Dispersion of waves in a plane acoustic layer with flexible elastic walls

A plane acoustic layer bounded by elastic membranes is considered. Dispersion relations for symmetric and antisymmetric waves are derived. The limit behavior of dispersion curves is investigated for wave numbers tending to zero and to infinity. With the use of the resulting asymptotic expansions, the two-point Pade approximations are constructed. The orthogonality relations for eigenmodes are presented.     

Methods of constructing optimal stabilizers

The problem of transforming a linear dynamical system in the neighbourhood of a state of equilibrium [1,2] is solved using the special problem of the damping of the system by controls of minimum intensity after a finite time interval. The possibility of using other problems of optimal control is discussed. The main attention is devoted to constructing algorithms of the operation of a device (a stabilizer) which is able, in real time, to generate a stabilizing control circulating in the closed optimal system when unknown perturbations operate constantly [3, 4]. The proposed method is based on the constructive theory of optimal control [5, 6]. Another form of this theory for solving the problem of stabilization is presented in [7](see also [8]).     

Method for determining the first excited “hole” state in radicals

A technique is presented for determining th eexcited hole state in radicals using the approximation of an (N – 3)-electron, quenched molecular shell. Results are given on the equilibrium geometry and the transition energies in emission and absorption for the radicals SiH, CH, CN, NH₂, and PH₂ with the CNDO approximation. The equilibrium geometry of the radicals in the excited state corresponds well with the experimental results. A qualitative correlation for the calculated and experimental values of the transition energies is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 65–69, July, 1986.     

The crystal and molecular structure of cesium 9,10,11-trimethyl-7,8-dicarba-nido-undecaborate(1-) Cs[9,10,11-Me3-7,8-C2B9H9]

Conclusions By a complete x-ray diffraction study of cesium 9,10,11-trimethyl-7,8-dicarba-nido-undecaborate(1-) we proved the axial orientation of the Me group attached to the B¹⁰ atom of the open face of the nido-carborane polyhedron. This serves as an additional proof of the stereospecificity of the alkylation reaction of the dicarbollide ions and the necessity for a migration stage of the boron atom with the substituent to the site of the deficient apex of the icosahedron to form a derivative with an equatorial disposition of the alkyl group.The atoms in the carborane polyhedron are numbered as in [1].Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2474–2481, November, 1979.     

Chemistry of heteroanalogs of isoflavones

Condensation of 2-pyridylacetonitrile with polyphenols gave the corresponding -(2-pyridyl)-acetophenones, which were converted to the pyridine analogs of natural isoflavones and to 3-pyridylchromones with methyl, trifluoromethyl, and ethoxycarbonyl groups in the 2 position. The antimicrobial activity of 3-pyridylchromones and their reaction with alkylating and acylating agents and phosphorus pentasulfide were investigated.See [1] for communication V.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1180–1185, September, 1977.     

Porphyrins. 33. Proton magnetic resonance spectra of hematoporphyrin derivatives. properties of a dimethoxy derivative (dimegin) in aqueous solution

The PMR spectra of derivatives of hematoporphyrin IX have been investigated in organic and aqueous solution. It has been shown that the presence of the two chiral centers at positions 2 and 4 of the macrocycle is displayed in the specific splitting of the signals of the meso protons. The structures of dimeric associates of 2,4-di(-methoxyethyl)-deuteroporphyrin IX (dirnegin) have been studied in aqueous solution over a wide pH range and have the structure of a skewed sandwich according to PMR data.For Communication 32, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 198–204, February, 1996.     

Vibrational spectra and stereoisomerism of the hexopyranose ring in epoxysaccharides

Journal of Structural Chemistry - Investigation of the potential surface of methyl 2,3-anhydro-2,3,4-trideoxy-β-D-lyxohexopyranoside has shown that the molecule has seven conformers with...     

Structural chemistry of bimetallic hydride complexes of titanium and aluminium: I. Crystal and molecular structure of [(η5-C5H5)2,Ti(μ-H)2AlH2]2(CH3)2NCH2CH2N(CH3)2C6H6

The structure of a titanium aluminium hydride complex of composition [(C₅H₅)₂TiAlH₄]₂(CH₃)₂NC₂H₄N(CH₃)₂C₆H₆ has been determined by X-ray diffraction. The complex forms triclinic crystals with unit cell dimensions a = 8.406(2), b = 10.117(2), c = 11.269(3) Å; α = 112.01(2)°, β = 109.25(2)°, γ = 87.04(2)°, space group P$\text{1}$, Z = 2 and density d = 1.21 g/cm³. The structure was refined to give a discrepancy index R = 0.056. The crystals are composed of centrosymmetric molecules of (Cp₂TiAlH₄)₂TMEDA (Cp = η⁵-cyclopentadienyl) and molecules of crystal benzene. Two moieties of Cp₂TiH₂AlH₂ are linked by a tetramethylethylenediamine molecule (r_AlN 2.11 Å). The aluminium atom is bonded to a titanium atom by a double hydride bridge (r_AlH b = 1.8, 1.6 Å, r_TiH b = 1.6 Å), and has trigonal bipyramidal stereochemistry, [H₄N] (r_AlH t = 1.6 Å).