0000000000049182
AUTHOR
J. V. Beltran
Bézier Solutions of the Wave Equation
We study polynomial solutions in the Bezier form of the wave equation in dimensions one and two. We explicitly determine which control points of the Bezier solution at two different times fix the solution.
A Characterization of Quintic Helices
A polynomial curve of degree 5, @a, is a helix if and only if both @[email protected]^'@? and @[email protected]^'@[email protected]^''@? are polynomial functions.
Graded Poisson structures on the algebra of differential forms
We study the graded Poisson structures defined on Ω(M), the graded algebra of differential forms on a smooth manifoldM, such that the exterior derivative is a Poisson derivation. We show that they are the odd Poisson structures previously studied by Koszul, that arise from Poisson structures onM. Analogously, we characterize all the graded symplectic forms on ΩM) for which the exterior derivative is a Hamiltomian graded vector field. Finally, we determine the topological obstructions to the possibility of obtaining all odd symplectic forms with this property as the image by the pullback of an automorphism of Ω(M) of a graded symplectic form of degree 1 with respect to which the exterior der…
Poisson-Nijenhuis structures and the Vinogradov bracket
We express the compatibility conditions that a Poisson bivector and a Nijenhuis tensor must fulfil in order to be a Poisson-Nijenhuis structure by means of a graded Lie bracket. This bracket is a generalization of Schouten and Frolicher-Nijenhuis graded Lie brackets defined on multivector fields and on vector valued differential forms respectively.