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.     

Harmonic maps with fixed singular sets

Suppose Ω is a smooth domain in R^m,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0. R. H.’s research partially supported by the National Science Foundation.     

Correlations beyond the horizon

It is a fundamental feature of quantum field theory that correlations between observable quantities occur over all spacetime regions. In particular, in cosmological models with horizons, such correlations will be present in regions which lie outside of each other's horizon. Such correlations may play an important role in processes occurring in the early universe.This essay received the first award from the Gravity Research Foundation, 1992—Ed.     

Orthostructures from sesquilinear forms. A primer

We make a linkage with the ultimate generalization of Hilbert space, anR-module with an orthogonality relation, and certain constructs due to Foulis and Randall and other related structures suggested by Cattaneo, Franco, and Marino.     

Time decay for nonlinear wave equations in two space dimensions

The Cauchy Problem for the equation u_tt–u+|u|^p–1u=0 (x², t>0, >1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For >5, it is shown that the maximum amplitude of such a wave decays at the expected rate t^–1/2 as t. For 1+8<5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when >_o, where _o is the root of the cubic equation ³-2²-7-8=0; thus _o4.15.Alfred P. Sloan Research Fellow     

Recurrence vs. transience for spatially inhomogeneous birth and death in a random environment

Summary We consider birth and death in a random environment, having probabilitiesp(,x) andq(,x) of a step to the right or left, respectively, from statex in environment. Under several sets of conditions involving the existence of limp(,x) and limq(,x) asx, we give conditions for certain extinction or escape to when 0 is absorbing, corresponding to recurrence or transience when 0 is reflecting. The environmental sequence is assumed to be stationary ergodic, and for some results stronger assumptions are required.     

Polymerization and polymers of silicic acid

Linear relationships among molecular weight, polymerization time, and gelation for the condensation of any monomer, including those of unknown size and functionality, are developed and applied to data on soluble silicic acids generated from tetraethyl silicate and from sodium silicate. The results suggest the formation of monomers containing ca. 12–15 ? OSi units with functionality of ca. 2.05 that condense with a rate constant of ca. 10^?4 liter/mole sec and an activation energy of 40–70 kJ/mole. One model compatible with these characteristics and the stoichiometry involved is a ladder polymer ca. 3 ? SiO units wide. Polymer isolation was achieved by replacing residual ? OH with (CH₃)₃Sio? , as well as by freezing of of aqueous solutions, which yielded fibers under special conditions. Solutions of the uncapped and capped polymers and melts of the latter had low viscosity even for fractions with M?_n ～100,000. This implies a coiled or globular nature for the polymers, which is supported by their limited propensity for film and fiber formation. Attemps to improve this situation by copolymerization, the use of other capping agents, and by the polymerization of precapped monomers were unsuccessful.     

Structure, 31P and 13C chemical shift anisotrophy of (CH3)3P, (CH3)3PO, (CH3)3PS and (CH3)3PSe as determined by liquid crystal NMR spectroscopy

The ¹³P and ¹³C spectra of the triply ¹³C labelled molecules (CH₃)₃P, (CH₃)₃PO, (CH₃)₃PS and (CH₃)₃PSe oriented in a nematic phase are reported. The CPC bond angles have been measured. The ¹³P chemical shift tensor shows a large anisotropy except in the case of (CH₃)₃P. The abnormal large value observed for the PSe bond length suggests a large anisotropy of the ¹J(PSe) spin coupling.     

Synthesis of 1,4-annulated cyclooctatetraenophanes based on a novel cubane building block approach

A general synthetic approach to strained 1,4-annulated cyclooctatetraene-based cyclophanes is described. A key feature in this approach is exploitation of the cubane core as a masked cyclooctatetraene synthon. Thus, 1,4-disubstituted cubanes 3 and 4 used as precursors to cyclooctatetraenophanes have been prepared in four steps from the readily available 1,4-cubanedicarboxaldehyde (5). The synthesis of 3 was effected by palladium/copper-mediated coupling of 1,4-bis[(Z,Z)-2-iodovinyl]cubane (6) and 1,4-bis[(Z,Z)-but-1-en-3-ynyl]cubane (8). For the synthesis of 4, on the other hand, modified Eglington-Glaser coupling was applied for the macrocyclization step. The general characteristic of Rh(I) to induce [2 + 2] cycloreversion of the cubane core to syn-tricyclo[4.2.0.0(2,5)]octa-3,7-diene followed by thermal rearrangement to cyclooctatetraene was applied as a key structural transformation toward targeted cyclooctatetraenophanes 1 and 2.     

Anthracene Based Bulky Diol Hosts. Crystal Structures of a Free Host and of Inclusion Compounds with Dipolar Guests

X-ray crystal structures are reported of a free host compound 1, comprising two diphenylmethanol terminal groups attached to a central 9,10-ethynyl substituted anthracene unit, and of three inclusion compounds of a fluoren-9-ol substituted analogous host 2 with acetone, dimethyl sulphoxide (DMSO) and dimethylformamide (DMF) as guest, respectively. Despite the presence of two hydroxyl groups in 1, there is no O–H...O hydrogen bond between the molecules in the guest free crystal – only weaker C–H...O interactions and van der Waals' type connections. In the inclusion compounds of 2, H-bonded 1:2 host–guest associates are formed, where each of the host hydroxyl groups binds to a guest oxygen atom. The orientations of the host–guest connections in these complexes vary, being E for acetone and Z for both DMSO and DMF guests, relative to the host anthracene unit. The DMSO and DMF inclusion compounds of 2 proved to be isostructural.