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Now showing items 1-10 of 112

#### Critical Riemannian metrics

(1990)

Let $(M,g)$ be a compact oriented n-dimensional smooth Riemannian manifold. Consider the following quadratic Riemannian functional$$SR(g) = \int\sb{M}\ \vert R\sb{ijkl}(g)\vert \sp{2}d\mu$$which is homogeneous of degree ...

#### Energy minimizers, gradient flow solutions, and computational investigations in the theory of biharmonic maps

(1998)

We present the definitions, derive the relevant Euler-Lagrange equations, and establish various properties concerning biharmonic maps. We investigate several classes of examples exhibiting singular behavior. Existence of ...

#### A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming

(1997)

Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal ...

#### A global convergence theory for a general class of trust region algorithms for equality constrained optimization

(1993)

This work is concerned with global convergence results for a broad class of trust region sequential quadratic programming algorithms for the smooth nonlinear programming problem with equality constraints. The family of ...

#### Anomalies in finite dimensions

(1993)

A problem in quantum mechanics is finding a determinant function on linear maps between two vector spaces. In this paper we consider the question in the context of finite dimensional vector spaces. Given two finite dimensional ...

#### Generalized billiard paths and Morse theory for manifolds with corners

(1999)

A billiard path on a manifold M embedded in Euclidean space is a series of line segments connecting reflection points on M. In a generalized billiard path we also allow the path to pass through M. The two segments at a ...

#### Krylov-secant methods for solving large-scale systems of coupled nonlinear parabolic equations

(1997)

This dissertation centers on two major aspects dictating the computational time of applications based on the solution of systems of coupled nonlinear parabolic equations: nonlinear and linear iterations. The former aspect ...

#### On a transmission inverse problem

(1995)

In crosswell seismic experiments, seismic sources are fired in one well, and the wave-fields generated are measured in another well. The goal of the crosswell seismology is to find physical parameters, especially the ...

#### Can you hear the size of the vertices? An inverse spectral problem of Laplacians on weighted graphs

(1998)

Let G be a simple graph with n vertices. We define a Laplacian $\Delta$ on G which depends on an assignment of a weight to each vertex of G. One of the eigenvalues of $\Delta$ will always be 0. We fix the remaining (n $-$ ...

#### Harmonic maps of trivalent trees

(1991)

This thesis is a study of harmonic maps of trivalent trees into Euclidean space. The existence of such maps is established, and uniqueness is shown to hold up to a certain isotopy condition. Moreover, within its particular ...