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The electronic structure of quasiperiodic lattices is studied. An alloy theory, including short-range order effects, is used to approximate Fibonacci and Thue–Morse lattices. Short-range order is treated by embedding small clusters in an alloy that itself incorporates a two-site approximation, and...
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Any pure operator band can be expanded so that each component of the band is reflexive.
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McDowell's 1985 electronic bath theory of charge transfer is used to investigate the effect of varying surface temperature on the process of ion scattering from a solid surface. As a specific example, the system of Na+ scattered from W is modeled. The neutralization probability is found to have a si...
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Some new relations for the Appell function F 1 (a, b, b′; c; w, z) are obtained including differentiation and integration formulas, integral representations, series and recurrence relations. Some integrals are given which can be expressed in terms of F 1 and confluent Appell functions (Humbert fun...
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We call E subset-of-or-is-equal-to {0,1}kappa projective if for some countable A subset-of-or-is-equal-to kappa there is an E(A) subset-of-or-is-equal-to {0,1}A such that E = E(A) x {0,1}kappa/A and E(A) is a projective subset of the Cantor set {0,1}A. We construct a model where Haar measure on {0,1...
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A higher dimensional Markov switching position dependent random map is a random map where the probabilities of switching from one higher dimension transformation to another are the entries of a stochastic matrix and the entries of stochastic matrix are functions of positions. In this note, we pr...
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The introduction of non-orthogonal atomic orbitals, into the tight-binding approximation, gives rise to the existence of overlap terms in electronic band-structure calculations. In contrast to the zero-overlap situation, it is helpful to employ a tensorial Green-function approach to access the surfa...
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A simple analytic formula is derived for use in solving the Hubbell radiation rectangular source integrals . Tables of results are given to compare the numerical values derived from the approximation formula with those given earlier in the literature.
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A set of vertices in a graph is said to be dependent if it is not independent. Let p(k)(G) denote the number of dependent sets of size k in the graph G. We show that, for any graph G, the sequence {p(k)(G)} is logarithmically concave. (C) 2001 Elsevier Science.
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An algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let L-a denote left mulfiplication by any nonzero element a is an element of A. Several results are proved concerning the s...