Degree Sums and Covering Cycles

It is shown that if in a simple graph G of order n the sum of degrees of any three pairwise non-adjacent vertices is at least n, then there are two cycles (or one cycle and an edge or a vertex) of GF that contain all the vertices. © 1995 John Wiley & Sons, Inc.     

Interfacial adsorption phenomena at a weakly first-order phase transition

We study the interfacial adsorption phenomena of the ferromagnetic five-state Potts model on the square lattice, whose transition is of weakly first-order, by using Monte Carlo simulations and finite-size scaling theory. It is shown that the net-adsorption has a finite-size effect according to the first-order phase transition even for systems much smaller than the bulk correlation length.     

Nuclear magnetic resonance of poly-β-alanine

Nuclear magnetic resonance of poly-β-alanine samples differing in solubility in water was studied over a wide temperature range as part of an investigation of their physical properties. Water-soluble poly-β-alanine has more branches and a lower degree of crystallinity than water-insoluble poly-β-alanine. NMR spectra of poly-β-alanine show one component at 77°K. which splits into two components, broad and narrow, at room temperature. Two transition regions were observed in curves for line width and second moment versus temperature. The higher transition temperature, corresponding to the glass transition of the polymer, appears to decrease with increasing water content. The second moment for the water-soluble polymer differs from that of the water-insoluble polymer at 77°K. This is interpreted in terms of the difference in the degree of crystallinity of the polymers.     

Semiconductor-catalyzed photooxygenation of aromatic olefins

Irradiation of semiconductors (TiO₂ and CdS) suspended in organic solvents containing 1,1-diphenylethylene and its derivatives under oxygen afforded the corresponding epoxides and benzophenone. A possible mechanism is discussed.