Oscar Rojo

  • Citations Per Year
Learn More
Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique linear dispersion relation(More)
Abstract. Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2, . . . ,n. Let di be the degree of the vertex i. The Randić matrix of G , denoted by R, is the n× n matrix whose (i, j)−entry is 1 √ did j if the vertices i and j are adjacent and 0 otherwise. The normalized Laplacian matrix of G is L = I−R,(More)
Let G = (V (G), E(G)) be a unicyclic simple undirected graph with largest vertex degree . Let Cr be the unique cycle of G. The graph G− E(Cr ) is a forest of r rooted trees T1,T2, . . .,Tr with root vertices v1, v2, . . ., vr , respectively. Let k(G) = max 1 i r {max{dist(vi , u) : u ∈ V (Ti )}} + 1, where dist(v, u) is the distance from v to u. Let μ1(G)(More)
Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α ∈ [0, 1], write Aα (G) for the matrix Aα (G) = αD (G) + (1− α)A (G) . Let α0 (G) be the smallest α for which Aα(G) is positive semidefinite. It is known that α0 (G) ≤ 1/2. The main results of this paper are: (1) if G is d-regular then α0 =(More)
Let G be a simple, undirected, connected and finite graph. For i = 1, . . . , r, let Ki,si be a star in G with si > 1 and let Hi be an arbitrary graph of order si . Let G(H1, . . . , Hr) be the graph obtained from G and the graphs H1, . . . , Hr by identifying the vertices of Hi with the pendent vertices of K1,si . It is proved that (i) if μ ̸= 0 and μ ̸= 1(More)
The Cooper pair binding energy vs center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong. PACS Number: 74.20.Fg Corresponding author: M.(More)
A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d ≥ 3 and n ≥ 6 be given. Let Pd−1 be the path of d − 1 vertices and Sp be the star of p + 1 vertices. Let p = [p1, p2, ..., pd−1] such that p1 ≥ 1, p2 ≥ 1, ..., pd−1 ≥ 1. Let C (p) be the caterpillar obtained from the stars Sp1 , Sp2 , ..., Spd−1 and the path Pd−1 by(More)