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.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

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.     

三氟化硼引发四氢呋喃聚合的研究——Ⅳ.1,4-丁二醇的影响

前报中已证明用三氟化硼-环氧氯丙烷(ECH)引发四氢呋喃(THF)聚合具有较高的引发效率,并对在Ac_2O、水和无水存在下的聚合反应进行了研究。本文报道1,4-丁二醇(BG)对BF_3引发THF聚合反应的影响。通常认为在BG存在下,BF_3是不能引发THF聚合的,但本工作证明BG是有效的分子量调节剂,制备分子量在     

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.