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A many-electron theory of resonant charge transfer, originally formulated for the scattering of an atom with an empty valence orbital from a surface, is extended to treat the case where the valence orbital is initially occupied by one or two electrons. The scattering of He and He+ from the Si(001) s...
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The electron transmission properties of a semiconducting wire are investigated via the tight-binding approximation. The wire is modeled as a chain of sp-hybrid orbitals, including overlap effects. The transmission probability is calculated using the tensorial Green function method. An impurity in th...
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The current state of knowledge concerning liftings for noncomplete probability spaces is discussed. This is a somewhat expanded version of the author's talk given at the 1991 Summer Conference on General Topology and Applications in Honor of Mary Ellen Rudin and Her Work.
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We consider the problem of comparing the suitability of various magnetic lattices for the spin polarization of neutrons. To do this, we use a discrete model to construct measures of transmission through one-dimensional lattices. We examine the model for non-periodic lattices that are generated from ...
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We survey the theory of square integrable group representations for the non-compact, semisimple lie group SU(1,1), which has three different series of representations: principal, complementary and discrete. As a result of our survey we conclude that the discrete series representations are the only o...
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The d-dimensional Schrödinger's equation is analyzed with regard to the existence of exact solutions for polynomial potentials. Under certain conditions on the interaction parameters, we show that the polynomial potentials V8(r) = ∑k = 18αkrk,α8>0 and V10(r) = ∑k = 110αkrk,α10>0 are exactly...
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Infinite series of the type Sigma(n=1)(infinity)(alpha/2)n/n 1/n!F-2(1)(-n,b;gamma;y) are investigated. Closed-form sums are obtained for alpha a positive integer, alpha = 1, 2, 3,.... The limiting case of b --> infinity, after gamma is replaced with x(2)/b, leads to Sigma(n=1)(infinity)(alpha/2)...
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We investigate the cofinality of the partial order N-kappa of functions from a regular cardinal kappa into the ideal N of Lebesgue measure zero subsets of R. We show that when add(N) = kappa and the covering lemma holds with respect to an inner model of GCH, then cf(N-kappa) = max{cf(kappa(kappa)), ...
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A dynamical-systems model of plasma glucose concentration, andits regulation by insulin and glucagon, is described, as pertains to types 1 and2 diabetes. The hyperglycemic case is seen to be dependent only on insulinconcentration, while the hypoglycemic case requires consideration of both in-sulin a...
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We focus on matrix semigroups (and algebras) on which rank is commutable [rank(AB) = rank(BA)]. It is shown that in a number of cases (for example, in dimensions less than 6), but not always, commutativity of rank entails permutability of rank [rank(A(1)A(2)...A(n)) = rank(A(sigma(1))A(sigma(2))... ...
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