Stability of solutions of control problems for the convection–diffusion–reaction equation with a strong nonlinearity

We consider a boundary control problem for the stationary convection–diffusion–reaction equation in which the reaction constant depends on the concentration of matter in such a way that the equation has a fifth-order nonlinearity. We prove the solvability of the boundary value problem and an extremal problem, derive an optimality system, and analyze it to derive estimates for the local stability of the solution of the extremal problem under small perturbations of both the performance functional and one of the given functions.     

Effect of matrix polymerization conditions on the structure and adsorption properties of porous polymers on the basis of divinylbenzene,acrylonitrile, and methyl methacrylate

A comparative study was carried out on the matrix polymerization of divinylbenzene, acrylonitrile, and methyl methacrylate in SBA-15 silica mesoporous molecular sieves. The occupancy of the matrix mesopores by the starting monomer, the medium, the polymerization temperature and time as well as the means of removing the exotemplate were all found to affect the spatial organization and porous structure of the polymer materials. Surplus occupancy of the mesopores by the monomer (1–1.5), polymerization in vacuum, and an alkaline method for matrix removal were found to be optimal. IR spectroscopy was used to find the conversion of the starting polymer by following the relative change in intensity of the vinyl group bands. Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 44, No. 6, pp. 371–375, November–December, 2008.     

Thermodynamic properties of ferrites of composition GdMIIFe2O5.5 (MII = Mg, Ca, Sr)

Ferrites with the composition GdM^IIFe₂O_5.5 (M^II = Mg, Ca, Sr) were synthesized from the corresponding oxides by the solid-phase method. The temperature dependence of the specific heat was studied by dynamic calorimetry in the temperature range 298.15 673 K. Equations describing this temperature dependence were derived. The temperature dependences of the thermodynamic functions were calculated.     

Structured polyphenylenes as carriers of palladium nanoparticles used as selective hydrogenation catalysts

Structured polyphenylenes that are used as matrices for immobilization of palladium nanoparticles are synthesized through the cyclocondensation of acetylaromatic compounds followed by structuring at different temperatures and, as a result, different crosslink densities. The relationship between the structure and structuring temperature of the polymers is investigated. It is shown that the sizes of palladium nanoparticles immobilized in polyphenylene matrices depend on the conditions of polymer structuring. The resulting catalytic systems are examined for the selective hydrogenation of triple bonds in acetylene alcohols.     

Oxidative Alkoxylation of Hypophosphite in Coordination Sphere of Iron(III)

The kinetics of oxidation of sodium hypophosphite with oxygen in Fe(III) alcoholic solutions is studied. At 50-90°C, hypophosphite was found to be oxidized to dialkyl phosphite (RO)₂HPO, di-, and trialkyl phosphates (RO)₂(OH)PO, (RO)₃PO. The redox potentiometry, IR, UV, EPR, Mössbauer, and ³¹P NMR spectroscopies, X-ray powder diffraction analysis, and gas-liquid chromatography were used to determine the key stages of the process: the Fe(III) reduction with hypophosphite with the formation of the phosphorus ethers and the reoxidation of Fe(II) with oxygen. The molar ratio of the products depends on the composition of the Fe(III) coordination sphere.     

Surface Microreliefs and Voltage–Current Characteristics of Gold Electrodes and Modified Thick-Film Graphite-Containing Electrodes

The surface microreliefs and voltage–current characteristics of gold electrodes and modified thick-film graphite-containing electrodes were studied. The relationship between the formation of an analytical signal of mercury(II) and the surface microrelief was determined. It was found that the surface of a modified graphite-containing electrode is a self-organizing ensemble of microelectrodes.     

Polar cycloaddition of 2-pyridinetellurium trichloride to multiple bonds

A reaction of 2-pyridinetellurium trichloride with unsaturated hydrocarbons leads to [1,3]tellurazolo[3,2-a]pyridinium-4 derivatives — the products of polar cycloaddition of tellurium-containing electrophile at the multiple bond.     

