G. N. Kuz’mina

Gennadii Mikhailovich Goluzin and geometric function theory

G. M. Goluzin crucially influenced the development and extension of geometric function theory. His results received world-wide recognition, and his monograph “Geometric theory of functions of a complex variable” has been a reference book for several generations of analysts. This paper is a survey of Goluzin’s scientific work on the occasion of the 100th anniversary of his birth. §1. Dates of G. M. Goluzin’s life and work Gennadĭı Mikhăılovich Goluzin was born January 24, 1906, in the town of Torzhok (nowadays, in the Tver′ region) in a family of a railwayman. In 1924, he entered the Faculty of Mathematics of Leningrad State University, from which he graduated in 1929. In the same year, Goluzin’s diploma work was published in “Matematicheskĭı Sbornik”. After graduation from the University and until the end of his life, Goluzin taught at the University. In 1936, when he defended his Candidate dissertation, the Scientific Council bypassed the Candidate degree and awarded him a higher academic degree of Doctor of physico-mathematical sciences. From 1939 on, Goluzin was the Chairman of the division of the theory of functions of a complex variable in Leningrad State University. Goluzin loved teaching and taught with great energy. For a number of years, he taught the course of mathematical analysis for students specializing in mathematics, as well as a number of special courses, and directed a seminar on the geometric theory of functions of a complex variable. Goluzin’s lectures were always very well structured and very well presented. Many scientists grew up in Goluzin’s seminars, his students including Yu. E. Alenitsyn, S. A. Gel′fer, L. I. Kolbina, N. A. Lebedev, and I. M. Milin. Goluzin was an exceptionally modest and kind person, which made his contacts with students and colleagues informal and fruitful. From the moment of foundation of the Leningrad Branch of the Mathematical Institute of the Academy of Sciences of the USSR in 1940, Goluzin simultaneously worked in this institute, too. For his scientific merits, Goluzin was awarded the University First Prize for the year of 1946 and the State Prize for the year of 1947. A result of Goluzin’s scientific and pedagogical activity is his monograph “The geometric theory of functions of a complex variable”, which was first published in 1952. The second edition of the monograph, complemented by several of Goluzin’s papers and by an extensive survey of up-to-date developments written by Leningrad mathematicians, was 2000 Mathematics Subject Classification. Primary 30-02, 30C55.

Formation and Properties of the Triboactive Nanoparticles of Molybdenum Sulfides

The methods of synthesizing molybdenum trisulfide nanoparticles soluble in lubricants and active antifriction and antiwear additives into oils are proposed. Bis(tetraalkylammonium)tetrathiomolybdates that are the precursors of the formation of molybdenum trisulfide nanoparticles are synthesized by the interaction between ammonium thiomolybdate and tetraalkylammonium halides involving alkyl groups of different nature. The methods of UV and IR spectroscopy along with thermogravimetry are used to study the properties of the obtained molybdenum compounds. Molybdenum trisulfide nanoparticles are produced by the thermolysis of bis(tetraalkylammonium)tetrathiomolybdates, and small angle X-ray scattering is applied to determine their sizes and size distribution. With the use of different types of tribometers, the antifriction and antiwear activities of both tetraalkylammonium derivatives of thiomolybdates and molybdenum trisulfide nanoparticles are shown.

Comparison of antiwear properties of titanium-containing compounds

In search for environmentally friendly lubricant additives, titanium 2-ethylhexanoate and titanium oleate, which titanium compounds soluble in white oil, have been synthesized, as well as titanium dioxide nanoparticles modified with tetra-(2-ethylhexyl)thiuram disulfide and di(2-ethylhexyl)thiophosphonodisulfide. These titanium compounds have been characterized by elemental analysis, thermogravimetry, and IR spectroscopy. By means of the small-angle X-ray scattering technique, it has been found that the TiO2 nanoparticles have a size of 1–10 nm. Evaluation of antiwear properties of titanium compounds on a ChS-hMT-1 tribometer in a white oil solution shows that the decrease in wear scar diameter is 38–49% compared with the white oil. Analysis of the friction surfaces by atomic-force microscopy and X-ray microanalysis has shown a decrease in roughness of the friction surface caused by the presence of titanium atoms in the surface layers.

