The catalytic effect of Zirconia Sulfuric Acid (ZrSA) nanoparticle which is synthesized from thereaction of ZrO with chlorosulfonic acid has been investigated in the synthesis oftetrahydrobenzo[a]xanthene-11-ones by one-pot three-component reaction of β-naphthol,aromatic aldehydes, and dimedone. Different reaction conditions were studied in the presence ofZrSA nanoparticle as catalyst. The resu...

It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces can ...