Homogeneous symplectic structures of second order on loop spaces and symplectic connections

Scientific Industrial Association, All-Union Scientific Research Institute of Physicotechnical and Radiotechnical Measurements. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 2, pp. 65–67, April–June, 1991.     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Compatible Dubrovin–Novikov Hamiltonian Operators,Lie Derivative,and Integrable Systems of Hydrodynamic Type [Erratum]

Correction to the paper published in Vol. 133, No. 2, November, 2002.     

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.     

The 13C NMR spectra and structure of ferrocenylcarbenium ions

The ¹³C NMR spectra ofthe series of α,α’ -dideuterated ferrocenylcarbenium ions and their precursors, ferrocenylcarbinols as well as other ferrocene derivatives have been measured. The structures of ferrocenylcarbenium ions is discussed.     

Electronic effects in the cyclopentadienyl ring. The 13C NMR spectraof monosubstituted ferrocenes

The chemical shifts of C(2,5) and C(3,4) carbons in the ¹³C NMR spectra of monosubstituted ferrocenes have been assigned using deuterium labelling. An analogy is observed between the shielding of C(2,5) and C(3,4) carbons of ferrocene derivatives and ortho- and para-carbons of benzene derivatives withthe same substituents. Electron-density distribution in the cyclopentadienyl ring is discussed on the basis of ¹³C NMR data.     

Colloid and nanodimensional catalysts in organic synthesis: VIII. Hydrogenation of C=N bond with hydrogen in the presence of colloid nickel

Hydrogenation of azomethines with hydrogen at atmospheric pressure using nickel nanoparticles as catalyst was carried out. Reaction may be used for the preparation of secondary amines under mild conditions on an available catalyst. Continuation of studies will lead to development of a convenient method for the reductive amination of carbonyl compounds.     

Condensation of adamantanone with methylene-active compounds

A convenient method was developed for the preparation of potentially bioactive substances with 2-adamantyl radical and of intermediates for their synthesis. Condensation of adamantanone with methylene-active compounds was performed, and the reaction features were determined.