Synthesis and physicochemical properties of tetraalkylammonium thiomolybdates as precursors of triboactive molybdenum sulfides

Tetraalkylammonium thiomolybdates with different alkyl groups as ligands were synthesized. The composition and structure of the molybdenum complexes were studied by elemental analysis and UV and IR spectral techniques. The thermogravimetric characteristics of these compounds were determined. The tribological properties of the molybdenum complexes were assessed in terms of the coefficient of friction.

Sulfur-containing molybdenum compounds as high-performance lubricant additives (Review)

Published data on the use of sulfur-containing molybdenum compounds as additives for lubricants used in modern technology are reviewed. Various types of sulfur-containing molybdenum compounds as friction modifiers have been considered, and aspects of their activity and mechanism of action have been discussed. The role of these additives as inhibitors of oxidation of hydrocarbon materials has been shown. The environmental problems of using heavy metal compounds in lubricant additive formulations are discussed. The results of recent studies on the use of nanosized molybdenum sulfide particles as friction modifiers are presented.

A composition of organic hetero compounds as an antioxidant and antiwear additive for mineral lubricating oils

As a multifunctional additive exhibiting antioxidant and antiwear activity for mineral lubricating oil, a composition of ammonium dialkyldithiophosphate (ADTP) with tetraalkyl thiuram disulfide (TDS) has been proposed, which provides lower sulfated ash, phosphorus, and sulfur contents compared with the traditional additive zinc dialkyldithiophosphate used for the same functions. Ammonium dialkyldithiophosphates bearing various alkyl radicals have been synthesized using structurally different amines. The antioxidant efficiency of ADTP samples has been shown by monitoring the formation and degradation of hydroperoxides in a hexadecane medium as a model of mineral oil. The tribological parameters of these compounds have been determined under boundary lubrication conditions.

Nanosized structures in high-temperature oxidation of lubricating oil hydrocarbons

Peculiarities of high-temperature (150–170°C) oxidation of hexadecane as a model mineral lubricant are considered. Kinetic features of the oxidation process are presented, indicating a nonisothermal reaction mode, which can be caused by accumulation and decomposition of associated polyhydro-peroxides in the oxidizing system. The association of polyhydro-peroxides leads to formation of structures like reversed micelles, and evidence for their formation was obtained by the dye solubilization technique. The formation a microheterophase system at early stages of oxidation leads to reaction inhibition due to the formation of micellar aggregates in hydrocarbon oxidizing systems.

Influence of the structure of higher paraffin hydrocarbons and their derivatives on the mechanism of high-temperature liquid-phase oxidation

The specifics of oxidation kinetics at 160°C for structurally different hydrocarbons (normal and isobranched chains) and some of their functional derivatives were studied. A comparative analysis of products of the high-temperature oxidation of hydrocarbons was made and changes in the phase composition were studied using squalane and hexadecane as examples. It was shown that the spatial structure of a hydrocarbon subjected to oxidation makes a substantial contribution to the formation of reversed micelles. The kinetic behavior of squalane in oxidation and the solubilization of methyl orange by its oxidation products support the assumption that polyhydroperoxides form via the intramolecular 1,3-hydrogen abstraction mechanism.

Tribological properties of bis(tetraalkylammonium) tetrathiomolybdates as precursors of molybdenum sulfide nanoparticles

Tetraalkylammonium tetrathiomolybdate derivatives containing different alkyl groups as ligands have been synthesized. It has been found that the compounds exhibit antiwear and antifriction properties in dioctyl phthalate, a medium that models synthetic lubricating oil. A change in the surface profile (decrease in roughness) by the action of molybdenum sulfide produced from nitrogen-containing molybdenum compounds in tribocontact has been shown by atomic force spectroscopy.

Lubricating properties of oil cooling fluids with tribologically active additives in the metal cutting process

The tribological characteristics (roughness of the surface, properties of shaving, residual stress in surface layers, and resistance test of cutting tools) are studied in lubricating oils with various tribologically active additives during metals cutting. Molybdenum dialkyldithiocarbamate ((n-C4H9)4N2C2Mo2S8) at its content in oil of 1–2 wt % is shown to exhibit the best properties among the studied additives.