See also my publication title page and presentation page.
For both magnetostatic computational methods, the coercivity decreases
from H_c/M_s = 0.06 ± 0.003 to 0.014 ± 0.003 over the range
3 < d/l_ex < 80, where the uncertainties reflect the field
step size. Also over this interval, as d/l_ex increases, the
magnetization exhibits three modes of reversal: nearly uniform
rotation, transverse switching of end domains followed by propagation
of head-to-head domain walls from the ends to the center of the
particle, and nucleation and propagation of vortices accompanied by
more complex domain structures.
Title page.
One motivation for the questions studied here arises from the area of "artificial neural networks," where the problem can be stated in terms of the growth in the number of "neurons" (the elements of S) needed in order to achieve a desired error rate. The focus on non-Hilbert spaces is due to the desire to understand approximation in the more "robust" (resistant to exemplar noise) L_{p}, 1<=p<2 norms.
The techniques used borrow from results regarding moduli of smoothness in
functional analysis as well as from the theory of stochastic processes on
function spaces.
AMS classification: 41A25, 46B09, 68T05.
Title page.
michael.donahue@nist.gov