A finitely presented group of piecewise projective homeomorphisms

In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. It is in fact the first such example which is torsion free. We will also develop a means for representing the elements of the group by labeled tree diagrams in a manner which closely parallels Richard Thompson's group F.Comment: Formerly "A geometric solution to the von Neumann-Day problem for finitely presented groups". Section added on tree diagrams. Minor revisions elsewher

A five element basis for the uncountable linear orders

In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, omega_1, omega_1^*, C, C^* where X is any suborder of the reals of cardinality aleph_1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.Comment: 21 page

Prediction of VO\u3csub\u3e2\u3c/sub\u3e Peak Using Sub-Maximum Bench Step Test in Children

The purpose of this study was to develop a valid prediction of maximal oxygen uptake from data collected during a submaximum bench stepping test among children ages 8-12 years. Twentyseven active subjects (16 male and 11 female), weight 36.1 kg, height 144.4 cm and VO2 47.4 ± 7.9 ml/kg/min participated. Subjects completed a maximal oxygen consumption test with analysis of expired air and a submaximal bench stepping test. A formula to predict VO2max was developed from height, resting heart rate and heart rate response during the submaximum bench stepping test. This formula accounted for 71% of the variability in maximal oxygen consumption and is the first step in verifying the validity of the submaximum bench stepping test to predict VO2max. VO2max = -2.354 + (Height in cm * 0.065) + (Resting Heart Rate * 0.008) + (Step Test Average Heart Rate as a Percentage of Resting Heart Rate * -0.870

Robotic navigation of smooth contours

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaf 10).The goal of this work is to develop a method for robotic navigation of smooth contours depending on the current and desired locations and orientations. Efficient trajectory generation is an essential capability for many autonomous mobile robots, operating in a variety of situations such as military, medical, and home environments. In this thesis, we propose a method that is based on fitting a spline curve that passes from the initial position and orientation of the robot to a goal position and orientation. The spline is continually recomputed as the robot moves through space. This yields a simple and inefficient method for robot navigation. The method has been implemented and tested in simulation using Matlab and good performance has been demonstrated. Future work should perform experiments with this method on a real robot and should introduce obstacle detection and avoidance.by Justin C. Moore.S.B