The Central Oregon High Cascade Range is an anomalously mafic segment of the Cascade Arc due to ongoing intra-arc extension, which allows most magmas to traverse the crust without stalling and evolving to more evolved compositions. North Sister, a composite volcano in this arc segment, has produced a seemingly monotonous...
Vitamin E was first described in 1922 as an unknown factor required for impregnated rats to carry their offspring to term. In fact, when vitamin E was chemically characterized it was given the name "tocopherol" derived from the Greek: tokos = childbirth; phero = to bear; and –ol, indicating an...
We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=f(x), with deg(f)=2g+2. By introducing a new sequence of polynomials defined in terms of the partial quotients of the continued fraction expansion of y, we are able to bound the sum of...
Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
We show that Pappus Curves, introduced by R. Schwartz to study his dynamical system in the real projective plane generated by iterated applications of the classical Pappus Theorem, are algebraic exactly in the linear case. Our approach is to use properties of projective curves such as singular points, genus, number...
The primary goal of my studies was to elucidate the mechanisms for the well-recognized interaction between two nutrients, vitamins E and K. The outcomes from my studies assess mechanisms for adverse effects of vitamin E and provide novel information on mechanisms for vitamin K homeostasis. These findings will provide information...
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 invariant under balanced translation covers.
We give a new characterization of elements in the Veech group of a translation surface. This provides a computational test for Veech group membership. We use this computational test in an algorithm that detects when the Veech group is a lattice (has co-finite area), and in this case computes a...
In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been...