Dynamics of codeposition of metals inside porous electrode operating in direct-flow mode

Using an extended dynamic model of liquid flow-through porous electrode (PE), the effect of kinetics of deposition of individual components and conditions of potentiostatic electrolysis on the dynamics and final parameters (the cathodic deposit weight, the ratio between the amounts of components, and the spatial distribution of components) of codeposition of two metals M₁ and M₂ is studied. An equipotential PE operating in the direct-flow mode in the absence of anodic dissolution of electronegative component M₂ is considered. The effects of concentration, exchange currents, a difference between the equilibrium potentials M₁ and M₂, a prescribed voltage on PE, and solution flow velocity and direction are analyzed. It is shown that, for this version of codeposition of metals, the rates of M₁ and M₂ deposition averaged over the PE width are constant in time. However, this does not mean that their local deposition rates are constant. The general tendency is that the metal deposition rate on the rear part of PE decreases with the time, whereas the deposition rate on the frontal zone of PE, which is closer to the anode, increases. As a result, the final profiles for M₁ and M₂, which are calculated for equal deposition times taking into account and ignoring the redistribution of current during the deposition, differ essentially.     

Synthesis and study of the composition and properties of chelate complexes of benzoyl acetonates of rare-earth elements and use of these in gas chromatography

Chelate complex cerium [Ce(BA)₃)] and europium [Eu(BA)₃] benzoyl acetonates were synthesized. According to IR spectroscopic data and elemental analyses, the composition of the complexes is described by the empirical formulas M(BA)₃·2H₂O. Sorbents based on a mesoporous silica gel modified with cerium and europium benzoyl acetonates were obtained. The nitrogen porosimetry demonstrated that, as the complexes are deposited onto the surface of the starting support, the specific surface area and the pore volume become smaller. The polarity of the sorbents Chromaton N-AW + SiO₂ + M(BA)₃ with respect to all classes of test compounds decreases in the order Ce^III > Eu^III. According to the data obtained for the capacity factors, the sorbent modified with cerium benzoyl acetonate selectively separates alcohols, and Chromaton N-AW + SiO₂ with deposited chelates Eu(BA)₃ shows the best separating capacity for alkanes and alcohols. It was shown that the sorbents can be used in practice for separating gaseous mixtures of light hydrocarbons.     

Nanocrystalline Calcium Carbonate Hydroxyapatites Containing Multiwall Carbon Nanotubes: Synthesis and Physicochemical Characterization

Nanocomposites (NCs) based on carbonated calcium hydroxyapatite (CHA) (bioapatite, an analogue of the inorganic component of mammalian bone tissue), carbonate apatite (Ca₁₀(PO₄)₆CO₃, CA), and multiwall carbon nanotubes (CNTs) are prepared in the system CaCl₂–(NH₄)₂HPO₄–NH₄HCO₃–NH₃–CNT–H₂O (25°C) by coprecipitation of calcium and phosphorus salts with CNTs from aqueous solutions. The physicochemical properties of nanocomposites are studied as dependent on their formation conditions and composition using the solubility (residual concentrations) method and pH measurements. The composition, crystal structure, morphology, spectroscopic and thermal characteristics of the synthesized CHA/CNT and CA/CNT NCs are determined using chemical analysis, X-ray powder diffraction, thermal analysis, and IR spectroscopy. Either CHA/CNT NCs of composition Ca₁₀(PO₄)₆(CO₃)_x(OH)_2–2х · yCNT · zH₂O, where х = 0.2; 0.5; 0.8; y = 1, 2, 3; z = 6.8–10.8, or (when х = 1) CA/CNT NCs of composition Ca₁₀(PO₄)₆CO₃ · yCNT · zH₂O, where y = 1–3; z = 6.9–10.8, are formed as the carbonate and CNT contents of the NC increase. Our results favor the understanding of the effect of carbonization and CNTs on the metabolic formation of native bone tissue apatite and can be used for the design of efficient ceramics for bone implants.