An important problem in computer graphics is to determine where contour lines and ridges appear in a surface constructed from a triangle mesh. In this presentation we will investigate a new answer to this problem – the horizon measure. The horizon measure determines the likelihood of contour lines to appear...
In this paper we explore the eight geometries of Thurston's geometrization conjecture. We begin by discussing group actions, covering space topology, fiber bundles, and Seifert fiber spaces. We make precise the notion of a geometric structure. We then discuss the two dimensional geometries including a brief proof of the uniformization...
Currently, the technologies used to separate lignocellulosic biomass into its component parts (cellulose, hemicellulose, and lignin) and enzymatically hydrolyze the cellulose to glucose for conversion to ethanol could be improved economically and in terms of efficiency. A major impediment to utilizing the biomass is the presence of residual lignin. The...
Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to
topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds...
Managers and policy-makers across broad disciplines and organizations are calling for a better understanding of public opinion on natural resource issues. One such issue is that of fire and its role in the management of our forests and rangelands. Public perceptions of fuel reduction techniques, with a particular emphasis on...
Discordance in bone mass between young adult swimmers and soccer players may be a direct result of differences in bone loading patterns that influence bone mineralization during growth. Our aim was to evaluate whether sports participation (soccer and swimming) had an independent effect on bone mass accrual at the hip...
Sex differences in bone mass and size are thought to contribute to the greater incidence of vertebral fractures in women. While these sex differences are widely recognized, the relative contributions of bone mass, bone density, and bone size to the differences in vertebral strength and fracture risk between men and...
We evaluated anthropometric and performance measures which best predict bone
mineral density (BMD) in 54 adolescent girls (14.6±0.5y; 22.7±14.0 months past
menarche). BMD for the whole body, femoral neck, greater trochanter, lumbar spine (L2-L4), and mid-femoral shaft was assessed using dual-energy x-ray absorptiometry (DXA)
(Hologic QDR 1000/W). Whole body lean...
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 families of compact simply connected seven dimensional
Riemannian manifolds that may contain new examples of...