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.     

Chemistry of indole

Condensation of 1-alkyl-2-aminoindoles with malonic ester gives -carbonyl derivatives which, on the basis of the their UV, IR, and NMR spectra, and their chemical properties, are assigned the 2-oxo-4-hydroxy--carboline structure.For Part XVIII, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1207–1211, September, 1970.