We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology three-spheres [1, 2, 14] by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimen-sion two foliation endowed with an invariant transverse measure. We prove that the average asymptotic linking… (More)
We prove a theorem formulated by V. I. Arnold concerning a relation between the asymptotic linking number and the Hopf invariant of divergence–free vector fields. Using a modified definition for the system of short paths, we prove their existence in the general case.
The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes' propagating into the computational domain from the boundary. The… (More)
Typical panel data models make use of the assumption that the regression parameters are the same for each individual cross sectional unit. We propose tests for slope heterogeneity in panel data models. Our tests are based on the conditional Gaussian likelihood function in order to avoid the incidental parameters problem induced by the inclusion of… (More)
In  Y. Eliashberg and W. Thurston gave a definition of tight con-foliations. We give an example of a tight confoliation ξ on T 3 violating the Thurston-Bennequin inequalities. This answers a question from  negatively. Although the tightness of a confoliation does not imply the Thurston-Bennequin inequalities, it is still possible to prove restrictions… (More)
We show that a null–homologous transverse knot K in the complement of an overtwisted disk in a contact 3–manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self–linking number of K with respect to S satisfies sl(K, S) = −χ(S). In particular, every null–homologous topological knot type in an… (More)