A family of maximal subalgebras of R. Robinson's algebra

All maximal sub algebras of the algebra of primitive recursive functions <〉;+,*i>, whose basic sets contain the set $$A = \{ f:f \equiv 0V(x) (x > \Rightarrow f(x) > 0)\} ,$$ are described. It is shown that they are continuum in number.     

New series of weakly implicative selector sets

In this paper we specify classes of weakly implicative selector sets and describe their interconnections for the case when the number of variables n does exceed 3 (see A. N. Degtev and D. I. Ivanov, “Weakly Implicative Selector Sets of Dimension 3” Diskretn. Matem. 11 (3), 126–132 (1999)).     

Organic-solvent-free systems with phase separation as efficient and safe systems for extraction of metal ions

The possibilities of using organic-solvent-free extraction systems with phase separation, based on antipyrine derivatives, are examined. Ionic associates with tin(II) and tin(IV) anionic complexes and mixed chelates of indium with antipyrine and sulfosalicylic acid are extracted into the organic phase. The suggested systems show promise for the recovery and determination of macro- and microamounts of indium, tin(II), and tin(IV) ions.     

Extraction of triply charged metal cations in aqueous phase-separating system antipyrine–sulfosalicylic acid–water

Extraction of macro amounts of triply charged metal cations (0.01–0.05 mol L^?1) in aqueous phase-separating system antipyrine–sulfosalicylic acid–water containing no organic solvent is studied. Optimum conditions for phase separation are established and the influence of the concentrations of the major components, inorganic acids (H₂SO₄, HCl), salting-out agents, and the volume of the aqueous phase on the process in question is determined. It was found that the optimum antipyrine/sulfosalicylic acid ratio in the system was (1.5–2.0): 1.0. The introduction of inorganic salting-out agents causes the volume of the organic phase (0.8–1.8 mL) to increase to 2 mL and more. The extractability series of triply charged metal ions is as follows: Tl > Fe > Sc > In > Ga. It was shown that inorganic salts and hexamine influence the degree of extraction of metal cations and that inorganic acids and water affect the distribution mechanism and the composition of the complexes. The half-extraction pH values (pH₁/₂) of the cations are calculated and correlations between the pH₁/₂ values, the ionic radii of the cations, and the polarization ability of the metal ions are established.

     

Viktor Petrovich Zhivopistsev (on his 90th birthday)

Chronicle

Viktor Petrovich Zhivopistsev (on his 90th birthday)     

Sixtieth birthday of Mikhail Ivanovich Degtev

Chronicle

Sixtieth birthday of Mikhail Ivanovich Degtev     

Configurations of axisymmetric quasi-force-free magnetic systems. II

Three methods for obtaining equilibrium configurations, which are prototypes of quasi-force-free windings, are considered using the zero-thickness model. These methods include the formation of an equilibrium figure by iterations, application of diamagnetic shields, and poloidal current drainage from the end part of the magnet to its external zone. Combination of these methods makes it possible to construct configurations of thin-wall quasi-force-free magnets and to determine the limiting size of the end parts of windings, on which the magnetic pressures of the poloidal and toroidal fields on both sides of the current-carrying layer are balanced. The possibilities of constructing the outer zone of a thin-wall magnet with cylindrical reinforcements are considered. It is shown that it is possible to avoid the emergence of axial forces in the entire volume of the magnet in magnetic systems with an aspect ratio of two and smaller. A two-module configuration is considered and the possibility of additional reduction of stresses in this system as compared to a single balanced module is demonstrated. An equilibrium configuration of a three-layer magnet with zero-thickness layers is constructed. It is shown that the transition from this configuration to real finite-thickness layers does not introduce significant changes in the results of calculation of stresses in the most loaded parts of the magnet.