it over the next five decades, and recent scholarship shows that it has become an increasingly accepted interpretation. I begin with a study of the relevant historical antecedents—the ancient skeptical traditions of which early modern thinkers were aware—Pyrrhonism and Academicism. Then I discuss the influence of skepticism on three pre-Cartesians: Francisco Sanches, Michel de Montaigne, and Pierre Charron. Basing my arguments on an informed understanding of both ancient Greek skepticism and some of the writings of these philosophers, I contend that it is inaccurate to predominantly characterize Sanches, Montaigne, and Charron as skeptics. To support his thesis about the singular influence of skepticism on early modern thought, Popkin says that René Descartes’ metaphysical philosophy was formed as a response to a skeptical threat and that Descartes ultimately conceded to the force of skepticism. He also argues that David Hume was a Pyrrhonist par excellence. I disagree with Popkin’s claims. I argue that Descartes was not as deeply affected by skepticism as Popkin suggests and that it is inaccurate to characterize Hume as a Pyrrhonist. By offering this critique, I hope to make clear to the readers two things: first, that Popkin’s thesis, though it is both enticing and generally accepted by many scholars, is questionable with regard to its plausibility; second, that the arguments I present in this dissertation reveal that further research into the role of skepticism in early modern philosophy is in order.

The complementary prism of a graph G is the graph formed from a disjoint union of G and its complement ̄G by adding the edges of a perfect matching between the corresponding vertices of G and G. We study independent domination numbers of complementary prisms. Exact values are determined for complementary prisms of paths, complete bipartite graphs, and subdivided stars. A natural lower bound on the independent domination number of a complementary prism is given, and graphs attaining this bound axe characterized. Then we show that the independent domination number behaves somewhat differently in complementary prisms than the domination and total domination numbers. We conclude with a sharp upper bound.

The complementary prism of a graph G is the graph formed from a disjoint union of G and its complement ̄G by adding the edges of a perfect matching between the corresponding vertices of G and G. We study independent domination numbers of complementary prisms. Exact values are determined for complementary prisms of paths, complete bipartite graphs, and subdivided stars. A natural lower bound on the independent domination number of a complementary prism is given, and graphs attaining this bound axe characterized. Then we show that the independent domination number behaves somewhat differently in complementary prisms than the domination and total domination numbers. We conclude with a sharp upper bound.

Let G be a graph and Ḡ be the complement of G. The complementary prism GḠ of G is the graph formed from the disjoint union of G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. For example, if G is a 5-cycle, then GḠ is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, max {γ(G), γ(Ḡ)} ≤ γ (Ḡ)and max {γt(G), γt(Ḡ)} ≤ γt (Gγ), where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.