  Lower bounds are placed on the fermionic determinants of Euclidean quantum
electrodynamics in two and four dimensions in the presence of a smooth,
finite-flux, static, unidirectional magnetic field $B(r) =(0,0,B(r))$, where
$B(r) \geq 0$ or $B(r) \leq 0$, and $r$ is a point in the xy-plane.
