Creating Transverse Homoclinic Connections in Planar Billiards

Given a planar billiard system containing stable and unstable manifolds that intersect nontransversely, we show how to make a local perturbation to the boundary that causes the intersection to become transverse. We apply these ideas to billiards inside an ellipse. Bibliography: 19 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 122–134.his revised version was published in June 2005 with corrections in the author affiliation.     

On Vapnik‐Chervonenkis density over indiscernible sequences

In this paper, we study Vapnik‐Chervonenkis density (VC‐density) over indiscernible sequences (denoted VC_ind‐density). We answer an open question in [1], showing that VC_ind‐density is always integer valued. We also show that VC_ind‐density and dp‐rank coincide in the natural way.     

Vanadium-vitamin B12 bioconjugates as potential therapeutics for treating diabetes

The synthesis and blood glucose lowering properties of the first vanadium-vitamin B(12) bioconjugates are reported.