A strong triangle inequality in hyperbolic geometry

For a triangle in the hyperbolic plane, let $\alpha,\beta,\gamma$ denote the angles opposite the sides $a,b,c$, respectively. Also, let $h$ be the height of the altitude to side $c$. Under the assumption that $\alpha,\beta, \gamma$ can be chosen uniformly in the interval $(0,\pi)$ and it is given that $\alpha+\beta+\gamma c + h$ holds approximately 79\% of the time. To accomplish this, we prove a number of theoretical results to make sure that the probability can be computed to an arbitrary precision, and the error can be bounded

Fearless: Professor Janet Powers and Linnea Goebel

This week we would like to recognize Professor Janet Powers and recent graduate Linnea Goebel ’13 for their work in Bosnia this summer helping to set up a group of female embroiderers with an Amazon Marketplace account to sell their wares on the internet. [excerpt

Determination of space shuttle flow field by the three-dimensional method of characteristics

The newly improved three-dimensional method of characteristics program has been applied successfully to the calculation of flow fields over a variety of bodies including slab delta wings and shuttle orbiters. Flow fields over fuselage shapes for Mach numbers as low as 1.5 have been calculated. Some typical results are presented

Feasibility study of LITVC for shuttle SRB

A liquid injection thrust vector control (LITVC) system for the shuttle solid rocket booster (SRB) was analyzed. The LITVC was compared with the SRB baseline flexible seal. A table of LITVC advantages and disadvantages is presented. It is concluded that the LITVC performs well at low to moderate duty cycles, but not for high duty cycle requirements

Axioms for consensus functions on the n-cube

An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and anti-median functions on the n-cube.Comment: 12 page

Measure Factors, Tension, and Correlations of Fluid Membranes

We study two geometrical factors needed for the correct construction of statistical ensembles of surfaces. Such ensembles appear in the study of fluid bilayer membranes, though our results are more generally applicable. The naive functional measure over height fluctuations must be corrected by these factors in order to give correct, self-consistent formulas for the free energy and correlation functions of the height. While one of these corrections -- the Faddeev-Popov determinant -- has been studied extensively, our derivation proceeds from very simple geometrical ideas, which we hope removes some of its mystery. The other factor is similar to the Liouville correction in string theory. Since our formulas differ from those of previous authors, we include some explicit calculations of the effective frame tension and two-point function to show that our version indeed secures coordinate-invariance and consistency to lowest nontrivial order in a temperature expansion.Comment: 24 pp; plain Te

Active site studies on blood proteases

Issued as Final report, Project no. G-33-L02 (continuation of G-33-L01; continued by G-33-L03