Pentagon-hexagon-patches with short boundaries

Some Infinite Classes of Fullerene Graphs

A fullerene graph is a 3 regular planar simple finite graph with pentagon or hexagon faces. In these graphs the number of pentagon faces is 12. Therefore, any fullerene graph can be characterized by number of its hexagon faces. In this note, for any h > 1, we will construct a fullerene graph with h hexagon faces. Then, using the leapfrogging process we will construct stable fullerenes with 20 +...

A numerical evaluation of the scalar hexagon integral in the physical region

We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative corrections to multi-particle cross sections. The hexagon integral is represented in terms of n-dimensional triangle functions and (n+2)dimensional box functions. I...

An ab initio Study of the C 6 0 Particle - Hole Pair + and Cjj "

The C60 ions C^" and C ^ are discussed comparatively on the basis of ab initio calculations. The basis set employed is of 3-21 G* quality. By analogy with the neutral molecule the geometry of the anion is icosahedral (Ih). Both Ih systems differ, however, in the bondlength alternation. In the neutral molecule the hexagon-hexagon bondlength exceeds the hexagon-pentagon value; vice versa in the a...

Ab initio studies of quasi-one-dimensional pentagon and hexagon ice nanotubes

Explicit Description of Compressed Logarithms of All Drinfeld Associators

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations — hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algebra L generated by the symbols a, b, c modulo [a, b] = [b, c] = [c, a]. We describe explicitly the images of the log...