Isotopic substitution shifts in methane and vibrational band assignment in the 5560-6200 cm region

The absorption spectra of the ¹²CH₄ and ¹³CH₄ molecules have been recorded and assigned in the 5560-6200 cm⁻¹ region. The effects of isotopic substitution for ¹²C by ¹³C on the methane vibrational energy levels have been calculated from an ab initio potential energy surface and compared with experiment. Comparison of the results obtained for two isotopic species allows us to confirm the vibrational assignment for the strongest bands of ¹²CH₄ in this region. Good agreement of ab initio calculations with observed energy levels has been demonstrated. A list of the assigned ¹³CH₄ lines valuable in atmospheric applications is reported.     

Alternating copolymerization of 1- and 2-vinylnaphthalene with methyl methacrylate by using diethylaluminum chloride

The alternating copolymerization of 1- and 2-vinylnaphthalene (1-VNap and 2-VNap) with methyl methacrylate (MMA) by using diethylaluminum chloride (Et₂AlCl) in toluene at 0°C has been studied. No polymerization could occur without Et₂AlCl, and alternating copolymers were obtained only when an equimolar amount of Et₂AlCl with MMA was supplied. Through ¹H-NMR analyses on both dyad and triad of alternating deuterated 1- and 2-α-d-VNap–MMA copolymers, each configuration could be described successfully by a single parameter, coisotacticity σ, whose value was estimated as 0.41 for the former and 0.56 for the latter copolymer, respectively. A rather low coisotacticity of copoly(1-VNap–MMA) was explained in the terms of steric effect (peri effect) of 1-VNap monomer.     

Mass distribution of fission fragments in the19F+197Au reaction

Mass distributions of fission fragments have been measured for the reaction of¹⁹F on¹⁹⁷Au as a function of scattering angle. The mean fragment mass is dependent on the scattering angle, the asymmetry increasing with increasing projectile energy.     

Dual approach to minimization on the set of pareto-optimal solutions

LetX ^* be the set of Pareto-optimal solutions of a multicriteria programming problem. We are interested in finding a vectorxX ^* which minimizes another criterion. SinceX ^* is a nonconvex set, our problem is that of minimization over a nonconvex set. By exploiting the fact that the number of criteria is often very small compared with the number of variables, we use a dual approach to obtain a practical algorithm. We report preliminary numerical results on problems with up to 100 variables and 5 criteria.The authors express their special thanks to Professor H. P. Benson and the referees for many valuable comments and suggestions and for pointing out valuable references. They also thank Dr. Y. Ishizuka for the references of Theorem 2.2.