A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine the structure of the cohomology rings of three f ...

The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurf ...

Representations of SO(4,2;R) are constructed using 4 x 4 and 2 x 2 matrices with elements in H' ⊗ C . Using 2 x 2 matrix representations of C and H', the 4 x 4 representation is interpreted in terms of 16 x 16 real matri ...

Several studies in recent years have demonstrated that upper-division students struggle with partial derivatives and the complicated chain rules ubiquitous in thermodynamics. We asked several experts (primarily faculty ...

Cellular sets in the Hilbert cube are the intersection of nested sequences of normal cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert cube into cellular sets and using a quotien ...

Learning easily understandable decision rules from examples is one of the classic problems in machine learning. Most learning algorithms for this problem employ some variation of a greedy separate-and-conquer algorithm ...

A standard tool in general relativity is the 3+1 or ADM point of view, namely slicing spacetime into spacelike hypersurfaces of constant time and then describing physics in terms of time-dependent quantities on a typic ...

We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is in ...