16 research outputs found
Development and evaluation of ointment and cream vehicles for a new topical steroid, fluclorolone acetonide
THE USE OF A SEQUESTRENE-CITRATE MIXTURE IN THE ESTIMATION OF THE BLOOD SEDIMENTATION RATE
Discrete Moving Frames and Discrete Integrable Systems
Group based moving frames have a wide range of applications, from the
classical equivalence problems in differential geometry to more modern
applications such as computer vision. Here we describe what we call a discrete
group based moving frame, which is essentially a sequence of moving frames with
overlapping domains. We demonstrate a small set of generators of the algebra of
invariants, which we call the discrete Maurer--Cartan invariants, for which
there are recursion formulae. We show that this offers significant
computational advantages over a single moving frame for our study of discrete
integrable systems. We demonstrate that the discrete analogues of some
curvature flows lead naturally to Hamiltonian pairs, which generate integrable
differential-difference systems. In particular, we show that in the
centro-affine plane and the projective space, the Hamiltonian pairs obtained
can be transformed into the known Hamiltonian pairs for the Toda and modified
Volterra lattices respectively under Miura transformations. We also show that a
specified invariant map of polygons in the centro-affine plane can be
transformed to the integrable discretization of the Toda Lattice. Moreover, we
describe in detail the case of discrete flows in the homogeneous 2-sphere and
we obtain realizations of equations of Volterra type as evolutions of polygons
on the sphere