Eliminating graphs by means of parallel knock-out schemes

In 1997 Lampert and Slater introduced parallel knock-out schemes, an iterative process on graphs that goes through several rounds. In each round of this process, every vertex eliminates exactly one of its neighbors. The parallel knock-out number of a graph is the minimum number of rounds after which all vertices have been eliminated (if possible). The parallel knock-out number is related to well-known concepts like perfect matchings, hamiltonian cycles, and 2-factors.We derive a number of combinatorial and algorithmic results on parallel knock-out numbers: for families of sparse graphs (like planar graphs or graphs of bounded tree-width), the parallel knock-out number grows at most logarithmically with the number n of vertices; this bound is basically tight for trees. Furthermore, there is a family of bipartite graphs for which the parallel knock-out number grows proportionally to the square root of n. We characterize trees with parallel knock-out number at most 2, and we show that the parallel knock-out number for trees can be computed in polynomial time via a dynamic programming approach (whereas in general graphs this problem is known to be NP-hard). Finally, we prove that the parallel knock-out number of a claw-free graph is either infinite or less than or equal to 2.     

Infrared absorption and electron paramagnetic resonance studies of vinyl radical in noble-gas matrices

Vinyl radicals produced by annealing-induced reaction of mobilized hydrogen atoms with acetylene molecules in solid noble-gas matrices (Ar, Kr, and Xe) were characterized by Fourier transform infrared and electron paramagnetic resonance (EPR) spectroscopies. The hydrogen atoms were generated from acetylene by UV photolysis or fast electron irradiation. Two vibrational modes of the vinyl radical (nu7 and nu5) were assigned in IR absorption studies. The assignment is based on data for various isotopic substitutions (D and 13C) and confirmed by comparison with the EPR measurements and density-functional theory calculations. The data on the nu7 mode is in agreement with previous experimental and theoretical results whereas the nu5 frequency agrees well with the computational data but conflicts with the gas-phase IR emission results.     

An efficient approach to isoindolo[2,1-b][2]benzazepines via intramolecular [4+2] cycloaddition of maleic anhydride to 4-α-furyl-4-N-benzylaminobut-1-enes

Acylation of 4-α-furyl-4-N-benzylaminobut-1-enes with maleic anhydride gave 4-oxo-3-aza-10-oxatricyclo[5.2.1.0^1,5]dec-8-ene-6-carboxylic acid via amide formation followed by intramolecular Diels-Alder reaction of furan (IMDAF). The cycloaddition proceeded under mild reaction conditions (25 °C) and provided only the exo-adduct in quantitative yield. Treatment of this compound with PPA gave isoindolo[2,1-b][2]benzazepine derivatives via ring opening, aromatization and intramolecular electrophilic alkylation. In order to extend the scope of the reaction sequence, 7-oxo-5,11b,12,13-tetrahydro-7H-isoindolo[2,1-b][2]benzazepine-8-carboxylic acids were further transformed into useful synthetic intermediates.     

New synthetic approach to substituted isoindolo[2,1-a]quinoline carboxylic acids via intramolecular Diels-Alder reaction of 4-(N-furyl-2)-4-arylaminobutenes-1 with maleic anhydride

Acylation of substituted 4-(furyl-2)-4-arylaminobut-1-enes with maleic anhydride provided 2-allyl-6-carboxy-4-oxo-3-aza-10-oxatricyclo[5.2.1.0^1,5]dec-8-enes in high yield under mild reaction conditions. The Diels-Alder adducts are formed via an initial amide formation followed by a stereoselective intramolecular [4+2] exo-cycloaddition reaction. Treatment of the tricyclic compounds with phosphoric acid at high temperatures (70-120 °C) promoted cyclic ether opening, intramolecular cyclization and aromatization to give the corresponding tetracyclic compounds, 5,6,6a,11-tetrahydro-10-carboxyisoindolo[2,1-a]quinolines, in moderate yields. The influence of the acid and the reaction temperature on the cyclization reactions are also discussed.     

From microscopic to macroscopic nuclear collective dynamics

We apply smoothing procedures to response functions for isoscalar vibrations. For collective motion, we find a transition from a structured strength distribution to one corresponding to one incoherent, strongly overdamped mode. It is argued that the latter may be interpreted as macroscopic motion exhibiting, to some extent, features of the hydrodynamical model. We discuss the physical origin of this behaviour, in particular its relation to the disappearance of shell structure.Supported in part by the Deutsche Forschungsgemeinschaft     

The New Data for the Reaction of Arylenedioxy Trihalogenophosphoranes with Alkyl- and Arylacetylenes

The new data concerning the reaction between substituted arylenedioxy trihalogenophosphoranes and monoalkyl- or arylacetylenes are summarized. The reaction leads to formation of six-membered heterocycles-2-oxo-4-R-benzo[ e ]-1,2-oxaphosphorin-3-enes. The substituent effects in the phosphorane and acetylene molecules on the ipso -substitution and halogenation regiochemistry are discussed. The ipso -substitution of tert -butyl group on chlorine and the exchange of bromine on chlorine and iodine on hydrogen have been observed, along with formation of benzophosphorines. The interaction of tetrachloro- ortho -benzoquinone with phosphorus trichloride and arylacetylenes is proposed as a new modification of the reaction leading to the formation of benzo[ e ]-1,2-oxaphosphorines. The structures of some benzo[ e ]-1,2-oxaphosphorines are determined by the single crystal X-ray diffraction.     

Alternating-current losses in two-layer superconducting cables consisting of second-generation superconductors coated by U-shaped ferromagnetic materials

Alternating-current losses in a two-layer superconducting cable, each layer being composed of 15 closely-spaced rectangular wires made up of second-generation superconductors when the ends of wires are coated by either a non-magnetic or strong ferromagnetic material having a U profile is numerically investigated. Computations are carried out through the finite-element method. The alternating-current losses do not increase significantly if the relative permeability of the coating is increased three orders of magnitude, provided that the current amplitude is less than half of the critical current in a superconducting wire. However, the losses are much higher for ferromagnetic coating if the amplitude of the applied current oscillating at 50 Hz is close to the critical current. The ferromagnetic coating is seen to accumulate the magnetic field lines normally on its surfaces, while the field lines are parallel to the long axes of the wires, leading to more significant flux penetration in the coated regions. This facilitates a uniform low-loss current flow in the uncoated regions of the wires. In contrast, coating with a non-magnetic material gives rise to a considerably smaller current flow in the uncoated regions, whereas the low-loss flow is maintained in the coated regions. Moreover, the current flows in opposite directions in the coated and uncoated regions, where the direction in each region is converse for the two materials.