Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

On the phase structure of the compact abelian lattice Higgs model

This paper studies the vacuum overlap order parameter proposed by Fredenhagen and Marcu in the case of the compactU(1) gauge model with the Wilson action coupled to a Higgs field with fixed length ||=1. The existence of two distinct phases inD space-time dimensions (D4) is established.     

On two mean value properties and functional equations associated with them

Summary Motivated by different mean value properties, the functional equationsf(x) – f(y)/x–y=[(x, y)], (i)xf(y) – yf(x)/x–y=[(x, y)] (ii) (x y) are completely solved when, are arithmetic, geometric or harmonic means andx, y elements of proper real intervals. In view of a duality between (i) and (ii), three of the results are consequences of other three.The equation (ii) is also solved when is a (strictly monotonic) quasiarithmetic mean while the real interval contains 0 and when is the arithmetic mean while the domain is a field of characteristic different from 2 and 3. (A result similar to the latter has been proved previously for (i).)     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Forward-backward multiplicity correlations in σ+ p,K + p andpp collisions at 250 GeV/c

Forward-backward multiplicity correlations in σ⁺,K ⁺ p andpp collisions at 250 GeV/c ( \(\sqrt s \) =22 GeV) are given for all charges and for the different charge combinations. The correlations are found to be caused predominantly by centrally produced particles. It is demonstrated that this result is an agreement with observations at the ISR and the CERNp \(\bar p\) -Collider. The results are compared to expectations from LUND, DPM and FRITIOF Monte Carlo models and a geometrical picture relating correlations in hadron-hadron collisions toe ⁺ e ^? data in terms of impact parameters is tested.     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.