Structure of 2,2′-bis(3-allyl-4-cyanatophenyl)isopropylidene

The structure of the title compound (I) was determined by direct methods using MoK diffractometer data, and refined by full-matrix least squares toR=0.066 for 1536 reflections (I3 (I)). The structure shows a central tetrahedral carbon atom surrounded by two methyl and two 3-allyl-4-cyanatophenyl groups. The geometry of the cyanato group in this molecule compares well with those in 2,2-bis(4-cyanatophenyl)isopropylideneII) and 4-chloro-3,5-dimethyl-phenylcyanate (III), the only other examples of organic compounds bearing the cyanato moiety in the Cambridge Crystallographic Database (V.3).     

A partially observed control problem for Markov chains

A finite state, continuous time Markov chain is considered and the solution to the filtering problem given when the observation process counts the total number of jumps. The Zakai equation for the unnormalized conditional distribution is obtained and the control problem discussed in separated form with this as the state. A new feature is that, because of the correlation between the state and observation process, the control parameter appears in the diffusion coefficient which multiplies the Poisson noise in the Zakai equation. By introducing a Gâteaux derivative the minimum principle, satisfied by an optimal control, is derived. If the optimal control is Markov, a stochastic integrand can be obtained more explicitly and new forward and backward equations satisfied by the adjoint process are obtained.This research was partially supported by NSERC Grant A7964, the Air Force Office of Scientific Research, United States Air Force, under Contract AFOSR-86-0332, and the U.S. Army Research Office under Contract DAAL03-87-0102.     

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     

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.     

Quinazolines and 1,4-benzodiazepines. LXXXVII. Synthesis of 1- and 3-phenylimidazo[1,5-a] [1,4]benzodiazepines

The synthesis of the 1-phenylimidazobenzodiazepine 5 from 1 and the anion of the nitrone 2 is described. The 3-phenyl-derivative 14 was prepared via the ammo alcohol 11 which was obtained by condensation of the nitrosamine 9 with benzaldehyde followed by catalytic hydro-genolysis of the nitroso group.     

Linear dichroism and fluorescence polarization of diphenyl polyenes in stretched polyethylene films

A study of the linear diehroism and fluorescence polarization of diphenylpolyenes (C₆H₅—(CH=CH)_n—C₆H₅) with n = 1,2,3,4,6,8 in stretched polyethylene films shows that the polyenes orient in the anisotropic matrix with their transition dipole (emission and absorption, π → π^*) aligned with the direction of stretch. The maximum dichroic ratio is observed for 1,6-diphenyl-1,3,5-hexatriene (DPH), with n = 3, whereas the values are substantially lower for n < 3 or n > 3. The high orientation of DPH and poor alignment of the higher polyenes may be accounted for in terms of the growing flexibility of the polyene chains with increasing chain length. The results justify the use of DPH as a convenient fluorescence probe for biological and synthetic membranes.