Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous medium

A boundary value problem for Laplace’s equation in a bounded two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.     

Distribution of the cobalt-containing component in the pore space of HZSM-5 upon a postsynthetic modification of the zeolite with hydroxo compounds of Co<Superscript>2+</Superscript>

The distribution of the cobalt-containing modifying component in the pore space of zeolite HZSM-5 depending on the total cobalt content of the samples (0.5–5.0 wt %) was quantitatively studied for the first time. At cobalt concentrations to 3.0 wt %, the cobalt-containing modifying component mainly occurred as isolated Co _Oh ²⁺ ions in the micropores (channels) of HZSM-5 at the ion-exchange positions of the zeolite and in one-dimensional CoO and CoAl₂O₄ nanoclusters. A further increase in the cobalt concentration to 5.0 wt % resulted, in addition to the filling of micropores, in the partial filling of the mesopore space of the zeolite with a small amount of three-dimensional CoO and CoAl₂O₄ nanoparticles. Using sorption data and electronic diffuse reflectance spectra, we were the first to find that the effective density of a cobalt-containing modifying component in the pore space of a zeolite matrix was lower than the density of a bulk CoO phase by a factor of 6.     

A P-chiral bisdiamidophosphite ligand with a 1,4:3,6-dianhydro-d-mannite backbone and its application in asymmetric catalysis

A novel readily available P,P-bidentate diamidophosphite ligand with P^∗-stereocentres is prepared from an inexpensive C₂-symmetric 1,4:3,6-dianhydro-d-mannite. By using this efficient ligand, up to 98% ee is achieved in Pd-catalysed asymmetric allylic alkylation, up to 92% ee in Pd-catalysed asymmetric allylic amination and up to 87% ee in Rh-catalysed asymmetric hydrogenation. The influence of the precatalyst, substrate and solvent on the enantioselectivity is discussed.     

Existence and uniqueness of solutions of hyperbolic equations in divergence form with various boundary conditions on various parts of the boundary

We prove the existence and uniqueness of an energy class solution of an initial–boundary value problem for a semilinear equation in divergence form. We consider the case in which an inhomogeneous third boundary condition is posed on one part of the lateral surface of the cylinder in which the equation is studied and the homogeneous Dirichlet boundary condition is posed on the other part of the lateral surface.     

Diastereomeric P*-mono- and P*,P*-bidentate diamidophosphite ligands based on 1,4:3,6-dianhydro-d-mannitol in asymmetric metallocomplex catalysis

Synthesis of diastereomeric mono- and bidentate diamidophosphites bearing P*-stereo-centers and phosphabicyclo[3.3.0]octane backbone and their coordination with rhodium(i) and palladium(ii) are considered. Their use in Rh-catalyzed asymmetric allylation allowed one to achieve 87% ee values and the use in Rh-catalyzed asymmetric hydrogenation gave up to 98% ee.     

Reaction of methyl 1-bromocyclopentanecarboxylate with zinc and 1-aryl-5-phenylpenta-1,4-dien-3-ones

Methyl 1-bromocyclopentanecarboxylate reacted with zinc and 1-aryl-5-phenylpenta-1,4-dien-3-ones with the formation of isomeric 10-aryl-8-(2-arylethenyl)-7-oxaspiro[4.5]dec-8-en-6-ones.     

Adsorption of molecular hydrogen on aluminophosphate zeolites at 77 K

The H₂ sorption properties of the aluminophosphate zeolites AlPO-5, AlPO-31, AlPO-11, AlPO-36, and AlPO-8 at 77 K have been investigated. A series of H₂ adsorption isotherms has been obtained for cylindrical micropore channels in the aluminophosphate zeolites. The absolute values of the amount adsorbed α(P) for the mesoporous aluminophosphate materials and the effective density of adsorbed H₂ in the micropore space β*(P, d) have been determined. It has been demonstrated experimentally that the sorbate density depends on the size of the micropore channel of the zeolite d. Hydrogen sorption isotherms have been calculated from experimental isotherms. A procedure allowing β*(P, d) to be estimated for intermediate d values is presented.     

Phosphites and diamidophosphites based on mono-ethers of BINOL: a comparison of enantioselectivity in asymmetric catalytic reactions

Novel P-monodentate phosphite-type ligands have been synthesized in one step from BINOL mono-tosylate and BINOL mono-(?)-menthylcarbonate. The use of these ligands provides up to 96% ee in Pd-catalyzed asymmetric allylic substitution of (E)-1,3-diphenylallyl acetate and up to 99% ee in Rh-catalyzed asymmetric addition of phenylboronic acid to cyclohex-2-enone. The influence of the structural modules such as the nature of phosphorus-containing ring or exocyclic substituent on the enantioselectivity is discussed.     

Hydrothermal synthesis and characterization of nanorods of various titanates and titanium dioxide

The formation process of titania based nanorods during hydrothermal synthesis starting from an amorphous TiO2.nH2O gel has been investigated. Sodium tri-titanate (Na2Ti3O7) particles with a rodlike morphology were prepared by a simple hydrothermal process in the presence of a concentrated NaOH aqueous solution. The ion exchange reaction of the synthesized Na2Ti3O7 nanorods with HCl under ultrasonic treatment promotes a complete sodium substitution and the formation of H2Ti3O7 nanorods. Low-temperature annealing of the as-produced nanorods of Na2Ti3O7 and H2Ti3O7 leads to a loss of the layered crystal structure and the formation of nanorods of condensed framework phases-sodium hexa-titanate (Na2Ti6O13) and metastable TiO2-B phases, respectively. These transformations proceed without a significant change in particle morphology. The nanostructures were investigated by scanning electron microscopy (SEM), powder X-ray diffraction (XRD), the Brunauer-Emmett-Teller (BET) method, thermogravimetric analysis (TGA), and Raman spectroscopy. The structural defects of the synthesized nanorods were investigated by high-resolution electron microscopy. The presence of planar defects can be attributed to the exfoliation of the zigzag ribbon layers into two-dimensional titanates as well as to the condensation of the layers of TiO6 octahedra into three-dimensional frameworks.     

Carbon dioxide adsorption on carbon nanomaterials

The adsorption of CO₂ on a number of activated carbons, thermal carbon black, and oxide materials at 195 K was studied using static and dynamic techniques. The landing surface areas ω(CO₂) ≈ 0.19 nm² on thermal carbon black and the absolute values of sorption for P/P ₀ < 0.4 were determined. The density of adsorbed CO₂ in the micropore volume was estimated at ρ(CO₂) = 0.91 g/cm³. It was demonstrated that the previously found effect of a weakening of the sorption interaction of nitrogen molecules with thin-walled materials (which manifested itself in an analysis of sorption isotherms by a comparative method) was pronounced to a lesser degree for the sorption of CO₂. At the same time, the presence of supermicropores in activated carbon samples resulted in overestimated values of surface areas. A dynamic method was proposed to measure the spectra of CO₂ desorption at 195–260 K using a SORBI-MS system for evaluating the binding energy of sorbate molecules with the surface.