On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

Rigidity of Branch Groups Acting on Rooted Trees

Automorphisms of groups acting faithfully on rooted trees are studied. We find conditions under which every automorphism of such a group is induced by a conjugation from the full automorphism group of the rooted tree. These results are applied to known examples such as Grigorchuk groups, Gupta–Sidki group, etc.     

Investigation of 2-[(<Emphasis Type="Italic">E</Emphasis>)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3H-indolium as a new highly sensitive reagent for the spectrophotometric determination of nitrophenols

A new, simple, rapid, and sensitive spectrophotometric method has been developed for the determination of nitrophenols [picric acid (PA); dinitrophenols (DNP)] in wastewater samples. The method is based on the reaction of nitrophenols with 2-[(E)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3 H-indolium chloride reagent to form the colored ion associates, which are extracted by organic solvents. The molar absorptivity of the ion associates of PA with the investigated reagent ranges from 8.3×10⁴ to 11.3×10⁴ L mol^–1 cm^–1, depending on the extractant. Because only PA is extracted in an acidic medium with the investigated reagent, but both PA and DNP are extracted in an alkaline medium, it is possible to determine both substances in a mixture. Appropriate reaction conditions have been established. The absorbance of the colored extracts obeys Beers law in the range of 0.04–4.58 mg L^–1 PA, 1.0–18.4 mg L^–1 2,4-DNP and 1.2–14.7 mg L^–1 2,6-DNP, respectively. The limit of detections, calculated from a blank test (n=10; P=0.95), are 0.05 mg L^–1 PA, 0.9 mg L^–1 (2,4-DNP), and 1.1 mg L^–1 (2,6-DNP), respectively.     

Influence of reactant structure on composition and stability of adducts of bis-macrocyclic complexes of copper(II) with aliphatic α,ω-diamines

On the basis of spectrophotometric measurements, constants have been determined for adduct formation between bis-macrocyclic complexes of copper(II) and aliphatic diamines. For these systems, the influence of reactant structure on the specific features of complexation has been established. L. V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of the Ukraine, 31 Nauka Prospect, Kiev 252039, Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 2, pp. 83–87, March–April, 1997.     

Relaxation dynamics in glycerol-water mixtures: I. Glycerol-rich mixtures

We discuss the relaxation dynamics of glycerol-water mixtures, as studied by dielectric spectroscopy in the frequency range from 1 Hz to 250 MHz and at temperatures between 173 and 323 K. The experimental results obtained for the glycerol-rich mixtures suggest that the main dielectric relaxation process, as well as the so-called high-frequency "excess wing" (EW) and dc conductivity, follow the same temperature dependence. This result indicates that all of these processes are induced by the same molecular origin. A new phenomenological function is proposed to describe the whole dielectric spectrum in the covered frequency range, and some possible mechanisms of dielectric behaviors through the dc conductivity, the main relaxation process, and the EW are discussed.     

Structure of 2,4-Dihydrobenzylidene- and 5-Bromo-2-hydroxybenzylidene(methyl)amine N-Oxides

2,4-Dihydroxybenzylidene(methyl)amine and 5-bromo-2-hydroxybenzylidene(methyl)amine N-oxides were synthesized by condensation of N-methylhydroxylamine with the corresponding aldehydes. Their crystal structures were solved by X-ray analysis.     

Effect of the coordination number of the nickel(II) ion on the kinetic characteristics of the oxidation of its macrocyclic complexes by peroxodisulfate ions

A study of the kinetics of the oxidation by peroxodisulfate of macrocyclic complexes of nickel(II) with a pH-regulatable position of the thermodynamic equilibrium between the tetra- and hexacoordinated forms showed that the square-planar form is substantially more reactive than the hexacoordinated form. The observed effect may be a consequence of different mechanisms of the redox processes: intraspheral in the first case and extraspheral in the second.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, Nos. 5–6, pp. 442–447, September–December, 1992.     

Design of New Water Receptors Based on Oligomeric Complexes of Copper(II) and Nickel(II)

The interaction of mono- and oligomacromolecular complexes of copper(II) and nickel(II) with water vapor has been studied on a piezoquartz microbalance. It has been established that the effectiveness of adsorption is determined by the nature of the metal ion to a larger extent than the quantity of macrocyclic ligand in the receptor molecule. Oligomacrocyclic complexes of copper(II) are shown to have prospects for use as active coverings of moisture meters working over a wide range of relative humidity.     

Biosensors based on enzyme field-effect transistors for determination of some substrates and inhibitors

This paper is a review of the authors' publications concerning the development of biosensors based on enzyme field-effect transistors (ENFETs) for direct substrates or inhibitors analysis. Such biosensors were designed by using immobilised enzymes and ion-selective field-effect transistors (ISFETs). Highly specific, sensitive, simple, fast and cheap determination of different substances renders them as promising tools in medicine, biotechnology, environmental control, agriculture and the food industry.The biosensors based on ENFETs and direct enzyme analysis for determination of concentrations of different substrates (glucose, urea, penicillin, formaldehyde, creatinine, etc.) have been developed and their laboratory prototypes were fabricated. Improvement of the analytical characteristics of such biosensors may be achieved by using a differential mode of measurement, working solutions with different buffer concentrations and specific agents, negatively or positively charged additional membranes, or genetically modified enzymes. These approaches allow one to decrease the effect of the buffer capacity influence on the sensor response in an aim to increase the sensitivity of the biosensors and to extend their dynamic ranges.Biosensors for the determination of concentrations of different toxic substances (organophosphorous pesticides, heavy metal ions, hypochlorite, glycoalkaloids, etc.) were designed on the basis of reversible and/or irreversible enzyme inhibition effect(s). The conception of an enzymatic multibiosensor for the determination of different toxic substances based on the enzyme inhibition effect is also described.We will discuss the respective advantages and disadvantages of biosensors based on the ENFETs developed and also demonstrate their practical application.     

Electron interactions in crystalline dibenzotetraazaannulene

The characteristics of intra- and intermolecular electronic processes in crystalline dibenzotetraazaannulene were established based on an analysis of the electronic absorption spectra of thin films. It was shown that the specific spectral characteristics of this substance are due to its stack structure in the solid state.L V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of Ukraine, 252039 Kiev, Prosp. Nauki, 31. Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 32, No. 1, pp. 20–23, January–February, 1996. Original article submitted May 19, 1995.