Combinatorial identities,and completeness of eigenstates of the Heisenberg magnet

The completeness of the multiplet system constructed from the Bethe vectors is proved for the Heisenberg model of arbitrary spin and for the generalized Kondo model.This paper is devoted to the proof of the completeness of the multiplet system constructed from the Bethe vectors for the generalized Heisenberg model of arbitrary spin and for the generalized Kondo model.Translated from Zapiski Nauchykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 88–105, 1983.     

Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of p. Explicit formulae describing the bifurcation of the eigenvalues are derived. Application to the problem of excitation of unstable modes in rotating continua such as spherically symmetric MHD α ²-dynamo and circular string demonstrates the efficiency and applicability of the approach.     

Solving a Two-Dimensional Telegraph Equation with Anisotropic Parameters

We solve a two-dimensional telegraph equation with anisotropic parameters, which models the propagation of electromagnetic waves in the Earth–ionosphere waveguide, in the frequency range 0.1-30 Hz. The results are generalized to allow for the Earth's sphericity and the horizontal inhomogeneity of the waveguide. It is shown that the resonance character of reflection from the ionosphere at frequencies below 10 Hz becomes pronounced for the horizontal magnetic-field components and for the vertical electric-field component of a horizontal dipole. In the case of low solar activity under nighttime conditions, the oscillations in the frequency dependences of the field components are much more pronounced compared with the case of high solar activity.     

On a theorem of Marcinkiewicz and Zygmund

Let {ϕn(x)} be an orthonormal system on the closed interval [0,1], and let ∥ϕ _n ∥_∞ ≤M _n . In 1937 Marcinkiewicz and Zygmund obtained an estimate of the norm inL _q [0,1] of the sum of the series ∑ _n=1 ^∞ c _n ϕ _n (x) under the condition that {M _n } is monotone increasing. In this paper it is shown that this condition cannot be discarded. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 386–390, March, 1998. The author wishes to thank V. I. Kolyada for setting the problem and for his permanent attention to this work.     

Solvent effect on reaction rates in molten salts

Predominant solvation of activated complex is shown to be characteristic for chemical and electrochemical reactions in molten salts.

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Presented at EUCHEM Conference on Molten Salts, September 2–8, 1990, Rio-Patras, Greece     

Origin of a classical space in quantum inhomogeneous models

The origin of a classical background geometry in the quantum vacuum inhomogeneous master model is investigated. It is shown that the background appears at the moment when the horizon size has the order of the characteristic scale of the inhomogeneity of the universe and that the local anisotropy can be described by small perturbations. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 449–453 (10 October 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Urea (Polyurea) Greases

The review deals with greases in which organic ureas of various compositions and structures are used as thickeners. The nature of compounds participating in the synthesis of organic ureas and the main types of polyurea thickeners are considered. The physicochemical, tribological, and operation properties of plastic polyurea lubricants are discussed.     

Reformatsky Reaction of Methyl 1-Bromocyclohexanecarboxylate with N,N′-(1,4-Phenylene)bis(1-arylmethanimines)

Russian Journal of Organic Chemistry - Reformatsky reagent prepared from methyl 1-bromocyclohexanecarboxylate reacted with N,N′-(1,4-phenylene)bis(1-arylmethanimines) to produce...