We construct a subfactor planar algebra, and as a corollary a subfactor, with the ‘extended Haagerup’ principal graph pair. This is the last open case from Haagerup’s 1993 list of potential principal graphs of subfactors with index in the range (4, 3 + √ 3) . We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a descriptio...

We show that the twisted SL2 skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.

We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation for a normalized form of this polynomial.

We show that the action of Kauffman bracket skein algebra a surface Σ on module handlebody bounded by is faithful if and only quantum parameter not root 1.

silica exists in rice husk, an agriculture waste, as a naturally occurring phase. in first step, acidic pre-treatment and calcination of the rice husk were performed to obtain nano-silica, in which various sizes of the nano-silica, totally with sizes under 80 nm, were achieved. second, to reduce nano-silica to elemental si and subsequently formation of the composite, mg used as the reducing age...

A method for preparing colloidal particles formed by a magnetite nucleus and a biodegradable poly(DL-lactide) polymer coating is first described. The method is based on the so-called double-emulsion technique, employed to obtain polymeric spheres loaded with therapeutic drugs, to be used as drug delivery vectors. The aim of this work was to obtain, in a reproducible and rather simple way, collo...

Let k be a subring of the eld of rational functions in x; v; s which contains x 1 ; v 1 ; s 1. If M is an oriented 3-manifold, let S(M) denote the Hommypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Hommypt skein relations: (1) x ?1 L + ? xL ? = (s ? s ?1)L 0 ; (2) L with a positive twist = (xv ?1)L; (3) L t O ...