Design of thin-walled viscoelastic shells with allowance for damage

Azerbaidzhan Institute of Construction Engineering, Baku. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 55–64, January, 1991.     

Intramolecular heterocyclization with accompanying exoiminization in the reaction of ammonia with 2-chloroperfluoro-1-cyclohexene-1-thiocyanate

The reaction of ammonia with 2-chloroperfluoro-1-cyclohexene-1-thiocyanate leads to 2-amino-7-iminoperfluoro-4,5,6-trihydrobenzo-1,3-thiazole (II) due to intramolecular heterocyclization in the Thorpe reaction with the concurrent exoiminization. Analysis of the IR spectra of (II) in CCl₄ and in the solid phase indicated that molecules of (II) in the crystal form hydrogen-bonded centrosymmetric dimers (D), which are in equilibrium with free molecules of (II) in solution.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2366–2370, October, 1991.The authors express their gratitude to D. I. Zagorevskii for taking the mass spectrum of (II) and to L. S. German for a useful discussion of this work.     

Integral manifolds and the reduction principle in stability theory. III

It is shown how, with the help of approximate integral manifolds, to solve the reduction problem in stability theory in the nonsingular critical case. A generalization of the first fundamental Lyapunov-Malkin theorem in critical cases is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1324–1329, October, 1991.     

托卡马克能量约束及自举电流效应的初步考虑

基于Lee等人的离子温度梯度模导致的反常热能输运系数,本文研究了辅助加热托卡马克等离子体的能量约束行为,并对自举电流的效应作了初步考虑。结果表明,计算得到的能量约束时间随等离子体电流I_p和托卡马克大半径R增大而增长,随注入功率P_t、环向场B_t以及等离子体小半径α的增大而缩短。这些结果与Kaye-Goldston的经验约束定标具有相同的趋势。自举电流的存在总是导致能量约束时间的增加,当自举电流与总电流的比值γ较小时,能量约束时间的增加率约为γ/2。此外,自举电流将造成锯齿反转半径的减小。     

Coulomb blockade electrometer with a high-T c island

We report on a successful attempt to fabricate a Coulomb blockade electrometer consisting of an ultrasmall YBa₂Cu₃O_7−δ (YBCO) island coupled to two gold electrodes through a high-resistance native surface tunnel barrier. A third electrode placed near the island was used as an electrostatic gate. Spectra typical for tunneling into the YBCO superconductor were reproducibly measured. At temperatures below 0.5 K the low-bias conductance was suppressed by the Coulomb blockade. The blockade could be periodically varied by the gate potential. An external magnetic field of up to 5 T strongly influenced the transport via the island but without any change in the period of the Coulomb oscillations. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 112–117 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fredholm property of elliptic boundary value problems for partial differential and differential- operator equations

In this paper we find conditions on boundary value problems for elliptic differential-operator equations of the 4-th order in an interval to be fredholm. Apparently, this is the first publication for elliptic differential-operator equations of the 4-th order, when the principal part of the equation has the form u′?n(t) + Au″(t) + Bu(t), where AB^-1/2 is a bounded operator and is not compact. As an application we find some algebraic conditions on boundary value problems for elliptic partial equations of the 4-th order in cylindrical domains to be fredholm. Note that a new method has actually been suggested here for investigation of boundary value problems for elliptic partial equations of the 4-th order.     

Magnetic-Field-Dependent Electronic Relaxation of Gd3+ in Aqueous Solutions of the Complexes [Gd(H2O)8]3+, [Gd(propane-1,3-diamine-N,N,N′,N′-tetraacetate)(H2O)2]−, and [Gd(N,N′-bis[(N-methylcarbamoyl)methyl]-3-azapentane-1,5-diamine-3,N,N′-triacetate)(H2O)] of interest in magnetic-resonance imaging

EPR Spectra have been measured for aqueous solutions of a series of Gd³⁺ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an ⁸S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ², and a correlation time, τ_v, with activation energy, E_v. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to ¹H-NMR relaxivity.     

Pion pair production in photon-photon collisions

The process γγ→π⁺π^? was measured using the detector MD-1 at VEPP-4. The two-photon reactionse ⁺ e ^?, μ⁺ μ^? and π⁺ π^? pair production were separated using scintillation counters, Cherenkov counters and shower-range chambers. A radiation widthГ _γγ(f ₂(1270))=3.1±0.35±0.35 keV was obtained.     

An approach to deducing approximate solutions to the Cauchy problem for nonlinear differential equations

A new technique for the construction of numerical methods based on continued fractions is proposed. A characteristic feature of these algorithms is the fact that for certain values of the parameters it is possible to obtain both novel and traditional (explicit and implicit) numerical methods for the solution of the Cauchy problem for ordinary differential equations. Two-sided formulas are proposed by means of which it is possible to obtain on each integration step not only upper and lower approximations to the exact solution, but also information concerning the magnitude of the leading term of the error without the need for additional calculations of the right-hand side of the initial differential equation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1695–1701, December, 1992.