Dipolar 31P NMR spectroscopy of crystalline inorganic phosphorus compounds.

The ability of the 90 degrees-t1-180 degrees pulse sequence to produce accurate dipole-dipole coupling information in solids is investigated. To this end, the experimental 31P spin echo decays are measured for eighteen crystalline phosphides and phosphorus chalcogenides and compared with simulations, based on the known internuclear distances in these compounds. The experimental results are generally found accurate in compounds where the dominant contribution to the dipole-dipole coupling arises from nuclei in structurally inequivalent sites with large chemical shift anisotropies. For this situation, the quantum mechanical "flip-flop" term in the dipolar Hamiltonian is suppressed and the dipole-dipole coupling is entirely heteronuclear in character. All of those compounds that do not obey this condition show accelerated spin echo decays due to a fractional contribution of the flip-flop term and possibly incomplete refocusing of chemical shift terms on the time scale of the experiment. The results confirm on an empirical basis that the spin echo NMR technique can provide accurate dipole-dipole coupling information (and thus distance distributions) in disordered solids and glasses.     

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.     

CertainC*-algebras with real rank zero and their corona and multiplier algebras: II

We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM A/A in terms ofK _*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK _*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation.