Observation of splitting of the E2g mode and two-phonon spectrum in graphites

We have found the two-phonon mode of the disorder-induced line at 1370 cm^-1 for the single crystal and polycrystalline graphites having disorder. The degenerate E_2g mode of the D_6h symmetry for graphite is split for the disordered graphites, having frequencies at 1590 cm^-1 and 1627 cm^-1. Brewster angle measurements using lasers at 6328A and 10.6 μm yield n and k with good consistency even for surfaces with moderate roughness. Our results suggested that distortion of the crystal structure is present.     

Boson fields under a general class of local relativistic invariant interactions

We consider a boson field (x) under an interaction of the form V((x))dx, whereV() is a bounded continuous real function of a real variable . IfV() has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction.     

On a Hypergraph Matching Problem

Let H = (V, E) be an r-uniform hypergraph and let A matching M of H is (α, )-perfect if for each F ∈ , at least α|F| vertices of F are covered by M. Our main result is a theorem giving sufficient conditions for an r-uniform hypergraph to have a -perfect matching. As a special case of our theorem we obtain the following result. Let K(n, r) denote the complete r-uniform hypergraph with n vertices. Let t and r be fixed positive integers where t≥r≥2. Then, K(n, r) can be packed with edge-disjoint copies of K(t, r) such that each vertex is incident with only o(n ^{r ?1}) unpacked edges. This extends a result of Rödl [9].     

Packing 4-Cycles in Eulerian and Bipartite Eulerian Tournaments with an Application to Distances in Interchange Graphs

We prove that every Eulerian orientation of K_m,n contains arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.Received February 6, 2004