No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the N-body problem. Variational methods with finite order symmetry group are used to construct minimizing non-collision periodic orbits. We study the question of stability or instability of periodic and symmetric periodic solutions of the rhombus and the equal mass parallelogram four body problems. We first study the stability of periodic solutions for the rhombus four body problem. An analytical description of the variational principle is used to show that the homographic solutions are the minimizers of the action functional restricted to rhombus loop space [23]. We employ techniques from symplectic geometry and specifically a variant of the Maslov index for curves of Lagrangian subspaces along the minimizing rhombus orbit to prove the main result, Theorem 4.2.2, which states that the reduced rhombus orbit is hyperbolic in the reduced energy manifold when it is not degenerate. We second study the stability for symmetric periodic solutions of the equal mass parallelogram four body problem. The parallelogram family is a family of Z_2× Z_4 symmetric action minimizing solutions, investigated by [7]. In this example, the minimizing solution [7] can be extended to a 4T-periodic solution using symmetries through square and collinear configurations. The Maslov index of the orbits is used to prove the main result, Theorem 5.3.1, which states that the minimizing equal mass parallelogram solution is unstable when it is non-degenerate. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-11-26 11:30:29.688

A controversy exists among contempory coaches and physiologists relative to the effectiveness of interval vs. continuous running. The purpose of this study was to compare interval and continuous running on the aerobic capacities of young men. Twelve college age men were divided into two groups, matched according to V02 max (ml/kg-min). One group trained on a short distance (110-660 yards) interval program, while the other group trained on long, steady, continuous runs. Both groups were tested, trained, and re-examined. The testing periods consisted of one all out run to exhaustion and at least two submaximal runs, all on thetreadmill. Variables recorded were V02 (ml/kg-min), V02 (1/min), VE , and heart rate. It was found that both training methods significantly increased the aerobic capacity in terms of V02 max (ml/kg-min); however, neither method was superior. In addition, it was noted that both training methods reduced the cost of running in terms of V02 (1/min) and heart rate but neither method was more effective.