The Murphy operators in the Hecke algebra Hn of type A are explicit commuting elements, whose symmetric functions are central in Hn. In [8] I defined geometrically a homomorphism from the Homfly skein C of the annulus to the centre of each algebra Hn, and found an element Pm in C, independent of n, whose image, up to an explicit linear combination with the identity of Hn, is the mth power sum o...

Scoliosis is a deformity of the spine known since Hippocrates times. The value of certain methods of conservative treatment remains controversial. Some of them have only a psychological value both for the physician and his or her caregivers. Based on current literature and the Scoliosis Research Society Report of Alternative Methods of Treatment of Idiopathic Scoliosis, we describe the effectiv...

This paper illustrates the use of the differentiation matrix technique for solving differential equations in finance. The technique provides a compact and unified formulation for a variety of discretisation and time-stepping algorithms for solving problems in one and two dimensions. Using differentiation matrix models, we compare time-stepping algorithms for option pricing computations and pres...

The E6 state sum invariant is a topological invariant of closed 3manifolds constructed by using the 6j-symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 subfactor planar algebra, and develop its linear skein theory by showing many relations in it. By using this linear skein, we give an elementary self-contained construction of...

We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.

Taiwanese species of the crane fly subgenus Antocha (Antocha) Osten Sacken, 1860, are reviewed. Antocha (Antocha) taiwanensis, new species, is described and figured. Previously known species, Antocha (A.) bifida Alexander, 1924a and Antocha (A.) styx Alexander, 1930 are redescribed and illustrated. Antocha (A.) javanensis Alexander, 1915 is removed from the list of Taiwanese crane flies. Antoch...