Oxidation of CO in microchannels of ceramic membranes modified with oxide catalytic coatings

Ceramic and cermet membranes containing catalytic coatings in the internal volume of their channels were obtained. A relationship between the permeability and kinetic regularities of CO oxidation describing the transmembrane flow of gases was studied. The pre-exponential factor and apparent activation energy change as the loading of the membrane channels by the catalyst proceeds. The study of gas permeability through the membranes showed that the catalyst with a loose branched surface is distributed in the membrane microchannels. The reaction rate constant increases in parallel with an increase in the relative fraction of the catalyst surface. The CO oxidation rate is assumed to depend statistically on the number of active sites, which increases with filling of the membrane channels by the catalytic material.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2613–2619, December, 2004.     

Vacuum condensates in supersymmetric gluodynamics

We analyse the restrictions imposed by supersymmetric Ward identities on the dimension-six condensates in supersymmetric gluodynamics. It is shown that the system of the Ward identities admits a nonzero value for the four-fermion condensate \(\left\langle {\left( {\lambda \sigma _\mu T^a \bar \lambda } \right)^2 } \right\rangle _0 \) while 〈f ^abc F _μν ^a F _νρ ^b F _ρμ ^c 〉₀ must vanish.     

Low-temperature heat capacity of sodium erbium molybdophosphate Na<Subscript>2</Subscript>Er(MoO<Subscript>4</Subscript>)(PO<Subscript>4</Subscript>)

Adiabatic calorimetry is used to measure the low-temperature heat capacity of Na₂Er(MoO₄)(PO₄)from 6.41 to 347.87 K. Experimental data are used to calculate the thermodynamic functions of Na₂Er(MoO₄)(PO₄), which at 298.15 K are as follows: C _p ⁰ (298.15 K) = 243,3 ± 0.4 J/(K mol), S ⁰(298.15 K) = 312.8 ± 0.8 J/(K mol), H ⁰(298.15 K) ? H ⁰(0 K) = 45280 ± 90 J/mol, and Φ⁰(298.15 K) = 136.1 ± 0.3 J/(K mol). A diffuse heat-capacity anomaly associated with splitting of the Stark levels (Schottky anomaly) is discovered in the low-temperature region.     

Structure and dehydration of hydrous tin dioxide xerogel

Hydrous tin dioxide xerogel with the composition SnO2 · 1.75H₂O is built of tin-oxygen-hydroxide fragments. Water molecules (no more than 1 mol) in the grain structure are kept by hydrogen bonds. Xerogel is dehydrated in the range 50–890°C in two stages. Below 123°C, molecular water is removed and the polycondensation of ≡Sn-O(H)-Sn≡ bridge groups occurs. There also takes place the transition of some water molecules from the molecular to hydroxide form as follows: ≡Sn-O-Sn≡ + H₂O → 2≡Sn-O-H. All processes occur within individual grains. Above 123°C, water removal is due to the polycondensation of tin-oxygen groups. As a result, grains are coarsen. After 200°C, their structure is determined as cassiterite coated by tin oxyhydrate.     

Iron-containing nanoparticles based on the 2-hydroxypropyl-β-cyclodextrin in aqueous solutions

The water-soluble hybrid nanoparticles based on high-substituted 2-hydroxypropyl-β-cyclodextrin were formed in situ during the reduction of iron(+2) salts by hypophosphite ion in alkaline medium. These nanoparticles are high sensitive to temperature and ultrasonication. It was established that the temperature and ultrasonication time of exposure increase leads to the successive dissociation of the nanoparticles.     

Self-similar potentials and theq-oscillator algebra at roots of unity

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq ³ = 1 and the particularq ⁴ = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively.     

Gas phase electron diffraction study of the hafnium perchlorate molecule

The structure of the Hf(ClO₄)₄ molecule was investigated by electron diffractometry in the gas phase. The model with D₄ symmetry is in best agreement with experimental data; it contains ClO₄ fragments in the form of distorted tetrahedra bridged by two oxygen atoms to the central Hf atom. Ivanovo Chemical Technological Academy. Moscow State University, Chemical Faculty. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 3, pp. 487–493, May-June, 1996.     

Calorimetric determination of the enthalpy of formation for pyrophyllite

A calorimetric study of the natural pyrophyllite was performed by high-temperature melt calorimetry on a Tian-Calvet calorimeter. Based on experimentally determined in this work for pyrophyllite and gibbsite, as well as previously obtained for corundum and quartz, the total value of the enthalpy increment for the sample heated from room temperature to 973 K and the enthalpy of dissolution at 973 K by Hess’s law, the enthalpy of formation of pyrophyllite of Al₂[(OH)₂/Si₄O₁₀] composed of elements was calculated at 298.15 K: Δ_f H _el^o(298.15 K) = −5639.8 ± 5.7 kJ/mol.     

Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials

The notion of Frobenius-Stickelberger-Thiele (FST) polynomials is introduced. Spectral transformations for these polynomials analogous to the Christoffel and Geronimus transformations for orthogonal polynomials are constructed. They yield an integrable discrete time chain (the FST chain) related to the generalized -algorithm. Relations of the FST polynomials to the Padé interpolation problem and to general and symmetric biorthogonal rational functions are considered in detail. This work is supported in part by the Russian Foundation for Basic Research (RFBR) grant no. 06-01-00191 and the Grant-in-Aid for Scientific Research no. 15540119 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.     

Modified Elliptic Gamma Functions and 6d Superconformal Indices

We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed whose superconformal index uses the double elliptic gamma function and obeys W(E ₇)-group symmetry.