Rado's criterion over squares and higher powers

Sums of Squares, Cubes, and Higher Powers

Higher Powers in Gravitation

We consider the Friedmann-Robertson-Walker cosmologies of theories of gravity that generalise the Einstein-Hilbert action by replacing the Ricci scalar, R, with some function, f(R). The general asymptotic behaviour of these cosmologies is found, at both early and late times, and the effects of adding higher and lower powers of R to the Einstein-Hilbert action is investigated. The assumption tha...

Squares from Sums of Fixed Powers

In this paper, we show that if p and q are positive integers, then the polynomial exponential equation p + q = y2 can have at most two solutions in positive integer x and y. If such solutions exists, we are able to precisely characterize them. Our proof relies upon a result of Darmon and Merel, and Chabauty’s method for finding rational points on curves of higher genus.

Powers of Commutators as Products of Squares

Minimax Problems Related to Cup Powers and Steenrod Squares

If F is a family of mod 2 k-cycles in the unit n-ball, we lower bound the maximal volume of any cycle in F in terms of the homology class of F in the space of all cycles. We give examples to show that these lower bounds are fairly sharp. This paper is about minimax estimates for the volumes of cycles in complicated families. The simplest example of a minimax problem is a classical result about ...