The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

Untersuchung von Textilien und Textilrohstoffen

Ohne Zusammenfassung     

Correction to: On Webs of Maximum Rank (Geom. Dedicata 31 (1989), 19–35)

We correct an error in Example (3.4) in Geom. Dedicata 31 (1989), 19–35.     

The mixed-aldehyde synthesis of difunctional tetraarylporphyrins

The synthesis is reported of nine unsymmetrical, meso-substituted porphyrins. Among the compounds prepared are the following 5-(R)-10,15,20-tri-p-tolylporphyrins; R = 2,6-dinitrophenyl, 4-hydroxy-3-ethoxy-phenyl, 4-hydroxy-3-methoxy-5-nitrophenyl, 5-hydroxy-2-nitrophenyl and 4-hydroxy-3-nitrophenyl. Other porphyrins reported include 5-(2-(1-butoxy)phenyl)-15-(2-nitrophenyl)-10-15-di-p-tolylporphyrin and the two 5-(R)-10-15,20-tripropylporphyrins in which R = 2-nitrophenyl and 2-hydroxyphenyl. The disubstituted porphyrins offer a rational route to the synthesis of difunctional “tailed-porphyrins”.     

Mechanistic Aspects of Carbon Nanotube Nucleation and Growth

The discovery, synthesis, characterization, and applicability of carbon nanotubes have produced tremendous excitement and interest among scientists and engineers. In particular, the use of these unique tubular nanostructures for new strong lightweight materials, nanoelectronics, fuel storage and cells, electron emitters and bio, scanning probe microscopy, and chemical sensing devices has created an intense effort to advance the synthesis so as to mass produce carbon nanotubes with control over diameter and helicity. The massive and controlled synthesis of this heralded nanostructure has been a great challenge. Although significant progress has advanced the preparation, more synthetic development is required. The syntheses have so far involved three main approaches: arc discharge vaporization, laser vaporization, and catalytic chemical vapor deposition. The synthetic trend has progressed to a point where further advancement with these techniques will require a better understanding of the mechanism of nucleation and growth. The mechanics of carbon nanotube nucleation and growth involve very complex and diverse phenomena occurring under extreme conditions and on the mesoscopic scale. As yet the detail mechanism is unknown. Difficulties with experimental probing and computational simulation have increased the mystery of this mechanism. This review presents an account of research on the synthesis of carbon nanotubes and the mechanism of formation. This overview includes all three mentioned synthetic approaches and hybrids thereof. On the basis of this broad account a comprehensive mechanism for carbon nanotube nucleation and growth naturally arises. This mechanism is qualitative and it hopes to inspire more quantitative exploration and synthetic advancement.     

Aerobic alcohol oxidation catalyzed by a new, oxygen-bridged heterometallic compound [PPh4][Ru(N)Me2(μ2-O)2Pd((−)-sparteine)]

The reaction between the new hydroxy compound [PPh₄][Ru(N)(OH)₂Me₂] and Pd(OSiMe₃)₂((−)-sparteine) produces (Me₃Si)₂O, H₂O and a new heterobimetallic compound [PPh₄][Ru(N)Me₂(μ₂-O)₂Pd((−)-sparteine)] in good yield. The Ru/Pd bimetallic compound catalyzes the oxidation of aryl and allyl alcohols to the corresponding carbonyl compound in air and the rearrangement of allylic alcohols unsaturated aldehydes. It also oxidizes PPh₃ to O-PPh₃ under O₂.     

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.     

The remarkable ability of lithium ion to reverse the stereoselectivity in the conjugate addition of Li[BuCuI] to a chiral N-crotonyl-2-oxazolidinone

[reaction: see text] The influence of lithium ions on the conjugate addition of the monoorganocuprate reagent, Li[BuCuI], to a chiral crotonate has been investigated. The results show that iodotrimethylsilane (TMSI) is crucial for the asymmetric conjugate addition of the copper reagent, but only in THF or when 12-crown-4 is used. The reaction is thought not to involve any halosilane in any critical steps in the organocopper mechanisms conducted in Et(2)O.     

Synthesis of some dibenzodiazepinone derivatives as potent and m2-selective antimuscarinic compounds

Two series of 5-[[4-[4-(dialkylamino)butyl]-l-cyclohexyl]acetyl], and 5-[(dialkylamino)acyl]-10,11-dihydro-5H- dibenzo[b,e][1,4]diazepin-11-ones were synthesized as potential m2-selective ligands 1,2. Their affinity and selectivity for the muscarinic cholinergic receptor m-AChR subtypes were determined. Replacing a nitrogen with CH in the piperidine ring of 5-[[4-[4-(dialkylamino)butyl]-l-piperidinyl]acetyl]-10,11-dihydro-5H-dibenzo-[b,e][1,4]diazepin-11-ones 3 significantly altered the affinity and selectivity to the muscarinic receptor subtypes.