Mixed-integer bilinear programming problems

This paper addresses a class of problems called mixed-integer bilinear programming problems. These problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued, and they arise in various production, location—allocation, and distribution application contexts. We first identify some special cases of this problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex. For the more general case, we employ a linearization technique and design a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm. Extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm.     

Barycentric coordinates for convex polytopes

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, theadjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordinate functions for the polytope are rational combinations of adjoints of various dual cones associated with the polytope.     

A ROLE FOR STEROLS IN THE PORPHYRIN MEDIATED PHOTOSENSITIZATION OF YEAST

The yeast Saccharomyces cerevisiae was used as a model system to determine the role of sterols in the porphyrin mediated photosensitization of yeast. A sterol auxotroph, RD5-R, was grown on sterols with different levels of unsaturation and assayed for photosensitivity in the presence of either protoporphyrin IX or hematoporphyrin (both at 100 micrograms/ml). Cells grown on the completely saturated sterol (stanol), cholestanol, were substantially more resistant to the photosensizing effects of the porphyrin. We hypothesize that this resistance arises from the inability of the porphyrin to mediate the oxidation of the membrane sterol. Our results indicate that photodegradation of the native yeast sterol, ergosterol, can account for substantial losses of cell viability.     

The correlation energy of the dangling silicon bond in a  Si:H

Photothermal deflection spectroscopy measurements of the optical absorption for undoped and phosphorus doped a  Si:H films are presented. Comparision of the energy shift of the dangling bond absorption shoulder shows that the correlation energy is between 0.25 and 0.45 eV. The singly and doubly occupied dangling silicon bonds are approximately ～1.25 eV and ～0.9 eV from the conduction band, respectively.     

Pavinane and isopavinane alkaloids: Correlation of absolute configurations by synthesis

(?)-Caryachine (9) and (?)-Reframoline (10) have been synthesised from a common intermediate; this confirms the absolute configuration in the isopavinane series deduced previously by application of the aromatic chirality rule. This also represents the first synthesis of an optically active pavinane alkaloid.     

On uniqueness of solutions for nonlinear creep problems in symmetric pressure vessels

Uniqueness is established for positive solutions of a nonlinear integral equation which governs the effective stress in internally loaded spherical and incompressible cylindrical pressure vessels subject to primary or secondary transient creep.     

A note on the stress singularity at a penny-shaped crack in three-dimensional electrostriction

Zusammenfassung Diese Mitteilung behandelt eine vollständige Bewertung der Spannungs-Singularität am Rande eines flachen kreisförmigen Spaltes unter der Einwirkung von Elektrostriktion. Die Ergebnisse bestätigen die Schlussfolgerungen, welche früher bei zweidimensionalen Problemen gezogen wurden.Die der Elektrostriktion zuzuschreibende Singularität zeitigt eine rein radiale Spannung, welche nicht dazu neigt, die schon bestehenden Spalten ihrer Ausdehnungs-Oberfläche entlang auszubreiten.

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Research supported by the National Science Foundation under grant NSF GP 22567.

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Research supported by the United States Atomic Energy Commission.     

Anisotropic effects in the angular distribution of photoelectrons from cesium 6s

Dirac-Fock calculations show dramatic variations of the asymmetry parameter with energy for Cs 6s in contrast to the β = 2 prediction of more approximate theories.     

Aquation of (N,Ndimethylformamide) pentaamminecobalt (III) perchlorate in aqueous perchlorate media

The first-order rate constants for aquation of Co(NH₃)₅(DMF)³⁺ were determined in aqueous perchlorate media. The rate constants were independent of hydrogen ion concentration and ionic strength, but decreased with increasing perchlorate ion concentration. Proton magnetic resonance studies showed that dimethylformamide was not hydrolyzed to formic acid and dimethylamine in the aquation step. Mass-spectrometer studies showed that cobalt–oxygen bond breaking occurred in 98 percent, or more, of the aquation acts. Enthalpies and entropies of activation were determined. It was concluded that aquation occurred by an I_d mechanism.