Asymptotic behavior of unbounded solutions of linear Volterra integral equations

The asymptotic behavior as t → ∞ of solutions of ∝₀^tu(t ? s) dA(s) = f(t) is studied when f(t) satisfies a “o” estimate as $\text{t ” ∞}$, and A belongs to a weighted space and its Laplace-Stieltjes transform has finitely many zeros in its closed half-plane of convergence. Results for systems of integral equations as well as for integrodifferential systems are also given.     

Remote impact analysis by use of propagated acceleration signals,II: Comparison between theory and experiment

The techniques for remote impact analysis developed in Part I [1] are analyzed from an experimental point of view. Comparison is made between the theoretical and experimental Timoshenko transfer functions between the remote acceleration transform and the impact force-time history transform. The inversion process has been applied with success to experimental impacting data; good representations of impact force-time histories have been obtained even in the presence of signal contamination.     

Application of the MC SCF method to the π → π* excitation energies of ethylene

The MC SCF method is employed to calculate the N → T and N → V π → π^* vertical excitation energies of ethylene. To obtain accurate excitation energies it is found to be necessary to utilize an expanded valence space containing two π and two π^* orbitals. Relatively small MC SCF calculations, allowing at most one-electron excitations from the sigma space, are found to yield excitation energies and spatial extents of the excited states in excellent agreement with the predictions of large multi-reference or iterative-natural-orbital CI calculations. These results show that within an MC SCF framework σ-σ correlation is unimportant for describing the π → π^* processes. We also conclude that the neglect of the effects of unlinked cluster terms in some of the CI calculations may have introduced small, but important, errors in the excitation energies and predictions of the spatial extent of the V state.     

Theoretical study of the vertical electron affinity and ionization potentials of C3

The electron affinity and first three ionization potentials of C₃ are calculated using the multiconfigurational SCF and configuration interaction methods and by Möller-Plesset perturbation theory. Whereas Koopmans' theorem and SCF calculations indicate that the first cation state is ²Π_u, upon inclusion of correlation effects both the ²Σ_u and ²Σ_g cation states are found to lie lower in energy. CI calculations indicate that the ground state (²Π_g) anion is stable by 1.74 eV. Allowing for the error in the calculated electron affinity of the carbon atom, C₃^? is estimated to be stable by 2.0 eV, in excellent agreement with the 2.05 eV value determined from recent photodetachment measurements. No excited anion states are found to be bound at the equilibrium geometry of the neutral molecule.     

Auditoria acoustics: Development in recent years

A review of current literature and publications since the appearance of the author's previous article discloses some important new trends in development. While the discussions on criteria have lingered on, the methods of analysis and the attempts to correlate physical and subjective data have improved considerably. In particular, the methods of multidimensional scaling, together with improved methods of artificial reproduction of concert hall performances, have created important new tools in this work on correlation. This work is only a beginning which may be expected to yield important results in the near future. The section on new auditoria is confined to the report on the two largest auditoria of the recently inaugurated Sydney Opera House.     

Buchbesprechung

Ohne Zusammenfassung     

Reaction of copper(II) with ferrocene and 1,1'-dimethylferrocene in aqueous acetonitrile: the copper(II/I) self-exchange rate

The kinetics of the reactions of copper(II) with ferrocene (Fc) and 1,1'-dimethylferrocene (Dmfc) have been studied at 25 degrees C in aqueous acetonitrile (AN) containing 50-97.5 vol % AN. With increasing % AN, the rate constant increases along with the driving-force for the reaction. The results are analyzed in terms of Marcus theory to estimate the Cu(II/I) electron self-exchange rate constant (k11) for the system. Over the solvent range studied, the calculated k11)changes from 1.1 x 10(-9) to 17 x 10(-9) M(-1) s(-1), with an average value of 5 x 10(-9). In addition, the structures of the trifluoromethanesulfonate salts of [Cu(AN)4]+, [Cu(OH2)2(AN)2]2+, and [Cu(AN)4]2+ are reported. It is found that the Cu-NCCH3 bond-length difference between the Cu(I) and Cu(II) oxidation states is only approximately 0.02 A.