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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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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 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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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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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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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...
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In cellular networks, channels must be assigned to call requests so that interference constraints are respected and bandwidth is minimized. The number of call requests per cell is continually changing, making channel assignment naturally an online problem. We describe two new online channel assignme...
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A theoretical study of the electronic structure of the (111) surfaces of CoSi2 and NiSi2 and their interfaces with Si has been carried out with particular attention paid to the existence of localized states. A Green function method has been used within the empirical tight-binding approximation to ca...
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A tight-binding investigation is performed of the electronic structure of a semi-infinite monatomic chain, whose atomic orbitals are assumed to be non-orthogonal, so that the effects of overlap can be taken into account. In addition to markedly modifying the bulk band-edges, the presence of overlap ...
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A brief overview is given of the theory of surface-ion neutralization (SIN) by highlighting studies from the pioneering days to the present time. Emphasis is placed on the 1-electron time-dependent Newns-Anderson (TDNA) model, which has played such a key role in studying resonance charge transfer. R...
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A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K > 1 there exists an irreducible operator band on the Hilbert space l(2) which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each ...
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A methodology of transmission through two-dimensional tight-binding lattices is presented. The theory is formulated in terms of matrix algebra and the relationships between the matrices are examined in detail. The features specific to tight-binding systems are contrasted to those for more general tr...