Ergodicity and mixing of non-commuting epimorphisms

We study mixing properties of epimorphisms of a compact connectedfinite-dimensional abelian group X. In particular, we show thata set F, with |F| > dim X, of epimorphisms of X is mixingif and only if every subset of F of cardinality (dim X) + 1is mixing. We also construct examples of free non-abelian groupsof automorphisms of tori which are mixing, but not mixing oforder 3, and show that, under some irreducibility assumptions,ergodic groups of automorphisms contain mixing subgroups andfree non-abelian mixing subsemigroups.     

Synthesis and photophysical properties of colloids fabricated by the layer-by-layer polyelectrolyte assembly onto Eu(III) complex as a core

The luminescent colloids have been synthesized through the layer-by-layer assembly of poly(sodium 4-styrenesulfonate) (PSS) and polyethyleneimine (PEI) onto the luminescent core. The latter has been obtained by the reprecipitation of complex Eu[(TTA)(3)1] (where TTA(-) and 1 are thenoyltrifluoroacetonate and 2-(5-chlorophenyl-2-hydroxy)-2-phenylethenyl-bis-(2-methoxyphenyl)phosphine oxide, respectively) from organic solvent to aqueous solution. The variation of Eu(III) complexes indicates the role of the complex core in the development of such core-shell colloids. Complex Eu[(TTA)(3)1] is most convenient precursor of Eu-doped luminescent nanocomposites. The fluorometric measurements at each step of the layer-by-layer polyelectrolyte assembly onto Eu[(TTA)(3)1] core, at various pHs and additives reveal the quenching of Eu-centered luminescence as a result of the interfacial interaction of the core and the dye. The AFM images and electrochemical behavior of PSS-(PEI-PSS)(n)-Eu[(TTA)(3)1] colloids deposited on the surface indicate the stability of the polyelectrolyte multilayer in the dried state.     

Assessment of porosities of SBA-15 and MCM-41 using water sorption calorimetry

Water sorption calorimetry has been used for characterization of 2D hexagonally ordered mesoporous silica SBA-15. Experimental data on water sorption isotherm, the enthalpy, and the entropy of hydration of SBA-15 are presented. The results were compared with previously published results on MCM-41 obtained using the same technique. The water sorption isotherm of SBA-15 consists of four regimes, while the sorption isotherm of MCM-41 consists only of three. The extra regime in the water sorption isotherm for SBA-15 arises from filling of intrawall pores, that are present in SBA-15 but absent in MCM-41. The water sorption isotherms of the two types of mesoporous silica were analyzed using the Barrett-Joyner-Halenda approach. For the BJH analysis, t-curves of silica with different degrees of hydroxylation were proposed. Comparison of water and nitrogen t-curves shows that, independent of hydroxylation of silica surface, the adsorbed film of water is much thinner than the adsorbed film of nitrogen at similar relative pressures. This fact decreases the uncertainty of the assessment of porosity with water sorption originated from variations in surface properties. The pore size distribution of SBA-15 calculated with BJH treatment of water sorption data is in good agreement with nitrogen NLDFT results on the same material.     

Structural chemistry of titanium and aluminium bimetallic hydride complexes: IV. Molecular structures and catalytic properties of {[η5-C5(CH3)5]2Ti(μ2-H)2Al(H)(μ2-H)}2 and [η5-C5(CH3)5]2Ti(μ2-H)2Al(H)(μ2-H)2Ti[η5-C5(CH3)5]2

Interaction between (η⁵-C₅Me₅)₂TiH₂BH₂ LiAlH₄ in ether produced the complex [(η⁵-C₅Me₅)₂TiH₂AlH₂]₂. The compound crystallized in a monoclinic unit cell with the parameters a 11.196(4), b 8.915(3), c 20.777(7) Å, γ 101.74(3)°, space group P2₁/n, Z = 4. The linkage between the Ti and Al atoms is accomplished via the double hydrogen bridge TiH₂Al, whereas dimerization occurs via the AlH₂Al bridges. The coordination polyhedron for the Al atom is a distorted trigonal-bipyramid with five hydride ligands at its apices. Decomposition of [(η⁵-C₅Me₅)₂TiH₂AlH₂]₂ in solution produced the complex [(η⁵-C₅Me₅)₂Ti]₂AlH₅, crystallizing in a triclinic unit cell with the parameters a 11.881(4), b 18.951(8), c 8.868(3) Å, α 93.04(3), β 104.33(3), γ 79.26(3)°, space group P$\text{1}$, Z = 2. The Al atom in this compound is assumed to have coordination number 5 and to be surrounded by hydride hydrogens only. The isomerization rate for 1-hexene in the presence of [(η⁵-C₅Me₅)₂TiH₂AlH₂]₂ was 0.3 mol olef/g-atom Ti·min, while the hydrogenation rate of the complex [(η⁵-C₅Me₅)₂Ti]₂AlH₄Cl was 38 mol H₂/g-atom Ti·min.     

Effect of reduction temperature on the dehydrocyclizing activity of pure chromia and chromia containing K2O and CaO

The dehydrocyclization of n-heptane at 520–550°C over pure chromia and chromia with added CaO and K₂O (5 wt.% each) has been investigated. Introduction of an alkaline additive into Cr₂O₃ decreases markedly the yield of toluene. Raising of the reduction temperature of alkali-containing samples from 550 to 700°C results, in contrast to pure Cr₂O₃ and chromia-alumina systems, not in diminished, but in increased yields of toluene, the activity enhancement being particularly pronounced for the CaO-containing catalyst. These increased activities cannot be correlated either with variations in specific surface area or changes in the content of Cr⁶⁺ during subsequent oxidation, and presumably should be ascribed to more extensive catalyst reduction at higher temperatures.

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- 520–550° CaO K₂O ( 5% .). Cr₂O₃ . 550° 700° , Cr₂O₃ , , , CaO. , , .