Colouring Arcwise Connected Sets in the Plane II

Let ? be the family of finite collections ? where ? is a collection of bounded, arcwise connected sets in ℝ² where for any S,T∈? such that S∩T≠?, it holds that S∩T is arcwise connected. Given ? is triangle-free, and provided the chromatic number χ(G) of the intersection graph G=G(?) of ? is sufficiently large, there exists α>1 independent of ? such that there is a subcollection ?^′⊂? of at most 5 sets with the property that the sets of ? surrounded by ?^′ induce an intersection graph H where . Received: November 13, 1995 Final version received: December 3, 1998     

Total synthesis of polemannones B and C

The first total synthesis of polemannones B and C, higly oxygenated benzoxanthenones derivatives from Polemannia montana, is reported employing our new catalytic Cu(II)/sparteine system for β,β-phenolic couplings and tandem inverse-electron demand Diels-Alder reaction cascade in 75-90% yield.     

Microdeformation behavior in nanotemplated epoxy thermosets: A study with in situ tensile deformation technique in transmission electron microscopy

Microdeformation behavior in nanostructured block copolymer‐toughened epoxy resins, or templated epoxy thermosets, was studied using an in situ tensile deformation technique performed directly in a transmission electron microscope. The observed microdeformation modes were found to correlate well with the macroscopic mechanical properties of the materials. In the order of decreasing macroscopic fracture toughness, the microdeformation modes were observed to change from large uniform plastic deformation over an extensive area, to localized plastic deformation bands, to little plastic deformation observed in the most brittle material. A similar trend was also observed when samples of the same material were tested at different temperatures, reflecting changes in the deformation mechanism as a function of temperature. Structural defects were observed in nanotoughening phases when plastic deformation was observed. The implication of the observed microdeformation modes to the macroscopic toughening mechanisms is discussed in the context of the micromorphology of the nanometer sized toughening phases and parameters of the epoxy matrix chemistry such as bromination, molecular weight, and interfacial miscibility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 393–406, 2009     

Bonds Intersecting Cycles In A Graph

Let G be a k-connected graph G having circumference c ≥ 2k. It is shown that for k ≥ 2, then there is a bond B which intersects every cycle of length c-k + 2 or greater.     

Measurement of time histories of stable intermediates during first stage ignition of n-heptane and its two isomers in a shock tube

We report the first shock tube measurements of formaldehyde (CH₂O) during the first stage ignition of n-heptane, 2-methylhexane and 3,3-dimethylpentane, in highly diluted fuel/oxygen mixtures in the pressure range of 7–10 atm and temperature range of 700–880 K. Combined time histories of all carbonyl (–C = O) species, CO and fuel were also measured simultaneously in an effort to study the impact of fuel structure on the concentration and the rate of evolution of first stage ignition products. Of the three isomers studied in this work, n-heptane was found to be the fastest, while 3,3-dimethylpentane was found to be the slowest. The differences in the time scale of formation, and plateau concentration of the intermediates between the isomers across the entire range of test conditions suggests a strong dependency of the measured time histories to fuel structure. These species therefore act as markers of the Negative Temperature Coefficient (NTC) behavior of fuels and can be used as targets for developing semi-empirical, hybrid chemistry models of complex, multi-component petroleum derived gasoline and jet fuels. The time histories reported in this work should prove very useful in the refinement of detailed kinetic models of n-heptane, and development of rate rules for branched alkane isomers.