Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

Synthesis of angular triquinanes from 1-Alkynylbicyclo[3.2. 0]hept-2-en-7-ones. A tandem alkoxy-cope ring Expansion/Transannular ring closure reaction

Addition of ethenyllithium reagents to the carbonyl group of dialkyl squarate-derived 1-alkynylbicyclo[3.2.0]hept-2-ene-7-ones (15), followed by a TBAF workup, results in a low-temperature anion-accelerated alkoxy-Cope rearrangement which proceeds by way of a strained cyclic allene intermediates (e.g.,17). This leads to the formation of angularly fused triquinanes (e.g., 20) in which each of the rings is functionally differentiated. Bicyclo[6.3. 0]undecadienones (e.g., 36) are the major products when the reactions are quenched with aqueous bicarbonate rather than TBAF. Under analogous conditions 2-alkylidene-1-alkynylbicyclo[3.2. 0]heptan-7-ones also give bicyclo[6.3.0]undecadienones by a mechanism that was established to involve a 1,5-hydrgen shift in a strained allene intermediate. The synthetic scope and mechanism of these and related transformations are discussed.     

Doppler-broadening measurements of microvoids at the Au/GaAs interface

Recent positron lifetime studies made on the Au/GaAs interface with an applied electric field returning a significant fraction of bulk implanted positrons to the interface have revealed the presence of microvoids( 1 nm diameter) at the interface. In this work an attempt has been made to study these microvoids by observing the Doppler broadening on the annihilation radiation coming from them. This is done both by observing theS-parameter as a function of applied bias and by applying the generalized least-squares method to the deconvolution of the annihilation radiation lineshape. The general conclusion is that the Doppler-broadened data are consistent with the majority of positrons trapping into microvoids, probably associated with grain boundaries. The data suggest that these open volume defects are more associated with the Au film rather than the Au-Ga alloyed interfacial region.Paper presented at the 132nd WE-Heraeus-Seminar on Positron Studies of Semiconductor Defects, Halle, Germany, 29 August to 2 September 1994     

Linked porphyrin systems

Porphyrin monomers, 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin ( 1 ), 5,10-(dipyridyl)-15,20-(diphenyl)-porphyrin ( 2 ), and 5,15-(dipyridyl)-10,20-{diphenyl)porphyrin ( 3 ), were linked by hydrocarbon chains to form a series of dimers, trimers and polymers. The 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin monomers were linked by 2, 4, 6, 8 and 10 carbon chains through the alkylation of the pyridine nitrogens using the appropriate diiodoalkane to form positively charged linked dimers 4–8 . A trimer 12 was synthesized from two 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin and one 5,10-(dipyridyl)-15,20-(diphenyl)porphyrin linked by a six carbon chain. Hydrocarbon linked (5,10-(dipyridyl)-15,20-(diphenyl)porphyrin)_n ( 13 ) and (5,15-(dipyridyl)-10,20-(diphenyl)porphyrin)_n ( 14 ) were also prepared.     

Oxy-cope rearrangements of bicyclo[3.2.0]heptenones. Synthesis of bicyclo[4.2.1]non-1(4)-en-6-ones and bicyclo[5.2. 1]dec-1(10)-en-5-ones

6-exo-Methylbicyclo[3.2.0]hepten-7-ones and their 2-alkylidene analogues are readily prepared from dialkyl squarates. These compounds undergo facial oxy-Cope ring expansions upon treatment with vinyllithium; the former leads to bicyclo[4.2. 1]non-1(4)-en-6-ones and the latter to the first examples of bicyclo[5.2.1]dec-1(10)-en-5-ones, compounds having exceptionally strained bridgehead double bonds. The transformations are controlled by the 6-exo-methyl group in the starting material along with the substituent at position-1 (bridgehead) which force attack of the lithium reagent from the concave face of the starting material, thus allowing the cyclopentenyl or alkylidene groups to participate in the sigmatropic event.