Synthesis, structure, and magnetic properties of heterometallic trinuclear complexes {MII��LnIII��MII} (MII = Ni, Cu; LnIII = La, Pr, Sm, Eu, Gd)

Trinuclear heterometallic complexes containing the {M₂Ln(Piv)₆(NO₃)} (M^II = Ni, Cu; Ln^III = Nd, Pr, Sm, Eu, Gd; Piv^? is the anion of pivalic acid) and {Cu₂Ln(Piv)₈)]^? (Ln^III = Eu, Gd) metal cores were synthesized, their structures and magnetic properties were studied. For the most compounds, it was shown that their magnetic properties can be interpreted taking no interaction of the 3d-metal ions and a lanthanide into account. Ferromagnetic exchange interactions were found to exist between the unpaired electrons of the paramagnetic centers in the exchange clusters of the gadolinium-containing heterometallic complexes {M-Gd-M} (M = Ni or Cu).     

The geometry of a quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables

The geometry of a system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using the Cartan method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasil’ev (for infinite groups). Systems of quasilinear equations with the first and second partial derivatives of two functions u and v in two independent variables x and y are classified.     

Factorization Representations in the Boundary Crossing Problems for Random Walks on a Markov Chain

Let τ be some stopping time for a random walk S _n defined on transitions of a finite Markov chain and let τ(t) be the first passage time across the level t which occurs after τ. We prove a theorem that establishes a connection between the dual Laplace-Stieltjes transforms of the joint distributions of (τ, S _τ) and (τ(t), S _τ(t)). This result applies to the study of the number of crossings of a strip by sample paths of a random walk.Original Russian Text Copyright © 2005 Lotov V. I. and Orlova N. G.The authors were partially supported by the Russian Foundation for Basic Research (Grant 05-01-00810) and the Grant Council of the President of the Russian Federation (Grant NSh-2139.2003.1).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 833–840, July–August, 2005.     

Peculiarities of dislocation structure at surface of deformed crystals

An experimental study of the distribution of edge and screw dislocation components in deformed LiF crystals at external surface parallel to Burgers vector of mobile dislocations was performed. At the surface we observed a layer with low density of edge and screw dislocations compared to the dislocation density in the bulk. The thickness of this layer was tens of microns. The experimental results are explained on the basis of analysis of dislocation structure evolution at surface layers during the plastic deformation.     

Quantum cyclotron resonance of two-dimensional holes in the Ge layers of Ge-Ge1−x Six heterostructures

Quantum cyclotron resonance of two-dimensional holes in strained germanium layers of the periodic heterostructure Ge-Ge_1−x Si_x has been observed and investigated for the first time. The results are compared with the data of electrophysical measurements in strong magnetic fields. A clear dependence of the magnitude of the longitudinal effective mass of the holes on the absolute magnitude of the elastic deformation of the germanium layers (splitting energy of the hole subbands) is observed. Fiz. Tverd. Tela (St. Petersburg) 39, 2096–2100 (November 1997)     

The use of a radiation inactivation method for characterization of the structure and catalytic properties of enzymes

The use of a radiation inactivation method for studies of the properties of enzymes of different classes is discussed. The possibilities of characterization of enzymes on the basis of the radiation-chemical parameters concerned are described.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No, 12, pp. 2828–2836, December, 1996.     

Angular distributions in proton-nucleus interactions in emulsion at 800 GeV

Data on angular distributions of heavily ionizing and shower particles in incoherent protonnucleus collisions in emulsion at 800 GeV are reported and discussed in details. Dependence of angular distributions on the mass number of a target nucleus and on the multiplicity of charged particles is investigated. The data presented are systematically compared with results of emulsion experiments at lower energies and with predictions of the Lund Monte Carlo model FRITIOF.