Connected Operators for the Totally Asymmetric Exclusion Process

We fully elucidate the structure of the hierarchy of the connected operators that commute with the Markov matrix of the Totally Asymmetric Exclusion Process (TASEP). We prove for the connected operators a combinatorial formula that was conjectured in a previous work. Our derivation is purely algebraic and relies on the algebra generated by the local jump operators involved in the TASEP. Keywords: Non-Equilibrium Statistical Mechanics, ASEP, Exact Results, Algebraic Bethe Ansatz.Comment: 10 page

Numerical techniques for conformal mapping onto a rectangle

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In particular, we study the following two classes of methods for the mapping of domains of the form . (i) Methods which approximate where f is an approximation to the conformal map of Q onto the unit disc, and S is a simple Schwarz-Christoffel transformation. (ii) Methods based on approximating the conformal map of a certain symmetric doubly-connected domain onto a circular annulus. Keywords: Conforma

On fundamental groups of quotient spaces

In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf spaces in general.Comment: 12 pages, 4 figures; added references, keywords, and Remark 1.2; accepted at Topology and its Application