ChemInform Abstract: Rare‐Earth Manganese Germanides RE2+xMnGe2+y (RE: La,Ce) Built from Four‐Membered Rings and Stellae quadrangulae of Mn‐Centred Tetrahedra.

La_2+xMnGe_2+y (I) and Ce_2+xMnGe_2+y (II) are prepared by arc‐melting of the elements in molar ratios of 2:1:2 followed by annealing (sealed silica tubes, 800 °C, 2 weeks).     

Post-Newtonian Expansions for Perfect Fluids

We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations that have a first post-Newtonian expansion. The results here are based on the elliptic-hyperbolic formulation of the Einstein-Euler equations used in [15], which contains a singular parameter , where v _T is a characteristic velocity associated with the fluid and c is the speed of light. As in [15], energy estimates on weighted Sobolev spaces are used to analyze the behavior of solutions to the Einstein-Euler equations in the limit , and to demonstrate the validity of the first post-Newtonian expansion as an approximation.     

Faithful Group Actions on Rooted Trees Induced by Actions of Quotients

We develop some new techniques of constructing (finite state) actions on rooted homogeneous trees and apply them to various groups. In particular we show that there is a faithful action of each amalgameted free product of the form ??_?? on a rooted homogeneous tree of finite degree, described by finite state automorphisms.     

Finite state wreath powers of transformation semigroups

The finite state wreath power of a transformation semigroup is introduced. It is proved that the finite state wreath power of nontrivial semigroup is not finitely generated and in some cases even does not contain irreducible generating systems. The free product of two monogenic semigroups of index 1 and period m is constructed in the finite state wreath power of corresponding monogenic monoid.     

Treatment of humic acids with ferric, aluminum, and chromium ions in water

The interaction of ferric, aluminum, and chromium ions with humic acids at different pH of mixture has been investigated. The concentration of metal ions, bound with humic acid is proportional to the concentration of metal ion in water solution at pH 3 at low metal ion concentrations. The ratio of the number of ferric ions, bound with humic acid, to the number of acidic groups in humic acid is more than 1.5 at high ferric ion concentration in solution. That is bound with the formation of dimers of ferric ions and their treatment with acidic groups of humic acid. The radius of particles formed in the reaction of humic acid with ferric ion does not depend on the pH and decreases in the reaction with chromium and aluminum ions at pH higher than 4. An increase of metal ion concentration leads to the increase of the particle radius at low metal ion concentration reaching the constant value at high metal ion concentration and pH 6.1.     

The isometry groups of the hamming spaces of periodic sequences

We consider the Hamming space of periodic (0, 1)-sequences and a continual family of its subspaces defined as direct limits of finite Hamming spaces. These subspaces form a complete lattice under inclusion which is isomorphic to the lattice of supernatural numbers. We explicitly describe the isometry groups of these spaces. This involves certain constructions similar to the hyperoctahedral groups but accounting for additional structures on the underlying sets.     

Complex formation of polyethyleneimine with copper(II), nickel(II), and cobalt(II) ions

An influence of the structure of a globule of polyethyleneimine on the complex formation of one with the copper(II), nickel(II), and cobalt(II) ions is described. A change of the coordination number from the pH of solution for complexes of ethylenediamine, diethylenetriamine, and polyethyleneimine with metal ions was found. The fraction of monomer links, bound with metal ions, depends on the volume of the globule of macromolecule as well as the condition of the proceeding reaction. The reaction of complex formation is controlled by the diffusion of metal ions into the polymer globule in solution. The effective equilibrium constants of complex formation were found. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 914–922, 2002; DOI 10.1002/pola.10157     

A transmission problem for quasi-linear wave equations

We prove the local existence and uniqueness of solutions to a system of quasi-linear wave equations involving a jump discontinuity in the lower order terms. A continuation principle is also established.