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It has come to our attention since the publication of the above paper [1] that another paper [2] on this subject appeared in the literature around the same time without the knowledge of the present authors though one of us was cited as a co-author in Ref. [2]. Reference [2] deals with the same class of problems as Ref. [1] but uses the pseudo-variational principle of Glansdorff and Prigogine [3]. The results of Ref. [1] are similar to those in Ref. [2] for simple model examples but provide more powerfull formulations for complicated situations.

The method of self-similar approximations suggested recently by one of the authors is extended here to the important class of quantum-mechanical problems containing power-law potentials. It is shown that this method allows us to easily calculate all eigenvalues of the corresponding Schrödinger operators in one- as well as in multi-dimensional spaces. The method is found to be more accurate than other known analytical methods.

A spectroscopic analysis of light emitted in the 200-600 nm wavelength range by Ar⁷⁺, Ar⁶⁺ and Ar⁵⁺ ions after charge exchange in 120 keV Ar⁸⁺-Li collisions is performed. Transitions with Δn = 1 and Δn = 2 for n = 8, 9, 10 and 11 states of Ar VIII following single electron capture are identified and the production cross sections for n = 8 and n = 9 are deduced from emission cross sections and compared with those calculated by the three-body classical trajectory Monte-Carlo method. Lines due to double capture process were observed and identified as Rydberg transitions 3snl-3sn'l' (n = 7, 8 and 9) in Ar VII. Lines due to triple electron capture process were found and identified as transitions 3s²nl-3s²n'l' and 3s3pnl-3s3pn'l' (n = 7, 8) in Ar VI. The configurations produced during the collision provides evidence that electron-electron interaction play an important role in double and triple charge exchange processes.

Spectra of nickel, emitted from hollow cathode discharges, have been recorded in the region 1700-55 000 Å (58 800-1800 cm⁻¹). Fourier transform spectrometers were used above 1800 Å, yielding very high accuracy and resolution. The number of classified Ni I lines has increased from 1071 to 1996. 289 of the lines have been resolved in 2-4 isotope components. The term system derived from the observations comprises 286 energy levels. The term structure and the coupling conditions have been studied by means of ab initio and parametric theory.

The R-matrix method is used to obtain cross-sections for the photoionization of the ground 1s²2s²2p^{6 1}S^e and first three excited 1s²2s²2p⁵3s^{3, 1}P^o, 1s²2s² 2p⁵ 3p³S^e states of S VII, for photon energies ranging from first ionization threshold to just above second threshold 2s2p⁶²S^e of the residual ion S VIII. The positions and effective quantum numbers for the Rydberg series corresponding to 2s2p⁶²S^e arising in the photoionization cross-sections are predicted.

The generalized nonlinear Schrödinger equation with the nonlinear term of a general form is considered. In particular cases this equation covers a saturable nonlinearity as well as higher-order nonlinearities. Modulational instability is investigated, and the possibility of dark soliton propagation is analyzed. It is shown that in the small-amplitude limit the generalized dark solitons are stable, and they are described by the Korteweg-de Vries equation. The condition to create anti-dark solitons is also formulated.

An operator version of the stokeslet method in the theory of creeping flow is suggested. The approach is analogous to the zero-range potential one in quantum mechanics and is based on the theory of self-adjoint operator extensions in the space L₂ and in the Pontryagin's space with an indefinite metric. The problem of Stokes flow in two channels connected through a small opening is considered in the framework of this approach. The picture of streamlines for such flow is obtained. The existence of infinite sequence of eddies is shown.

A mathematical model of the multihollow cathode with the supply of the working medium at the axial magnetic field is considered. The processes taking place in the non-equilibrium multicomponent plasma in the hollows, the redistribution of the working medium flow rate over the channels, the partial transmission of electrons through the magnetic field at the walls, the anisotropy of the design characteristics and the decrease of the work function when the working medium is adsorbed on the walls have all been taken into consideration. A relation for the Richardson constant in the case of atom adsorption has been obtained, which is consistent with the experimental data. As a result, the cathode model is represented as a closed system of 54 equations. The calculated characteristics have been confirmed by experimental data.

We investigate the optical properties of a metal/insulator superlattice with regular and random layer widths. The choice of materials, frequency and layer widths implies that a large range of optical transfer functions are available. An effective medium approach is introduced to make it easier to design a superlattice having the desired optical transfer function. We phrase our analysis in terms of the coupled photon-polarization modes of the superlattice; its elementary excitations. We find in particular the possibility of a Rydberg like series of localized photonic states. Our study also incorporates an analysis of a very thin superlattice, just one unit cell. We discuss how this system can be used for optical switching or filter action.

With regard to material in Section 3 of Ref. [1], mention of Ref. [2] was inadvertently omitted.

1. Shivamoggi B K, Rollins D K and Fanjul R, Physica Scripta 47 15 (1993)

2. Shivamoggi B K, ZAMM 69 459 (1989)