Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I

The method of the inverse scattering transform is used to solve a boundary-value problem on the half-plane for the two-dimensional stationary Heisenberg magnet with nontrivial background corresponding to helicoidal magnetic structures. The boundary conditions are formulated in terms of scattering data, and this leads to the appearance of gaps in the continuous spectrum of the auxiliary linear problem. Trace identities are obtained. The asymptotic behavior of some of the simplest solutions of soliton type is discussed.Scientific-Research Insititute of the Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika Vol. 90, No. 2, pp. 259–272, February, 1992.     

ε-WEAKLY CHEBYSHEV SUBSPACES OF BANACH SPACES

We will define and characterize c-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly Chebyshev if and only if X is reflexive.     

New measurements and reanalysis of 14N elastic scattering on 10B target

The angular distributions of elastic scattering of ¹⁴N ions on ¹⁰B targets have been measured at incident beam energies of 21.0 and 24.5 MeV. Angular distributions at higher energies 38–94.0 MeV (previously measured) were also included in the analysis. All data were analyzed within the framework of the optical model and the distorted waves Born approximation method. The observed rise in cross sections at large angles was interpreted as a possible contribution of the α-cluster exchange mechanism. Spectroscopic amplitudes SA₂ and SA₄ for the configuration ¹⁴N→ ¹⁰B +α were extracted. Their average values are 0.58±0.10 and 0.81±0.12 for SA₂ and SA₄, respectively, suggesting that the exchange mechanism is a major component of the elastic scattering for this system. The energy dependence of the depths for the real and imaginary potentials was found.     

Specifics of the formation of alloys and their hydrides in Ti-Zr-H system

Studies of the combustion processes in the Ti-H, Zr-H, and Ti-Zr-H systems made it possible to develop a principally new method for producing refractory metal alloys through the compaction of a titanium hydride-zirconium hydride powder mixture followed by dehydrogenation. The procedure is briefly described. Experimental data on the formation of titanium-zirconium alloys with different structures, including an ω-phase alloy obtained at atmospheric pressure, are discussed. The experimental results clearly show that the structure of the alloy depends on the composition of the initial charge and the hydrogen content in the hydrides used. The interaction of the alloys obtained with hydrogen under conditions of self-propagating high-temperature synthesis yielded Ti_0.9Zr_0.1H_1.87 (Ti₉ZrH_18.7), Ti_0.67Zr_0.33H_1.81 (Ti₂ZrH_5.42), Ti_0.5Zr_0.5H_1.37 (TiZrH_2.74), and Ti_0.3Zr_0.7H_1.96 (TiZr_2.3H_6.53) hydrides with face-centered cubic (fcc) and body-centered tetragonal (bct) structures. The removal of hydrogen from these hydrides (by annealing in vacuum at 700–1050°C) results in the recovery of the initial α and ω phases.     

Threshold dependence of the vibrational excitation of molecules on laser radiation intensity

The collisionless vibrational excitation of a polyatomic molecule in an IR laser radiation field has been theoretically studied. It has been shown that (i) the degree of vibrational excitation (namely, number 0000 of vibrational quanta of a molecular mode near-resonant with the IR laser field that are absorbed by the molecule) is low if laser pulse intensity P (energy flux density in the laser beam) is lower than a certain critical value P _cr; (ii) the degree of excitation abruptly increases after crossing the boundary where P = P _cr; (iii) this effect is attributed to two properties inherent in polyatomic molecules, namely, the anharmonicity of the vibrational mode interacting with the laser field and the energy exchange with other modes; and (iv) at P > P _cr, number 00000 is determined only by energy density Φ = Pτ_P, where τ_P is the laser pulse duration, 00000 monotonically increases with increasing Φ. The model is in good agreement with the experimental data.     

Measurement of the <Superscript>14</Superscript>C Content in Liquid Scintillators by Means of a Small-Volume Detector in the Low-Background Chamber of the Baksan Neutrino Observatory

A setup for measuring natural-radioactivity backgrounds and ultralow concentrations of the isotope ¹⁴C in samples of a liquid organic scintillator was created at the low-background laboratory of the Baksan Neutrino Observatory (Institute for Nuclear Research, Russian Academy of Sciences) at a depth of 4900 mwe. The concentration of the radiocarbon ^14C in a sample of a scintillator based on domestically produced linear alkylbenzene was measured, and it was found that ¹⁴C/¹²C (3.3 ± 0.5) × 10^?17.     

Nonlinear resistor based on a polymer-ceramic composition

The resistivity of composite nonlinear resistors (varistors) consisting of zinc oxide ceramic and high-density polyethylene, as well as IR spectra and X-ray diffraction patterns taken of the samples, are studied. The component composition of the resistor is shown to influence its resistivity and IR and X-ray spectra.