Degenerate billiards in celestial mechanics

In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is degenerate. Degenerate billiards appear as limits of systems with singularities in celestial mechanics. We prove the existence of trajectories of such systems shadowing trajectories of the corresponding degenerate billiards. This research is motivated by the problem of second species solutions of Poincaré.     

Synthesis and Study of Copper(II) Complexes with Aspartic Acid,Serine, and Valine

Binary and ternary copper(II) complexes with aspartic acid (H₂Asp), serine (HSer), and valine (HVal) were prepared by electrochemical and chemical procedures. The purity of the compounds was confirmed by elemental and thermogravimetric analyses. According to the IR spectra, all the complexes contain a five-membered chelate ring in which the Cu(II) atom is bonded with the oxygen atom of the carboxy group and nitrogen atom of the amino group. This is also confirmed by the ESR spectra.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 4, 2005, pp. 541–544.Original Russian Text Copyright © 2005 by Kryukova, Frolov, Kolokolov, Bolotin, Panyushkin.     

Sorption of chromium(VI) on ion-exchange resins and sorbents

Sorption of Cr(VI) on AV-17 and EDE-10P anion exchangers, KU-2 and KB-4 cation exchangers, activated charcoal, and foamed graphite (STRG) is studied.     

Compressive stability of multilayered delaminations in composites

The behavior of defects of the near-surface crack type was investigated in laminated composites. Multilayered delaminations in compressed elements were examined on the assumption that cylindrical bending of the delamination is accompanied by shear within the framework of a model similar to the Timoshenko model. The effect of the mechanical properties and thickness and number of layers in the delaminated section on the critical buckling strain and strain corresponding to the beginning of growth of the delamination was investigated. It was shown that when the delaminated section contains several bearing layers and the rigidity of the composite with respect to interlaminar shear is small, consideration of the shear in the delaminated section can lead to a significant change in the critical compressive strains and/or critical size of the delamination.Translated from Mekhanika Kompozitnykh Materialov. Vol. 33, No. 3, pp. 312–320, May–June, 1997.     

The generalized potential energy function for diatomic molecules

A new generalized potential energy function is suggested for diatomic molecules. The Dunham, Simons—Parr—Finlan, Thakkar and Ogilvie potentials are shown to be particular cases of the generalized potential energy function. It is also shown that the function suggested may reproduce the path of the potential curve with sufficient accuracy even for the cases of small expansion length.