Solubilities and Solution Chemistryin Liquid Alkali Metals

Summary.  Experimental solubility data for metals and non-metallic substances in liquid alkali metals have been collected from literature, critically evaluated, and selected for recommendation. Sometimes results for a selected system at a selected temperature vary over more than an order of magnitude. This is not uniquely connected with a poor precision of the measurements. Some impurities may spectacularly modify the solubilities and, moreover, definition of a saturating solute phase is not always a simple task. Based on supplementary experiments one may explain several phenomena which often accompany dissolution processes. These accompanying processes are essentially the same as those frequently observed in solution chemistry. Received February 3, 2000. Accepted (revised) May 8, 2000     

ADMET copolymerization of divinyltetraethoxydisiloxane with 1,9-decadiene catalyzed by Grubbs’ catalyst

The acyclic diene metathesis (ADMET) copolymerization of divinyltetraethoxydisiloxane with 1,9-decadiene, catalyzed by RuCl₂(=CHPh)(PCy₃)₂, is the first example of a siloxylene–vinylene–alkenylene copolymer reported in the literature. This copolymer was isolated and characterized by ¹H, and ¹³C NMR spectroscopy and GPC analysis (M_n=18 000, PDI=2.9).     

Recent results on iteration theory: iteration groups and semigroups in the real case

In this survey paper we present some recent results in the iteration theory. Mainly, we focus on the problems concerning real iteration groups (flows) and semigroups (semiflows) such as existence, regularity and embeddability. We also discuss some issues associated to the problem of embedddability, i.e. iterative roots and approximate iterability. The topics of this paper are: (1) measurable iteration semigroups; (2) embedding of diffeomorphisms in regular iteration semigroups in \({{\mathbb{R}}^n}\) space; (3) iteration groups of fixed point free homeomorphisms on the plane; (4) embedding of interval homeomorphisms with two fixed points in a regular iteration group; (5) commuting functions and embeddability; (6) iterative roots; (7) the structure of iteration groups on an interval; (8) iteration groups of homeomorphisms of the circle; (9) approximately iterable functions; (10) set-valued iteration semigroups; (11) iterations of mean-type mappings; (12) Hayers–Ulam stability of the translation equation. Most of the results presented here was obtained by the means of functional equations. We indicate the relations between the iteration theory and functional equations.     

Superintegrable systems on spaces of constant curvature

Construction and classification of two-dimensional (2D) superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of constant curvature and separable in the so-called geodesic polar coordinates are presented. The method proposed is applicable to any value of curvature including the case of Euclidean plane, sphere and hyperbolic plane. The main result is a generalization of Bertrand’s theorem on 2D spaces of constant curvature and covers most of the known separable and superintegrable models on such spaces (in particular, the so-called Tremblay–Turbiner–Winternitz (TTW) and Post–Winternitz (PW) models which have recently attracted some interest).