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.     

A Water Molecule Triggers Guest Exchange at a Mono-Zinc Centre Confined in a Biomimetic Calixarene Pocket: a Model for Understanding Ligand Stability in Zn Proteins

In this study, the ligand exchange mechanism at a biomimetic Zn^II centre, embedded in a pocket mimicking the possible constrains induced by a proteic structure, is explored. The residence time of different guest ligands (dimethylformamide, acetonitrile and ethanol) inside the cavity of a calix[6]arene-based tris(imidazole) tetrahedral zinc complex was probed using 1D EXchange SpectroscopY NMR experiments. A strong dependence of residence time on water content was observed with no exchange occurring under anhydrous conditions, even in the presence of a large excess of guest ligand. These results advocate for an associative exchange mechanism involving the transient exo-coordination of a water molecule, giving rise to 5-coordinate Zn^II intermediates, and inversion of the pyramid at the Zn^II centre. Theoretical modelling by DFT confirmed that the associative mechanism is at stake. These results are particularly relevant in the context of the understanding of kinetic stability/lability in Zn proteins and highlight the key role that a single water molecule can play in catalysing ligand exchange and controlling the lability of Zn^II in proteins.