96,662 research outputs found

    Navigation in Curved Space-Time

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    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

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    Let IL,ρI_{L, \rho} be a lattice ideal. We provide a necessary and sufficient criterion under which a set of binomials in IL,ρI_{L, \rho} generate the radical of IL,ρI_{L, \rho} up to radical. We apply our results to the problem of determining the minimal number of generators of IL,ρI_{L, \rho} or of the rad(IL,ρ)rad(I_{L, \rho}) up to radical.Comment: 14 pages, to appear in Journal of Algebr

    Boundedness of Maximal Operators of Schr\"odinger Type with Complex Time

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    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 sβ‰₯0s \geq 0 for which boundedness from the Sobolev space Hs(R)H^s(\mathbb{R}) into L2(R)L^2(\mathbb{R}) 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 Hs(R)H^s(\mathbb{R}) into L2([βˆ’1,1])L^2([-1, 1]), 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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