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...

It has been shown that the twist number of a reduced alternating knot can be determined by summing certain coefficients in the Jones Polynomial. In the discovery of this twist number, it became evident that there exist higher order twist numbers which are the sums of other coefficients. Some relations between the second twist number and the first are explored while noting special characteristic...

Trefoil factor 2 (TFF2) is a member of trefoil factor family found to be overexpressed in many cancers including cholangiocarcinoma (CCA). The majority of studies have focused on wild-type TFF2 (wtTFF2) expression, but information regarding alternative splicing variants of TFF2 mRNA has not been reported. In this study, we aimed to identify and qu...

The Ramsey number is known for only a few specific knots and links, namely the Hopf link and the trefoil knot (although not published in periodicals). We establish the lower bound of all Ramsey numbers of any knot to be one greater than its stick number. 1 Background and Definitions The study of Ramsey numbers of knots can be found at the intersection of knot theory and graph theory. 1.1 Knot T...

Experiments on the influence of the polar lobe on the development of molluscs have shown that after removal of the polar lobe cleavage is radially symmetrical and indications of bilateral symmetry do not appear (Wilson, 1904: Dentalium; Clement, 1952: Ilyanassa). In normal development the polar lobe fuses with one of the two cells of the trefoil stage, and this cell becomes the posterior side o...

Trefoil factor 3 (TFF3), also called intestinal trefoil factor or Itf, is a 59 amino acid peptide found as a homodimer predominantly along the gastrointestinal tract and in serum. TFF3 expression is elevated during gastrointestinal adenoma progression and has been shown to promote mucosal wound healing. Here we show that in contrast to other trefoil factor family members, TFF1 and TFF2, TFF3 is...