Analytic continuation of the Appell function <Emphasis Type="Italic">F</Emphasis><Subscript>1</Subscript> and integration of the associated system of equations in the logarithmic case

The Appell function F ₁ (i.e., a generalized hypergeometric function of two complex variables) and a corresponding system of partial differential equations are considered in the logarithmic case when the parameters of F ₁ are related in a special way. Formulas for the analytic continuation of F ₁ beyond the unit bicircle are constructed in which F ₁ is determined by a double hypergeometric series. For the indicated system of equations, a collection of canonical solutions are presented that are two-dimensional analogues of Kummer solutions well known in the theory of the classical Gauss hypergeometric equation. In the logarithmic case, the canonical solutions are written as generalized hypergeometric series of new form. The continuation formulas are derived using representations of F ₁ in the form of Barnes contour integrals. The resulting formulas make it possible to efficiently calculate the Appell function in the entire range of its variables. The results of this work find a number of applications, including the problem of parameters of the Schwarz–Christoffel integral.     

Symmetrical triindole as a central unit in the fluorene-containing polyphenol assembly

A new strategy was proposed for the synthesis of fluorene-containing indole polyphenols, based on the Suzuki–Miyaura reaction of hexabrominated symmetric indole trimer with the monoboryl N,N'-di[9,9'-bis(3',5'-dimethoxybenzyl)fluoren-2'-yl]aniline derivative and subsequent chemical transformations. The prepared compound was applicable for the development of a promising positive resist for electron-beam nanolithography capable of forming patterns with a 12 nm resolution.     

New polymer composites based on keratin and polyethylene

New biodegradable composites based on keratin and polyethylene have been produced under shear deformation. It has been demonstrated that the introduction of keratin leads to an increase in elastic modulus and to a decrease in ultimate tensile strength and elongation at break of the compositions. Elongation at break ε_b depends on the keratin dispersity; the highest ε_b values are observed for the compositions containing the smallest keratin particles. It has been shown that the compositions are susceptible to mold fungi; i.e., they are biodegradable.     

Drying of colloidal solutions of fluoroalkyl oligomers

The change in the supramolecular structure upon drying (solvent removal) of colloidal solutions of fluoroalkyl oligomers at atmospheric pressure has been studied using atomic force microscopy. In an initial colloidal solution, micrometer-sized particles of the dense phase consist of randomly oriented oligomers in the form of rigid rods of a 3–5 nm length forming a porous framework filled with solvent molecules, which solvate the oligomer chains. The drying-induced capillary pressure, which in nanosized pores is of the same order of magnitude as the solvation energy, leads to framework deformation, collapse of the pores, and the formation of lamellar and dendritic structures on a 50–100 nm scale. The ordering of these structures (formation of blocks of parallel oriented fibers typical of a fluoroplastic) increases as the heat-treatment temperature and the drying rate are increased, increasing the roughness of the surface (ratio of real to smooth surface area) and its hydrophobicity.     

Visualization of supramolecular framework of perfluorinated-oligomer colloid particles by supercritical drying

Aerogels of the tetrafluoroethylene radical polymerization products H(C₂F₄)_nR, where R is the radical formed by the abstraction of a hydrogen atom from a solvent molecule, have been obtained by replacing the solvent with supercritical CO₂ and its subsequent rapid evaporation. According to the data of scanning electron and atomic force microscopy, the aerogel consists of loosely bound particles of 1–3 μm in diameter, which is two to three times that of colloid particles in the initial solution, where the particles consist of an oligomer framework filled with solvent molecules. The internal structure of the framework is manifested in the surface topography with a roughness coefficient of 1.6–1.8. High roughness leads to the formation of ultrahydrophobic coatings with contact angles of >160°. A model of supercritical drying in which the solvent is removed from the colloidal particles without alteration of the supramolecular structure is discussed.     

Experimental study of gasification of vacuum residue in metal melt by alternating reactor feeding with carbonaceous feedstock and oxidant

Processes occurring in a metal melt during plasma-assisted melt gasification of carbonaceous feedstock have been studied in the mode of alternating feeding the reactor with the carbonaceous feedstock and oxidant. Vacuum residue was used as an oxygen-free carbonaceous material, and air and steam were used as an oxidant. The results of the study show that by alternating the carbonaceous-feedstock pyrolysis step and the step of carbon oxidation in the metal melt, it is possible to produce synthesis gas with any desired H₂/CO ratio.     

The relationship between self-organization and membrane effects of aqueous dispersion systems of the thyroliberin oligopeptide

The relationship between rearrangement of the dispersed phase inducing considerable changes in the pH and nonmonotonic concentration dependences of membrane effects in aqueous systems of the endogenous regulatory peptide, thyroliberin (thyrotropin-releasing hormone), in 10^–3–10^–16 mol/L concentration range was demonstrated for the first time. The membrane structure modification in the 10^–13–10^–16 mol/L range was found to be due to accumulation of nanoassociates, while the oppositely directed pronounced structural changes in the 10^–6–10^–12 mol/L range may be associated with the coexistence and rearrangement of dispersed phases of various nature (domains and associates) whose action on membrane lipid components is regulated in this concentration range by the correlated changes in the dispersed phase parameters and pH.     

Complex-forming and ion-selective properties of bis(2-diphenylphosphorylalkyl)phenyl ethers of ethylene glycols. Crystal structures of cadmium complexes

New complexes of cadmium iodide with 1,3-bis[2-(diphenylphosphoryl)phenoxy]propane [CdL⁰I₂], 1,2-bis[2-(diphenylphosphorylethyl)phenoxy]ethane [CdL^{1, 2}I₂], and 1,8-bis[2-(diphenylphosphorylethyl) phenoxy]-3,6-dioxaoctane [CdL^{3, 2}I₂] are synthesized and their IR spectra and crystal structures are studied. Electroanalytical characteristics of membranes of ion-selective electrodes based on L⁰, L^{1, 2}, L^{3, 2}, and known crown ethers are compared for cations of alkali, alkaline-earth, and transition metals. Ligand L^{3, 2} is the first podand with terminal diphenylphosphoryl fragments to exhibit selectivity with respect to the cadmium cation.     

Copper(II), nickel(II), and zinc(II) complexes with <Emphasis Type="Italic">o</Emphasis>-tozylaminobenzaldehyde 4,6-dimethylpyrimidyl hydrazone

o-Tosylaminobenzaldehyde dimethylpyrimidyl hydrazone and its copper(II), nickel(II), and zinc(II) complexesare synthesized and studied. According to the X-ray diffraction data, the zinc(II) complex has the structure of a tetragonal pyramid with the N₃O donor ligand environment. According to EPR and magnetochemistry data, the copper(II) complex has a similar structure of the chelate core. In the nickel(II) complex, the solvent molecule completes the coordination core to an octahedron.