Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

Relativistic correction to the triton binding energy in the framework of relativistic Hamiltonian dynamics

The relativistic correction to the triton binding energy approximated to the order (v/c)² is calculated in the framework of relativistic Hamiltonian dynamics. We discuss the generator representation of the Poincaré group for three relativistic particles and its connection with the Feynman diagrams in the infinite-momentum frame (the light-front dynamics). The relativistic correction enhances the attraction in the three-nucleon system. The five-channel calculation with the Reid soft-core potential yeilds the result =–0.54 MeV, which is governed mainly by theD-wave contribution. TheS-wave contributions to are only –0.10 MeV.     

Ecdysteroids of a culture of tissues and cells ofAjuga turkestanica

The possibility has been studied of obtaining ecdysteroids — ecdysterone and turkesterone — with the aid of a culture of the tissues and cells of the plantAjuga turkestanica. Conditions have been selected under which the yield of ecdysteroids in the culture of tissues and cells is comparable with amounts of the same substances in the organs of the whole plant.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 51–52, January–February, 1990.     

The role of electronic factors in reagents in controlling thestereochemistry of arylsulfenyl chlorides addition

For a series of substituted arylsulfenyl chlorides the stereochemistry of Ad_E-reactions with a series of substituted Z- and E-β-deuterostyrenes has been elucidated. Non-stereospecific reaction was observed only for the pair 2,4-dinitrobenzenesulfenyl chloride-p-methoxystyrene; for all the other reactants the reaction proceeded in a strictly stereospecific manner.     

Classification of heavy-metal fluorides. fluorides with fluorite-like cation arrangement

The main feature of fluorite structure type is four families of crystallographic planes with dense trigon cation nets which are mutually oriented as the faces of a regular octahedron. A complicated cation composition may cause lowering of general symmetry to tetragonal (only one four-fold axis remains in the octahedral complex), rhombohedral (one three-fold axis), orthorhombic, and monoclinic. The geometric parameters of the cation sublattice remain constant. They are close to the parameters of the ideal face-centered cubic cation sublattice of fluorite (the measure of similarity is 1.00–0.81). This is true for all analyzed fluoride structures and some U⁴⁺, Th⁴⁺, Zr, and Ln oxyfluorides. Thus, the concept is confirmed that the crystalline state is determined by systems of parallel planes filled by dense heavy-atom nets. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Institute of Crystallography, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 35, No. 1, pp. 71–80, January–February, 1994. Translated by T. Yudanova