Imbedding of pseudo-Riemannian manifolds in a pseudo-euclidean space

It is proved that every pseudo-Riemannian manifold M _{(p, q)} ⁿ with the C^k metric (3k) has an isometric C^k imbedding in the large in E _{(p, q)} ^{n(n+1)(3n+11)/2} , p(n+1)², q(n+1)².Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 193–198, February, 1971.     

Quantum transitions of relativistic electrons in a superstrong magnetic field

The probability of emission of a hard γ-quantum in relativistic electron transitions to the ground (or near it) level in a magnetic field H ～ H₀ = m²c³/e₀? = 4.41 × 10¹³G is obtained. For the inverse transitions from these levels the cross-section of electron photoexitation is calculated.     

Temperature dependence of surface impedance of Tl2Ba2CaCu2O8−δ and YBa2Cu3O6.95 single crystals measured in the microwave band

The real part R _s and the imaginary part X _s of the surface impedance Z _s=R _s+ iX _s of Tl₂Ba₂CaCu₂O_8−δ and YBa₂Cu₃O_6.95 single crystals have been measured with high precision at frequency ω/2π=9.4 GHz in the temperature range 0<T<140 K. In the Tl₂Ba₂CaCu₂O_8−δ crystal a linear temperature dependence R _s(T) has been found for T⩽50 K, and the magnetic field penetration depth λ(4.2 K)=X _s(4.2 K)/ω μ ₀≈3760 Å has been measured. Along with well known features of the function Z _s(T) in high-quality YBa₂Cu₃O_6.95 single crystals, such as the linearity of λ(T) and R _s(T) for T<T _c/3 and a maximum of R _s(T) at T∼T _c/2, the linearity range of λ(T) extends to T≃50 K, and this curve has a plateau in the range 60<T<85 K. The curve of R _s(T) in both the superconducting and normal states of YBa₂Cu₃O_6.95 is well described by a two-fluid model with the electron-phonon mechanism of quasiparticle relaxation. A formula describing the curve of λ ²(0)/λ ²(T) throughout the studied temperature range is also given. Zh. éksp. Teor. Fiz. 112, 2210–2222 (December 1997)     

Structural study of thermal-oxide films on silicon by cathodoluminescence

A study of cathodoluminescence spectra of silicon oxide films grown thermally on silicon is reported. It has been established that the cathodoluminescence properties of thermal films are nonuniform in depth and depend on the growth conditions and characteristics of the silicon substrate. Fiz. Tverd. Tela (St. Petersburg) 40, 1984–1989 (November 1998)     

An unusually strong intramolecular C-H...N hydrogen bond in 3-(α-hydroperfluoroisobutyryl)-2-(α-hydroperfluoroisobutyryl)imino-1,3-thiazolidine

An unusually strong intramolecular C-H...N hydrogen bond with the shortest known H...N distance of 2.00(3) » has been found by X-ray diffraction analysis.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1593–1595, August, 1995.     

Linear low-temperature dependence of the surface impedance of a Ba0.6K0.4BiO3 single crystal

The temperature dependences of the real part R _s and the imaginary part X _s of the surface impedance Z _s =R _s +iX _s of the superconductor Ba_0.6K_0.4BiO₃ (T _c ≃30 K) are measured at a frequency of 9.4 GHz. Its temperature dependence _{Z s} (T) and that of the complex conductivity σ _s (T) can be described on the basis of a two-fluid model under two assumptions: The density of superconducting carriers increases linearly, and the relaxation time increases as a power law (∝1/T ⁵), with decreasing temperature T<T _c . This model also describes well the curves Z _s (T) and σs (T) recently measured for YBa₂Cu₃O_6.95 and Bi₂Sr₂CaCu₂O₈ single crystals. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 783–788 (10 December 1996)     

Reaction of hexafluoroacetone ethoxycarbonylimine with trimethyl phosphite

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2879–2880. December, 1990.