The optical excitations in C70 and higher fullerenes, including isomers of C76, C78, and C84, are theoretically investigated. We use a tight binding model with long-range Coulomb interactions, treated by the Hartree-Fock and configuration-interaction methods. We find that the optical excitations in the energy region smaller than about 4 eV have most of their amplitudes at the pentagons. The osc...

The rise in defense spending since 1998, which this year may surpass 100% in real terms, is unprecedented over a 48-year period. In real percentage term, it is nearly as large as the Kennedy-Johnson and Reagan surges combined. Whether one looks at the entire DoD budget or just that part not related to the wars, current spending is above the peak years of the Vietnam era and the Reagan years. Lo...

In this paper we consider the achievable rate region of the Gaussian Multiple Access Channel (MAC) when suboptimal transmission schemes are employed. Focusing on the two-user MAC and assuming uncoded Pulse Amplitude Modulation (PAM), we derive a rate region that is a pentagon, and propose a strategy with which it can be achieved. We also compare the region with outer bounds and with orthogonal ...

The problem of predicting stoichiometries and patterns of chemical addition to a carbon framework, subject solely to the restriction that each addend excludes neighboring sites up to some distance d, is equivalent to determination of d-codes of a graph, and for d = 2 to determination of maximum independent sets. Sizes, symmetries, and numbers of d-codes are found for the all-heptagon Klein grap...

A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism, q, representing the deviation from the Pentagon condition. We uncover a binary tree representation for all diagrams involving a and q and provide a link to permutations and linear orderings. This leads to other notions of premonoidalness. We de...

In an earlier paper, I showed that the classes of pentagon-free two-graphs and of pentagon-and-hexagon-free two-graphs could be represented in terms of trees. This paper gives formulae for the numbers of labelled objects in each of these classes, as well as the numbers of labelled reduced two-graphs in each class. The proofs use various enumeration results for trees. At least some of these resu...

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle...