Frequencies of Free Oscillations of a Truncated Spherical Sector Covered with a Thin Elastic Spherical Shell

An analytic solution of the problem concerning the frequencies and shapes of free axially symmetric oscillations of a truncated spherical sector filled with an ideal compressible fluid is constructed. A spherical wall of smaller radius and the radial wall of the sector are absolutely rigid. A thin elastic shell whose edge is clamped in the radial wall is located on a spherical boundary of larger radius. The outer surface of the shell borders vacuum. The phenomenon of an anomalous decrease in the fundamental frequency as the spherical walls approach each other is discovered. An approximate formula for determination of the lowest fundamental frequencies, which are approximately proportional to the square root of the difference of the radii of spherical walls for small values of this difference, is constructed and tested numerically. Bibliography: 13 titles.     

Synthesis of a new tricyclic 3-(tetrazol-5-yl)pyridine system from 2-(azidomethyl)nicotinonitriles

2-Methyl-3-cyanopyridines were converted into the corresponding 2-azidomethyl derivatives, which then underwent an intramolecular cycloaddition reaction. A novel heterocyclic system containing a 3-(tetrazol-5-yl)pyridine unit was obtained in this way.     

Production of heavy nuclei in the interaction of <Superscript>7</Superscript>Li ions with copper nuclei at an energy of 35 MeV per nucleon

The absolute values of the cross sections for the production of target fragments in the interaction of copper with ⁷Li ions at an energy of 35 MeV per nucleon were measured. The measurements were performed by recording the yields of radioactive nuclear residues with the aid of a semiconductor detector from ultrapure germanium. The charge and isobaric distributions in the mass-number range 22–69 amu were used to deduce the mass yield of reaction products and to calculate the total interaction cross section. The results are presented that were derived from a comparison with data obtained for ¹²C + Cu reactions and with estimates based on theoretical models.     

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

A 13-membered crown ether with an azoxy subunit in the macrocycle: Synthesis and X-ray structure

The presented azoxy compound is an example of a new crown ether analogue. It has been synthesized by the reduction of an open chain dinitro compound with stannite under strongly alkaline conditions. A method for the separation of the azo and azoxy compounds formed simultaneously has been proposed. The structures of two crystallographically independent molecules of compound2 have been determined. In spite of the small size of the macroring in compound2, the phenyl residues around the azoxy group have atrans orientation. Supplementary Data relating to this article have been deposited with the British Library as Supplementary Publication No. 82157 (11 pages).     

Anionic polymerization of lactones initiated by alkali graphitides. IV. Copolymerization of ε-caprolactone initiated by KC24

The copolymerization of ε-caprolactone (ε-CL) with octamethylcyclotetrasiloxane (D₄) and styrene (St) under the action of the second-stage potassium graphitide KC₂₄ was investigated. The copolymerizations were carried out in bulk or in xylene at 20°C. The content of the block copolymer ε-CL/D₄ in the polymerization mixture was 60–95%, the molecular weight ranging between 150,000 and 300,000. The data for the copolymers' composition obtained by ¹H-NMR and GPC showed 14–20% of D₄-units in the copolymer. The amount of the block copolymer ε-CL/St in the polymerization products was 0–87%, and the molecular weights in the case of copolymer formation were between 100,000 and 500,000. The content of St-units in the copolymers was from 10 to 75% as shown by GPC and ¹H-NMR. The mechanism of action of the initiator is discussed.