Secondary ion emission of selected transition metals under nitrogen oxides

The emission of various positive secondary ions has been investigated for polycrystalline targets of Ti, V, Cr, Nb, Ta, Co, Ni, Cu, Pd and Pt, which were bombarded by Ar⁺ ions under dynamic SIMS (DSIMS) conditions in the presence of the gaseous nitrogen oxides N₂O, NO and NO₂ at fixed pressure and under residual gas. Besides ions of the Me⁺ type several fragmentary ions (e.g. N⁺, O⁺, NO⁺, MeN⁺ and MeO⁺) and also cluster ions Me _x O _y ⁺ (x 2, 0 y 2) were detected. Signals of a more molecular type with respect to the reactant gas, e.g. MeNO⁺, were only found for Co, Ni, Cu, Pd and Pt. From this, one may infer that for the other targets the nitrogen oxides will exist preferentially in a dissociatively adsorbed state at the metal surface. Several aspects of secondary ion emission can be explained assuming a different degree of oxidation for the metals under the influence of reactant gas.Part of the dissertation     

Cutting planes for integer programs with general integer variables

We investigate the use of cutting planes for integer programs with general integer variables. We show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0–1 variables. We also explore the use of Gomory's mixed-integer cuts. We address both theoretical and computational issues and show how to embed these cutting planes in a branch-and-bound framework. We compare results obtained by using our cut generation routines in two existing systems with a commercially available branch-and-bound code on a range of test problems arising from practical applications. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Corresponding author.This research was partly performed when the author was affiliated with CORE, Université Catholique de Louvain.     

Network flows and non-guillotine cutting patterns

Up till now there has been no exact and effective algorithm for the problem of finding optimal cutting patterns of rectangles which are not restricted to those with the ‘guillotine’ property. This problem can be interpreted in a resource constrained scheduling context. The contribution of this paper to this topic is a good characterization of the flow functions and graphs corresponding to cutting patterns.     

Zero-sum games with incompletely defined payoff

It is shown that a saddle-point solution exists in a two-person, zero-sum game whose payoff is given by a matrix which is not completely defined. On the other hand, we show that such games do not always have a value, so that a saddle-point solution is not necessarily an optimal solution.This work was supported by the Centre d'Etudes Atomiques, Saclay, France.     

Mixed halide complexes of lead. A comparison with theoretical predictions

Experimentally and theoretically derived formation constants of mixed lead halide complexes are compared at 25.0°C and one molar ionic strength. The formation constant of PbBrCl, ₁₁=79±10, is somewhat larger than the theoretical results, ₁₁=55, predicted using the formation constants of PbBr₂ and PbCl₂. The molar absorptivity of PbBrCl was observed to be intermediate in character between the molar absorptivities of PbBr₂ and PbCl₂. Determinations of the formation constants of PbBr₂Cl^– and PbBrCl₂ ^– are in reasonable agreement with the predictions based on the formation constants of PbBr₃ ^– and PbCl₃ ^–. Mixed ligand species dominated the complexation scheme of Pb(II) in our test media.     

Kinetic and NMR spectroscopic studies of chiral mixed sodium/lithium amides used for the deprotonation of cyclohexene oxide

The mixed-metal complex formed from n-butylsodium, n-butyllithium, and a chiral amino ether has been studied by NMR spectroscopy. Three different mixed-metal amides were used as chiral bases for the deprotonation of cyclohexene oxide. The selectivity and initial rate of reaction were compared for sodium-amido ethers, lithium-amido ethers, and mixtures of sodium and lithiumamido ethers in diethyl ether and tetrahydrofuran, respectively. The mixed sodium/lithium amides are more reactive than the single sodium and lithium amides, whereas the stereoselectivities are higher when lithium amides are used. The alkali-metal/gamma-amido ethers exhibit both higher initial reaction rates and stereoselectivities than their beta-amido ether analogues. NMR spectroscopic studies of mixtures of n-butylsodium (nBuNa), n-butyllithium (nBuLi), and the gamma-amino ethers in diethyl ether show the exclusive formation of dimeric mixed-metal amides. In diethyl ether, the lithium atom of the mixed-metal amide is internally coordinated and the sodium atom is exposed to solvent; however, in tetrahydrofuran, both metals are internally coordinated.