Integration of mappings of semiordered rings

Lebesgue type integrals of mappings f: E X, where X is a semiordered ring and E R, over a measure with values lying in X are studied. Usual properties of the integral are proved, including theorems on limits under the integral as well as those on absolute continuity and complete additivity of the (u, v)-integral. A theorem on the existence of a solution of a differential equation with (u, v)-derivatives is proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 547–555, July–August, 1992.     

The nucleolus for cooperative games with arbitrary bounds of individual rationality

We consider cooperative games with a given bound for individual rationality. We introduce the nucleolus with respect to the set of preimputations satisfying the newly defined bounds of rationality. An axiomatization of this nucleolus is given.     

Relaxation of spin polarized 3He by magnetized ferromagnetic contaminants

In the first in a series of three papers on wall relaxation of spin polarized ³He we have reported on a breakdown of relaxation times which is observed after exposing the ³He containing glass cells to a strong magnetizing field. In this third paper we give a quantitative analysis of this phenomenon, based on magnetic signal detection by means of SQUIDs, on the pressure dependence of relaxation times in magnetized cells, as well as on Monte Carlo simulations of ³He-relaxation in a macroscopic dipole field. Our analysis allows to identify the contaminants as being aggregates of dust-like Fe₃O₄ particles (magnetite) with a radius R ? 10 mR \approx 10~\mu m and a remanent magnetic moment of the order of m ≈O(10 ^-10 ^{-10}~ A m²). The particles are located at or close to the inner glass surface.     

Anisotropy of the ionic conductivity and dielectric response in orthorhombic and monoclinic inorganic fluorides

The anisotropy of the ionic conductivity and permittivity of (1) BaR₂F₈ (R=rare earth element) single crystals with monoclinic BaTm₂F₈ structure and of (2) (β-YF₃ structured) rare earth trifluorides is studied. Single crystals, eutectic composites and ceramics are investigated in a broad temperature range. In the monoclinic BaR₂F₈ crystals, a pronounced anisotropy of the ionic conductivity and a slight anisotropy of the permittivity are found. The fastest ionic transport with the lowest activation energy (0.563 eV) and the highest value of the permittivity are observed along thea axis. The temperature dependencies of the fluoride ion conductivities of various orthorhombic rare earth trifluorides differ only slightly from one another. For the bulky single crystals, the conductivity at 500 °C and the conduction activation enthalpy are equal to 1.1(4)×10⁻⁵ S/cm and 0.75(3) eV, respectively. The ionic conductivity is almost isotropic, but the anisotropy of the permittivity is significant. For the fluorides of both structural types, plausible conduction mechanisms are proposed, networks of most probable conduction paths are presented and the origin of the observed anisotropy of the ionic conductivity is elucidated. Paper presented at the 4th Euroconference on Solid State Ionics, Renvyle, Galway, Ireland, Sept. 13–19, 1997     

Stabilization of Long Electric Arcs by Rotating Magnetic Fields of Different Configurations

The results of the investigation of the direct current electric arc under the influence on it of the rotating magnetic fields of the inductors with a different number of poles pairs are given in the article. The analysis and the comparison of the arc energetic characteristics and of its movement parameters in the rotating magnetic fields of different configurations were carried out. The comparison of the experimental data and of the results of the theoretical analysis of the arc movement in the 2-poles and 4-poles inductors fields was carried out. A number of original methods for the application of the researched type of the magnetic effect on the electric discharge in plasma techniques and technology was suggested.     

Precise determination of Stokes shifts in stimulated-Brillouin-scattering-active substances with the use of Brillouin loop lasers pumped by Gaussian monochromatic beams

A method for determination of Stokes shifts in stimulated Brillouin scattering is suggested and implemented; the method is based on the jumplike behavior of the spatial structure of the emission of a Brillouin loopscheme laser upon change in the loop length in the vicinity of Δk _B L=π(2n+1), where Δk _B is the Brillouin shift,L is the loop length, andn is an integer.     

Strength and fracture of plutonium and its alloy with gallium under impact loading

Results are presented from a theoretical analysis of the conditions of cleavage fracture of plutonium and its alloy with 1.6 wt. % gallium under shock loading. Experimental data obtained earlier are used to determine the critical tensile stresses corresponding to the initial stage of macroscopic cleavage fracture of specimens. The elastoplastic properties of the materials and polymorphic transformations that occur in the alloy at normal and high (315°C) temperatures were taken into account in the calculations. Institute of Experimental Physics, Sarov 607190. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 135–140, July–August, 1998.