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#### Axially symmetric harmonic maps and relaxed energy

(1991)

Here we investigate some new phenomena in harmonic maps that result by imposing a symmetry condition. A map $u:B\sp3\to S\sp2$ is called axially symmetric if, in cylindrical coordinates, $u(r,\theta,z)$ = $(\cos\theta\si ...

#### Harmonic diffeomorphisms between manifolds with bounded curvature

(1991)

Let compact n-dimensional Riemannian manifolds $(M,g),\ (\widehat M,\ g)$ a diffeomorphism $u\sb0: M\to \widehat M,$ and a constant $p > n$ be given. Then sufficiently small $L\sp{p}$ bounds on the curvature of $\widehat ...

#### On the boundaries of special Lagrangian submanifolds

(1995)

An n-dimensional submanifold M in ${\bf C}\sp{n} = {\bf R}\sp{2n}$ is called Lagrangian if the restriction of $\omega$ to M is zero, where $\omega = \Sigma{\limits\sb{i}}dz\sb{i}\ \wedge\ d\bar z\sb{i}$. It is called special ...

#### Hyperbolic geometry, regular representations and curves on surfaces

(1995)

Tools and techniques in hyperbolic geometry are developed and applied primarily to questions about intersections of curves on surfaces. Formulae which explicitly relate the coefficients of a matrix to the geometric data ...

#### An abstract analysis of differential semblance optimization

(1994)

Differential Semblance Optimization (DSO) is a novel way of approaching a class of inverse problems arising in exploration seismology. The promising feature of the DSO method is that it replaces a nonsmooth, highly nonconvex ...

#### 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 ...

#### System identification for robust control

(1998)

In the design of a robust control system, one needs a nominal model together with a quantitative bound on the uncertainty that results from under-modeling and disturbances. In this thesis we do not intentionally seek a ...

#### Morse-Bott functions and the Witten Laplacian

(1997)

Given a compact Riemannian manifold (N, g), a flat vector bundle V over N, and a Morse-Bott function h, Witten considered the following one-parameter deformation of the differential d in the de Rham complex of V-valued ...

#### A restarted Lanczos process for computing a large percentage of the eigenvalues of a symmetric matrix

(1996)

The Lanczos algorithm is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a large-scale real symmetric matric arising in many scientific and engineering applications.
In this ...