The Radon-split and the Helly-core of a point configuration

We provide a systematic construction of point configurations with incompatible Radon-split and Helly-core. This provides a resolution of problems of Reay and Sierksma, and shows that it is computationally hard to decide the compatibility of the split and core of a configuration. Received 29 June 2000; revised 5 January 2001.     

Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums

In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. These conditions are variations of Bapat-Raghavan and Franklin-Lorenz conditions.     

Taming 3-manifolds using scalar curvature

In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that \mathbbR³{\mathbb{R}^3} is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented 3-manifolds with finitely generated fundamental group allowing such a metric.     

Effect of an energy reservoir on the atmospheric propagation of laser-plasma filaments

The ability to select and stabilize a single filament during propagation of an ultrashort, high-intensity laser pulse in air makes it possible to examine the longitudinal structure of the plasma channel left in its wake. We present the first detailed measurements and numerical 3-D simulations of the longitudinal plasma density variation in a laser-plasma filament after it passes through an iris that blocks the surrounding energy reservoir. Since no compensation is available from the surrounding background energy, filament propagation is terminated after a few centimeters. For this experiment, simulations indicate that filament propagation is terminated by plasma defocusing and ionization loss, which reduces the pulse power below the effective self-focusing power. With no blockage, a plasma filament length of over a few meters was observed.     

Thermal analyis of hexadecyltrimethylammonium–montmorillonites

Na-montmorillonite (Na-MONT) was loaded with hexadecyltrimethylammonium cations (HDTMA) by replacing 41 and 90% of the exchangeable Na with HDTMA, labeled OC-41 and OC-90, respectively. Na-MONT, OC-41, and OC-90 were heated in air up to 900 °C. Unheated and thermally treated organoclays heated at 150, 250, 360, and 420 °C are used in our laboratory as sorbents of different hazardous organic compounds from waste water. In order to get a better knowledge about the composition and nature of the thermally treated organoclays Na-MONT and the two organo-clays were studied by thermogravimetry (TG) in air and under nitrogen. Carbon and hydrogen contents in each of the thermal treated sample were determined and their infrared spectra were recorded. The present results showed that at 150 °C both organoclays lost water but not intercalated HDTMA cations. At 250 °C, many HDTMA cations persisted in OC-41, but in OC-90 significant part of the cations were air-oxidized into H₂O and CO₂ and the residual carbon formed charcoal. After heating both samples at 360 °C charcoal was present in both organo clays. This charcoal persisted at 420 °C but was gradually oxidized by air with further rise in temperature. TG runs under nitrogen showed stepwise degradation corresponding to interlayer water desorption followed by decomposition of the organic compound, volatilization of small fragments and condensation of non-volatile fragments into quasi-charcoal. After dehydroxylation of the clay the last stages of organic matter pyrolysis and volatilization occurred.     

Naphthologs of overcrowded bistricyclic aromatic enes: (E)-bisbenzo[a]fluorenylidene

(E)-11H-Bisbenzo[a]fluorenylidene (E-6) was synthesized by Barton’s double extrusion diazo-thione coupling method from 11H-benzo[a]fluoren-11-thione (11) and 11-diazo-11H-benzo[a]fluorene (13). The reaction is probably thermodynamically controlled; in the event that the less stable Z -6 is also formed, it would rapidly undergo Z → E diastereomerization to give E -6. The B3LYP/6-311G(d,p) calculated diastereomerization barrier for Z -6 → E -6 is ΔG ₂₉₈ = 57.0 kJ/mol (13.6 kcal/mol). The calculated equilibrium constant K _eq(E -6 → Z -6) = 92:8 (at 298 K) is indicative of a marked diastereoselectivity of the reaction leading to E -6. The structure of E-6 was established by ¹H-NMR and ¹³C-NMR spectroscopies and by X-ray analysis. PAE E-6 crystallizes in the monoclinic space group C2/c. The unit cell of the crystal structure E -6 contains eight molecules, arranged as four pairs of enantiomers. PAE E -6 adopts a twisted conformation with the pure twist of the central C¹¹=C^11′ bond ω = 39°. The dihedral angle ν in E -6 is 60.6°, which is significantly higher than the respective dihedral angle in PAEs Z -6, 2, E -7, Z -7, 14, and 15. The large syn-pyramidalization angles at C¹¹ and C^11′ (χ = 12.6° and 14.8°) of E-6 indicates the enhanced strain in the fjord regions of the molecule. The enhanced twist is primarily attributed to the double benzo[a]annelation of the bifluorenylidene moiety at the fjord regions. The B3LYP/6-311G(d,p) calculated structure of E -6 is in a very good agreement with the experimental X-ray structure. PAE E -6 adopts a twisted conformation in solution, with the downfield chemical shift of H¹/H^1′ (8.31 ppm); H¹⁰/H^10′ (δ = 7.20 ppm) and H⁹/H^9′ (δ = 6.86 ppm) in E -6 are positioned above the planes of the opposing naphthalene rings. PAEs E -6 and Z -6 are significantly higher in energy than their corresponding benzo[b]annelated isomers E -7 and Z -7.     

Intersystem crossing at singlet conical intersections

The energy of the lowest triplet state of organic molecules is intermediate between the ground state and the first excited singlet. At the S₁/S₀ conical intersection, the two singlet states are degenerate. It is shown that for some molecules (ethylene, benzene, toluene and pyrrole) the T₁ state is also degenerate with the two singlet states. Moreover, the spin orbit coupling matrix element at this structure is necessarily large, so that intersystem crossing can be quite efficient. If the lowest triplet state is repulsive (as in the studied molecules) it may significantly contribute to the dissociation yield under certain experimental conditions.     

Radical decomposition of <Emphasis Type="Italic">N,N</Emphasis>-bis-(3-chloro-1,4-naphthoquinon-2-yl) amine in basic conditions followed by EPR

EPR spectroscopy was used to assess the radicals produced upon basic decomposition of N,N-bis-(3-chloro-1,4-naphthoquinon-2-yl) amine (BClNQA). Three radicals have been trapped and identified: N-bis(3-chloro-1,4-naphthoquinone) hydrazine radical (6), 2-hydroxy-3-chloro-1,4-naphthoquinone anion radical (9) and 2-amino-3-chloro-1,4-naphthoquinone radical (8). The probable reaction mechanism, the structure of intermediates as well as the reaction profile are discussed.