arXiv subjects
Publications and source records attributed to R. Umble.
Let p be an odd prime. When n>2, we show that each tensor factor of form E \otimes Γin H(Z,n;Z_p) is an A-infinity bialgebra with non-trivial structure. We give explicit formulas for the structure maps and the quadratic relations among them. Thus E \otimes Γis a naturally occurring example of an A-infinity bialgebra whose internal structure is well-understood.
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this problem on simple surfaces such as surfaces of revolution and solves the problem two ways: First, we use conservation of mechanical energy and the Euler-Lagange equation; second, we use geometrical optics and the eikonal equation. We conclude with a discussion of the relativistic effects at relativistic velocities.