We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.

A D(3)-symmetric knotted cyclophane, with a subgraph of trefoil topology, was synthesized by cyclization of a D(3)-symmetric scaffold. Control of configuration at the three metal-based stereocenters arises from a bascule/pivot mechanism.

This article presents a comparative study of Kiepert’s trefoil and its related curves, combining variety tools from differential algebraic geometry, integrable systems, elastica theory, special functions. While this curve was classically known well studied in the literature, some open problems were recently solved, goal paper is to present characterize general solution equation that governs tre...

The physical sense of tight knots provided by the SONO algorithm is discussed. A method allowing one to predict their length is presented. An upper bound for the minimum length of a smooth trefoil knot is determined.

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed open configurations. Ideal knots are purely geometric abstractions for tightest configuration tied perfectly flexible, self-avoiding tube with an inextensible centerline undeformable cross-sections. Here, we construct realizations tight elastomeric rod, use X-ray to...

BACKGROUND The trefoil peptides are major secretory products of mucus cells of the gastrointestinal tract and show increased expression after inflammatory or ulcerative damage. Recombinant human TFF2 (spasmolytic polypeptide) has been shown to be cytoprotective, and enhances repair in models of gastric injury. AIMS To test the healing effects of recombinant human (h)TFF2 in a rat model of chr...