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.     

On retroactive occurrence and twin events in quantum mechanics

Bohr's well-known claim that only a registered phenomenon is a true phenomenon is further elaborated into occurrence in the past: If ideal occurrence of an eventP ((1–P)) is a state at a timet _i makes another eventQ ((1–Q))certain at a later timet _f, and, finallyU is the evolution operator fromt _i tot _f, then, it is proved that the final collapsed stateQ(U U ⁺)Q/TrQU U ⁺, which comes about in ideal occurrence ofQ att _f,equals the initial collapsed stateU(P P/TrP)U ⁺, which evolves from the state resulting from the ideal occurrence ofP in att _i. Utilizing the latter state is called theretroactive apparent ideal occurrence (RAIO) ofP in. A number of consequences, including the general notion of twin events (the case whent _f=t _i, andU=1) is derived. It is pointed out that RAIO is relevant in second-kind quantum measurement, in Wheeler's delayed-choice experiments in second-kind (or conditional) quantum preparators.     

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