Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 G2 of G1 and G2. We show that: τ(G1 G2) ≥ 2(n1−1)(n2−1) n1n2 (τ(G1)n1) n2+1 2 (τ(G2)n2) n1+1 2 and τ(G1 G2) ≤ τ(G1)τ(G2) [ 2m1 n1 − 1 + 2m2 n2 − 1 ](n1−1)(n2−1) . We also characteri...

Compositions of biotite from three different rock types of Mashhad granitoids, i.e., granodiorite, monzogranite and leucogranite in NE of Iran have been documented by electron microprobe and wet chemistry for Fe3+ and Fe2+. Mashhad granitoids have been geochronologically and petrologically grouped into G1 and G2 phases. Microprobe data show that the total Fe contents in biotite from G2 leucogra...

We construct the N = 1 supergravity analog of the Green-Schwarz and heterotic superstring theories in 10D. We find the SO(8) theory previously found by compactification of 10D on K3. We also find eleven G 2 × G 2 theories, two with symmetric matter content. It is not obvious how tenof the G 2 × G 2 theories can be gotten from 10D. Ten-dimensional superstrings [1], [2], [3], [4] are one of the m...

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of non-Gaussian phases of the Hermitean one-matrix model. A unified approach is proposed for description of “connected correlators” in the form of the phaseindepende...

We develop the formalism discussed previously in hep-ph/0601209 and hep-ph/0605246 to construct a kinetic theory that provides insight into the earliest “Glasma” stage of a high energy heavy ion collision. Particles produced from the decay of classical fields in the Glasma obey a Boltzmann equation whose novel features include an inhomogeneous source term and new contributions to the collision ...

This paper documents the extent to which homeowners use housing equity to smooth their consumption over time. Unlike drawing down other forms of saving, accessing accumulated home equity can be quite costly. Theoretically and empirically, a key distinction can be drawn between those refinancing their home mortgage to improve their wealth position from those who had a consumption smoothing motiv...

Let G1 and G2 be two graphs on disjoint sets of n1 and n2 vertices, respectively. The corona of graphs G1 and G2, denoted by G1 ◦ G2, is the graph formed from one copy of G1 and n1 copies of G2 where the i-th vertex of G1 is adjacent to every vertex in the i-th copy of G2. The neighborhood corona of G1 and G2, denoted by G1 ⋄ G2, is the graph obtained by taking one copy of G1 and n1 copies of G...