96,662 research outputs found
Navigation in Curved Space-Time
A covariant and invariant theory of navigation in curved space-time with
respect to electromagnetic beacons is written in terms of J. L. Synge's
two-point invariant world function. Explicit equations are given for navigation
in space-time in the vicinity of the Earth in Schwarzschild coordinates and in
rotating coordinates. The restricted problem of determining an observer's
coordinate time when their spatial position is known is also considered
Binomial generation of the radical of a lattice ideal
Let be a lattice ideal. We provide a necessary and sufficient
criterion under which a set of binomials in generate the radical
of up to radical. We apply our results to the problem of
determining the minimal number of generators of or of the
up to radical.Comment: 14 pages, to appear in Journal of Algebr
Boundedness of Maximal Operators of Schr\"odinger Type with Complex Time
Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator
with complex-valued time are improved by determining up to the endpoint the
sharp for which boundedness from the Sobolev space
into occurs. Bounds are established for not only the
Schr\"odinger maximal operator, but further for a general class of maximal
operators corresponding to solution operators for certain dispersive PDEs. As a
consequence of additional bounds on these maximal operators from
into , sharp results on the pointwise almost
everywhere convergence of the solutions of these PDEs to their initial data are
determined.Comment: 12 pages. One further minor correction. To appear in the Revista
Matem\'atica Iberoamerican
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