Differential operators, $n$-branch curve singularities and the $n$-subspace problem

The N-Membranes Problem

Singularities in the Newtonian n-body Problem

In this note, we study the structure of singularities of the Newtonian n-body problem where we establish certain relations between collisions and noncollision singularities. Based on our results, we conjecture that the set of all accumulation points of collisions in the extended phase space is exactly the set of initial conditions that lead to a noncollision singularity.

ON THE SINGULARITIES OF THE CURVED n-BODY PROBLEM

We study singularities of the n-body problem in spaces of constant curvature and generalize certain results due to Painlevé, Weierstrass, and Sundman. For positive curvature, some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projection—a property that offers a new method of approaching the problem in this particular case.

Factoring Differential Operators in n Variables

In this paper, we present a new algorithm and an experimental implementation for factoring elements in the polynomial nth Weyl algebra, the polynomial nth shift algebra, and Zgraded polynomials in the nth q-Weyl algebra. The most unexpected result is that this noncommutative problem of factoring partial differential operators can be approached effectively by reducing it to the problem of solvin...

the n-membranes problem