Vassiliev measures of complexity of open and closed curves in 3-space

In this article, we define Vassiliev measures of complexity for open curves in 3-space. These are related to the coefficients enhanced Jones polynomial continuous functions curve coordinates; as ends tend coincide, they converge corresponding invariants resulting knot. We focus on second measure from closed and For curves, can be computed by a Gauss code diagram it has an integral formulation, double alternating self-linking integral. The is topological invariant function coordinates polygonal obtains simpler expression terms geometric probabilities.