63,990 research outputs found
New vacuum solutions of conformal Weyl gravity
The Bach equation, i.e., the vacuum field equation following from the
Lagrangian L=C_{ijkl}C^{ijkl}, will be completely solved for the case that the
metric is conformally related to the cartesian product of two 2-spaces; this
covers the spherically and the plane symmetric space-times as special subcases.
Contrary to other approaches, we make a covariant 2+2-decomposition of the
field equation, and so we are able to apply results from 2-dimensional gravity.
Finally, some cosmological solutions will be presented and discussed.Comment: 15 pages, LaTeX, no figures, submitted to J. Math. Phy
Approximate Approximations from scattered data
The aim of this paper is to extend the approximate quasi-interpolation on a
uniform grid by dilated shifts of a smooth and rapidly decaying function on a
uniform grid to scattered data quasi-interpolation. It is shown that high order
approximation of smooth functions up to some prescribed accuracy is possible,
if the basis functions, which are centered at the scattered nodes, are
multiplied by suitable polynomials such that their sum is an approximate
partition of unity. For Gaussian functions we propose a method to construct the
approximate partition of unity and describe the application of the new
quasi-interpolation approach to the cubature of multi-dimensional integral
operators.Comment: 29 pages, 17 figure
Computation of volume potentials over bounded domains via approximate approximations
We obtain cubature formulas of volume potentials over bounded domains
combining the basis functions introduced in the theory of approximate
approximations with their integration over the tangential-halfspace. Then the
computation is reduced to the quadrature of one dimensional integrals over the
halfline. We conclude the paper providing numerical tests which show that these
formulas give very accurate approximations and confirm the predicted order of
convergence.Comment: 18 page
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