Linear Relations, Differential Inclusions, and Degenerate Semigroups

A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Catalysts Based on Fiberglass Support: IV. Platinum Catalysts Based on Fiberglass Support in Oxidation of Hydrocarbons (Propane and n-Butane) and Sulfur Dioxide

Platinum catalysts (0.003–0.52% Pt) based on leached sodium silicate and boron silicate fiberglass supports are studied in the complete oxidation of hydrocarbons (n-butane and propane) and high-temperature SO₂ oxidation. It was shown that platinum localized in the bulk of the glass matrix show a higher activity and thermal stability than metal particles supported on the outer surface of fiberglass. The experimental results for hydrocarbon oxidation on platinum-containing fiberglass gauzes at short contact times are discussed.     

Platinum nanoparticles generated in functionality-enhanced reaction media based on polyoctadecylsiloxane with long-chain functional modifiers

Functionality-enhanced nanostructured matrices generated by intercalating polyoctadecylsiloxane (PODS) with octadecene (ODC) or octadecylamine (ODA) are employed as reaction media in which to grow Pt nanoparticles. Small-angle X-ray scattering (SAXS) signatures confirm that the amphiphilic PODS matrix orders into lamellae with a periodicity (d) of 5.24 nm, which corresponds to the siloxy bilayer and a double layer of alkyl tails. The regular packing of the hydrophobic tails becomes distorted upon introduction of ODC or ODA. Incorporation of K[(C2H4)PtCl3].H2O (a Zeise salt) into the PODS/ODC matrix, followed by reduction of the Pt ions by NaBH4 or H2, results in the localization of Pt compounds and nanoparticles along the siloxy bilayers, which remain dimensionally unchanged. Electron density profiles deduced from PODS/ODA, however, provide evidence for considerable structural reorganization upon metalation with H2PtCl6.6H2O. In this case, the siloxy bilayers broaden due to the presence of PtCl62- ions, and the hydrophobic layers become distorted due to the formation of (PtCl62-)(ODAH+)2 complexes. Subsequent reduction by NaBH4 restores the inherent PODS organization, while H2 reduction partially preserves the distorted matrix, indicating that some Pt nanoparticles form in close proximity to the siloxy bilayer. Transmission electron microscopy reveals that relatively monodisperse Pt nanoparticles measuring approximately 1 nm in diameter are located along the siloxy bilayers, whereas anomalous SAXS further indicates that nanoparticles form aggregates of comparable size to d within the PODS double layers.     

Analytic description of the domain of existence of triple configurations with a negative slope of reflected shock

We consider triple configurations of compression shocks in supersonic flows of an inviscid perfect gas. The boundaries of the domain of existence of shock-wave structures of a new type (triple configurations with a negative slope of the reflected shock or negative triple configurations) on a set of flow parameters have been theoretically investigated.     

Ion-selective and complexation properties, vibrational spectra, and crystal and molecular structure of 1,5-bis[2-(hydroxyethoxyphosphoryl)phenoxy]-3-oxapentane

The ion-selective properties of 1,5-bis[2-(hydroxyethoxyphosphoryl)phenoxy]-3-oxapentane H₂R² have been described. The molecular and crystal structure of H₂R² has been determined by powder X-ray crystallography and IR spectroscopy. The molecule has the twofold symmetry axis, orthorhombic crystal system, space group Pbcn, a = 16.830(2) ?, b = 8.866(15) ?, c = 15.7190(2) ?, V = 2346.1(6) ?³, Z = 4. A new CuR² · 2H₂O complex has been synthesized and characterized.     

Study of temperature fields in a rectangular plate with a temperature-dependent internal source with the aid of fast expansions

The approximate analytic solution of the problem of temperature field in a rectangular plate with an internal temperature- dependent source is obtained by the method of fast expansions. The critical value of a parameter characterizing heat release, which fundamentally affects the analytic solution form, is found. The maximum solution error is shown to amount to 0.02 at the consideration of the first three terms of the Fourier series in fast expansion. Temperature fields are presented, and an analysis of the influence of the plate sizes and the heat release magnitude on their formation is given. Recommendations on the plate shape choice are given.