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.     

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.     

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.     

Potentiometric determination of diclofenac in pharmaceutical formulation by membrane electrode based on ion associate with base dye

The characteristics,performance and application of membrane electrode based on ion associate of diclofenac with base dye Safranine T are described.The electrode response to diclofenac has the sensitivity of 47±1.0 mV decade~(-1)over the range of 5×10~(-5)to 5×10~(-2)mol/L at pH 6-12,and the detection limit of 3.2×10~(-5)mol/L.The electrode is easy assembled at a relatively low cost has fast response time(2-4 s)and can be used for a period up to 3.5 months without any considerable divergence in potential.The proposed sensor displayed good selectivity for diclofenac in the presence of different substances.It was used to determine diclofenac in pharmaceuticals by means of the standard addition method.     

Poly[μ2‐chloro‐μ2‐1,4‐oxathiane‐κ2S:S‐copper(I)]

The title complex, [CuCl(C₄H₈OS)]_n, contains infinite spiral (CuS)_n chains linked by bridging Cl atoms into layers. The Cl atoms do not form polymeric fragments with Cu^I, but combine into isolated centrosymmetric Cu₂Cl₂ units. The compound is non‐isomorphous with the Br‐containing analogue, which contains Cu₈S₈ rings linked by Br atoms into chains. The O atom of the 1,4‐oxathiane mol­ecule does not realize its coordination abilities in the known copper(I)–halide complexes, while in copper(II)–halide complexes, oxathiane is coordinated via the S and O atoms. This falls into a pattern of the preferred inter­actions, viz. weak acid (Cu^I atom) with weak base (S atom) and harder acid (Cu^II atom) with harder base (O atom).     

Phosphorus-based p-tert-butylcalix[5]arene ligands

New calix[5]arene trivalent phosphorus derivatives have been synthesized which should be excellent ligands with which to study and control the interaction of a ligand atom with a metal. The larger cavity of the calix[5]arene (compared to calix[4]arene) provides a good balance between constraint and flexibility. Treatment of p-tert-butylcalix[5]arene with 2 equiv of either tris(dimethylamino)phosphine or dichlorophenylphosphine inserts two RP moieties into the calix[5]arene framework to give calix[5](PR)2(OH) (1, R = Me2N; 2, R = Ph). Further treatment of 1 with 4 equiv of HCl gives calix[5](PCl)2(OH) (3). Heating a solution of the monophosphorus compound calix[5](PNMe2)(OH)3 (4) releases dimethylamine to yield both monomeric calix[5](P)(OH)2 (6) and dimeric [calix[5](P)(OH)2](2) (7), the latter having a tubelike geometry. X-ray crystallographic studies confirm the structures and show that 1 and 2 have approximate cone conformations while 3 has an approximate 1,2-alternate conformation. The orientations of the phosphorus lone pairs and oxygen atoms in all derivatives provide a framework for both soft and hard ligand interactions within the calix[5]arene.     

Study of the nature and mechanism of the formation of paramagnetic species in nickel-based Brookhart-type catalytic systems

The catalytic systems NiBr₂(DPP-DAB) + 20 MAO and NiBr₂(DPP-BIAN) + 20 MAO (DPP-BIAN = bis(2,6-diisopropylphenyl)-bis(imino)-acenaphtene, MAO = methylaluminoxane), as well as a number of model systems, are studied under conditions of their activation and functioning. There are paramagnetic nickel complexes and radical-anion aluminum complexes in the systems under real conditions of activation and functioning. The highest activity is observed when the Ni(I) signal intensity in the ESR spectrum is maximal. A mechanism of paramagnetic species formation is proposed.