On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.     

New efficient method for activation of dormant chains in pseudoliving radical polymerization

With the use of the competitive inhibition method and ESR spectroscopy, it is shown that, in pseudoliving radical polymerization, the rate constant of decomposition of PS and poly(acrylic acid) adducts with nitroxide radicals significantly increases as the polarity of a medium increases. This phenomenon opens a new approach to the activation of chains in nitroxide-mediated polymerization.     

A finiteness theorem for subgroups of SP (4,Z)

This paper proves that there are only finitely many subgroupsH of finite index in Sp(4,Z) such that coresponding quotient of the Siegel upper half space of rank two is not of general type. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. vol. 56. Algebraic Geometry-9, 1998.     

Classification of heavy metal fluorides. Fluorides with high water contents

Five fluoride structures differing in the character of linkage of cationic polyhedra and in relative water contents are considered. The cationic sublattice is four-layered (ABAC) in K₂Cu(ZrF₆)₂·6H₂O, face-centered (F-type, ABC) in CuZrF₆·4H₂O primitive cubic (P-type) in Cu₃(ZrF₇)₂·16H₂O, hexagonal one-layered (AA) in Cu₂ZrF₈·12H₂O and hexagonal two-layered (AB) in Zr₂F₈·6H₂O. Some structures have considerably distorted symmetries of cationic sublattices compared to anhydrous structures because of the anisotropy of cation surroundings in the first, second, and third spheres, but al characteristic close-packed cation planes of the corresponding structural types are retained. In structures with cation-cation distances of ～3.5 Å, dimeric cations are arranged as single fragments for planes with d_hkl>3.5 Å or as separate fragments for planes with smaller d_hkl.     

Roll length of an annular underexpanded jet formed by a sonic nozzle with cylindrical rod on its axis

Experiments were made with annular nozzles with a central rod projecting beyond the nozzle to study the influence of the thickness of the nozzle gap, the curvature of the gap, the conical angle of the sonic nozzle, and the pressure difference on the length of the first roll of an underexparided jet. An expression was obtained for calculating the roll length as a function of these parameters for pressure differences greater than 4.4.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 167–171, July–August, 1980.