TL;DR: The bilevel linear fractional programming problem is considered and several proofs in that paper are shown to be incorrect and alternative proofs are provided.
TL;DR: Birtea et al. as mentioned in this paper showed that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.
TL;DR: The q-analogue of Hardy's result was given in this paper, where they replaced the above integral by the Jackson g-integral and gave the q-Analogous result.
Abstract: In 1939, G. H. Hardy proved that, under certain conditions, the only functions satisfying 1 0 f(λ m t)f(λ n t)dt= 0, where the λ n are the zeros of f, are the Bessel functions. We replace the above integral by the Jackson g-integral and give the q-analogue of Hardy's result.