Structural Aspects of Fluorosilicic Acid Reaction with Organic Bases

The results of systematic studies into the structures of products formed in reactions between fluorosilicic acid (FSA) and organic bases are presented. Different hydrolytically labile silicon fluoride complexes contained in these products are stabilized. A debatable problem of FSA state in aqueous solutions is discussed in the light of the data obtained.     

Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products

On the basis of the Euler identity, we obtain expansions for weighted pseudoinverse matrices with positive-definite weights in infinite matrix power products of two types: with positive and negative exponents. We obtain estimates for the closeness of weighted pseudoinverse matrices and matrices obtained on the basis of a fixed number of factors of matrix power products and terms of matrix power series. We compare the rates of convergence of expansions of weighted pseudoinverse matrices in matrix power series and matrix power products to weighted pseudoinverse matrices. We consider problems of construction and comparison of iterative processes of computation of weighted pseudoinverse matrices on the basis of the obtained expansions of these matrices.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1539–1556, November, 2004.     

Crystal and molecular structure of 2,2’-(quinoxaline-2,3-diyl)dipyridinium dinitrate (H<Subscript>2</Subscript> <Emphasis Type="Italic">L</Emphasis>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript>

The crystal structure of 2,2’-(quinoxaline-2,3-diyl)dipyridinium dinitrate (Н₂L)(NO₃)₂ is studied by X-ray diffraction (T = 150 K, R1 = 0.0467). The H₂L²⁺ cation is located on the twofold rotation axis and connected with two NO₃^? anions by strong N–H···O hydrogen bonds. Planar quinoxaline fragments of cations form stacks with the interplanar spacing of 3.308 Å. The structure of the diprotonated H₂L²⁺ cation is compared with those of the monoprotonated H₂L²⁺ cation and neutral L molecule.     

Resonant oscillations of a gas in an open tube in the shock-free wave mode

Nonlinear gas oscillations excited in an open tube by a flat piston at one of the tube ends are studied. The sinusoidal piston oscillations in the shock-free wave mode are created by a vibration exciter near the first eigenfrequency. Expressions for gas pressure oscillations are obtained for a tube with a nonrounded end without a flange and secondary flow velocity components. The influence of the piston displacement amplitude on the pressure range and secondary flow velocity of gas is studied. The theoretical calculations of the gas pressure are compared with experimental data. An estimate for the velocity of particle motion along the tube axis is presented with calculated values of the secondary flow velocity.     

Ionic mobility in ammonium-rubidium heptafluorozirconate (NH<Subscript>4</Subscript>)<Subscript>2.4</Subscript>Rb<Subscript>0.6</Subscript>ZrF<Subscript>7</Subscript> by (<Superscript>1</Superscript>H, <Superscript>19</Superscript>F) NMR data

NMR (¹⁹F, ¹H) methods are used to study ionic mobility in heptafluorozirconate (NH₄)_2.4Rb_0.6ZrF₇ in a range of temperatures from 150 K to 430 K. Types of ionic movements are determined, and their activation energy is evaluated. As a result of a phase transition a modification forms in which diffusion in the ammonium sublattice and isotropic reorientations of ZrF ₇ ^3? complex anions are observed. According to preliminary data, due to diffusion of ammonium ions the compound has relatively high ionic conductivity (σ ≈ 8.3 × 10^?5 S/cm at 423 K).     

Synthesis and study of complex formation of tri-and tetranitro-9-fluorenone oximes with 3<Emphasis Type="Italic">d</Emphasis> metals: Crystal and molecular structure of the 1: 1 solvate of 2,4,5,7-tetranitro-9-fluorenone oxime with acetonitrile

The complexes M(L^{1, 2})₂ · nH₂O, where M = Co(II), Ni(II), Cu(II), and Zn; n = 2 and 3, were synthesized by the reaction of Co(II), Ni(II), Cu(II), and Zn(II) chlorides with 2,4,7-trinitro-9-fluorenone oxime (HL¹) and 2,4,5,7-tetranitro-9-fluorenone oxime (HL²) and identified. It was shown that HL^{1, 2} were coordinated by metal cations in the anionic form in a 2: 1 ratio. A single crystal of the solvate of HL² with acetonitrile (1: 1) HL² · NCCH₃ was isolated, and its crystal structure was determined. The spectral characteristics were determined, and the acidity constant of HL¹ was calculated. The structures for the synthesized complexes were proposed.     

Synthesis of metal complexes with 2-[bis(2-phenylethyl)-thiophophorylhydroxymethyl]-1-organilimidazoles. Crystal structure of ZnCl2 · 2L

The reactions of Zn(II), Cd(II), Cu(II), Co(II), Pd(II) dichlorides with 2-[bis(2-phenylethyl)thiophosphorylhydroxymethyl]-1-organilimidazoles (L¹–L⁴) were studied. The novel complexes were synthesized and characterized by IR and NMR spectroscopies. Depending on the nature of imidazolephosphinesulfide, both monodentate (at the “pyridine” N(1) atom of heterocycle) and the N,S-bidentate binding of the ligand by a metal can be realized in the above metal complexes. The structure of the complex ZnCl₂ · 2L⁴(I) (L⁴ = 2-[bis(2-phenylethyl)thiophosphorylhydroxymethyl]-1-ethylbenzimidazole) was studied by X-ray diffraction. One of the two independent L⁴ molecules performs the solvate function, while another one, together with two Cl atoms, is coordinated through the atoms N(1) and S to the Zn atom at the vertices of a slightly distorted tetrahedron. The molecule of the complex is united with the solvate molecule into [ZnCl₂L₄]L⁴ associates by strong intermolecular hydrogen bonds to give nonplanar four-membered H-cycle OH₂N.     

Identification of the parameters of the stress–strain problem for a multicomponent elastic body with an inclusion

Explicit expressions for residual functional gradients are derived. They are used to identify, using gradient methods, the parameters of elastic problems for multicomponent bodies. The method employs the solutions of conjugate problems in the theory (developed by the authors) of optimal control of distributed multicomponent systems     

Expansions and polynomial limit representations of weighted pseudoinverses

Expansions of weighted pseudoinverses with positive definite or singular weights in matrix power series or power products with negative exponents and arbitrary positive parameters are proposed and analyzed. Based on these expansions, polynomial limit representations of weighted pseudoinverses are obtained. Issues related to the construction of direct and iterative methods for calculating weighted pseudoinverses and weighted normal pseudosolutions, as well as solving constrained least squares problems, are examined.     

Bis(2-alkyl-4-thiocarbamoyl-4-pyridinium) hexafluorosilicates

The reaction of 45% silicahydrofluoric acid with 2-ethyl-4-thiocarbamoyl-4-pyridine (L¹) and 2-propyl-4-thiocarbamoyl-4-pyridine (L²) yields (L¹H)₂SiF₆ and (L₂H)₂SiF₆ hexafluorosilicates. These hexafluorosilicates are characterized by the data of IR spectroscopy, mass spectrometry, potentiometry, and solubility. The structure of (L¹H)₂SiF₆ is determined by X-ray diffraction. In the ionic structure of the complex, the L¹H⁺ cations (the protonation center is the pyridinic N atom) and SiF ₆ ^2? anions (Si-F 1.657(2)–1.699(2) Å) are joined by a system of interionic hydrogen bonds NH?F. Correlation between the characteristics of the interionic hydrogen bonds and the solubility of the hexafluorosilicates is discussed.