Estimation of the parameters of a bivariate distribution of Gaussian random variables that cannot be observed simultaneously

A point estimator is proposed for certain numerical characteristics of a bivariate normal distribution with parameters that cannot be observed simultaneously. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 21–28, Perm, 1990.     

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.     

Regiochemistry of the addition of mercury salts to bornylene

The dependence of the regiochemistry of the mercuration of bornylene on the nature of the mercurating reagent and on the solvent has been found. The structures of the intermediate and transition state in these reactions have been proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 501–505, March, 1994.     

Reactions of mercury salts with benzo- and tetrafluorobenzobarrelenes

Regiochemistry and stereochemistry of the addition of mercury salts to benzobarrelene and tetrafluorobenzobarrelene have been studied in acetic acid and methanol. The effect of the substrate structure on the regiochemistry of the reaction is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1994.     

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.     

Kinetics and mechanism of azidomercuration of alkenes,cycloalkenes, and their derivatives with a mercuric acetate-sodium azide system

The kinetics of azidomercuration of alkenes, cycioalkenes, and their derivatives with a Hg(OAc)₂-NaN₃ system (1 1, 1 2, and 1 3) was studied. Based on the data on the product structure and kinetic results, it was concluded that HgOAcN₃ and Hg(N₃)₂ play the role of azidomercuration reagents. The reactions with alkenes having a strained double bond occur by a concerted scheme. With nonstrained alkenes, a multistep mechanism is realized, its first reversible step involving the formation of a mercurinium intermediate with an ion pair structure.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No.12, pp. 2479–2485, December, 1995.     

Salt effects and the mechanism of electrophilic mercuration of unsaturated compounds

The reaction of Hg(OAc)₂ with bornylene in THF-H₂O and CH₃CN-H₂O mixed solvents (75 25, v/v) was studied. The effects of the addition of NaOAc on the reaction rate and the composition of products were investigated. In the CH₃CN-H₂O mixture, the addition of NaOAc decreases the amount of the rearranged product, fundamentally changes the ratio between the regioisomeric solvoadducts, and promotes the formation of products of Hg(OAc)₂ addition. The reaction proceedsvia an ion pair and free mercurinium ion; the cation of the ion pair and the free mercurinium ion have dissimilar structures.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 544–548, March, 1995.     

Salt effects in the mercuration of unsaturated compounds. Kinetic evidence for the formation of ion pairs and a solvated ion

The kinetics of mercuration of bornylene and cyclohexene in different solvents in the presence of NaOAc and LiClO₄ has been investigated. Addition of NaOAc sharply decreases the rate of addition reactions of mercuric acetate to bornylene and cyclohexene in alcohols; the main direction of the mercuration of bornylene is the formation of acetoxy-adducts, and the yield of solvo-adducts decreases from 76 % in the absence of NaOAc, to 19 % in the presence of the salt (4·10^–3 mol L^–1). A reaction scheme involving the participation of intermediate ion pairs and a solvated mercurinium ion is suggested and confirmed by a steady-state concentration method. The influence of NaOAc on the rate of the reaction and on product formation is realized through the common ion effect.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 819–826, May, 1994.