On the bands of the Schrödinger operator with a matrix potential

In this article, we consider the one-dimensional Schrödinger operator with a Hermitian periodic matrix potential Q. We investigate the bands and gaps of the spectrum and prove that most of the positive real axis is overlapped by m bands. Moreover, we find a condition on the potential Q for which the number of gaps in the spectrum of is finite.     

A theorem for qualitative deductions in organic or inorganic chemistry regarding the relative stabilities,distortions and reactions of molecules

Regardless of symmetry, the qualitative behavior of molecules, individually or in classes, may be predicted vis-a-vis their relative stabilities, defor     

Crucial role of electron correlation in both the upper and lower states in optical transitions

The merits of the various methods, used for the determination of relativistic energies, are discussed on the basis of numerical results. It is concluded that, at present, the perturbation approach, based on the Pauli approximation of the Dirac-Breit equation, is more accurate (up to Z < 48) than the variational approach. Furthermore it is expected that, in any case, the prediction of ionization potentials and energy levels will be equally satisfactory by either method. Consequently, and taking into account the importance of the correlation effects (not only because of the contribution of the correlation energy but also because of their influence on the prediction of the hyperfine structure), it is suggested that it may be worthwhile to direct more efforts towards multiconfigurational Dirac-Breit-Pauli calculations.This work has been supported in part by the National Research Council of Canada.     

Synthesis of α,α′-bisdialkylphosphonoisopropylnitroxyls

Conclusions Some,-bisdialkylphosphonoisopropylnitroxyl radicals were obtained by the thermolysis of dialkyl -nitrosoisopropylphosphonates and isolated in the pure state.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1867–1868, August, 1979.     

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

New Broer–Kaup type systems of hydrodynamic equations are derived from the derivative reaction–diffusion systems arising in SL(2, R) Kaup–Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2 + 1 dimensional Chern–Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.