In my talk I am going to remind you what is the AK-invariant and give examples of its usefulness. I shall also discuss basic conjectures about this invariant and some positive and negative results related to these conjectures.
This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.
This paper gives an algorithm for computing the kernel of a locally finite higher derivation on the polynomial ring k[x₁,..., xₙ] up to a given bound.
An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.
Let k be a field of characteristic zero. We prove that the derivation , where s ≥ 2, 0 ≠ p ∈ k, of the polynomial ring k[x,y] is simple.