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.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-Resolved Photoacoustic Calorimetry: From Carbenes to Proteins

Why have molecules only been seen but not heard? For over a century chemists have probed reactions with various spectroscopic methods to learn about structures, dynamics, and reactivities of their molecules. What they have not done is to listen to their molecules react. Although the photoacoustic phenomenon has been known since 1880, it is only in the last twenty years that technology has developed to the point where sound waves produced by reacting molecules can be time resolved and the information contained within the waves deciphered. The information content within the photoacoustic wave is indeed rich, for one can learn about the dynamics and the magnitude of enthalpy changes associated with the reaction as well as the changes in molecular volume. This review article chronicles the development of time-resolved photoacoustic calorimetry and its application to a variety of reactions encountered in organic and organometallic chemistry and biochemistry.     

Chain “stationary” insertion mechanism and production of isotactic polypropylene with C 1 symmetric catalyst systems

In this contribution, the stereochemistry of propylene insertion/propagation reactions with a variety of C ₁ symmetric metallocene catalysts, containing bridged cyclopentadienyl-fluorenyl ligand for the preparation of highly stereoregular polypropylene is presented. The impact of the distal substitutent’s size and composition and changes that the catalytic sites undergo upon such substitution is elaborated. A comprehensive mechanism is proposed to explain the resulting catalytic changes that bring about the irreversible C _s/C ₁ site transformation and tactic behavior inversion. Furthermore the cyclopentadienyl’s combined distal/proximal and fluorenyl’s frontal substituent effects on molecular weight, regio-, and stereoregularity of the final polymers are discussed. Finally, stereoselectivities of C ₂ and C ₁ symmetric catalyst systems are compared. It is shown that current high performance C ₁ symmetric catalyst systems with central site chirality can be isotactic selective as well or even better in certain aspects than the C ₂ symmetric bridged bisindenyl-based metallocene catalysts. The text was submitted by the authors in English.