Second derivatives of solutions of some variational inequalities connected with elliptic nondiagonal systems

Variational inequalities connected with linear elliptic systems of general form are considered. The vector-valued functions, satisfying the variational inequalities in the domain of definition, take values in an arbitrary fixed convex set of the space R ^N ,N>1. It is shown that the second derivatives of the solutions belong to the space L _2, .An analogous result for a problem with a constraint of special form on the boundary of the domain (the classical Signorini problem) was obtained earlier by Kinderlehrer.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 6–18, 1990.     

Catalytic conversion of aliphatic alcohols on carbon nanomaterials: The roles of structure and surface functional groups

Carbon nanomaterials with the structure of graphene and different compositions of the surface groups are used as catalysts for the conversion of С₂–С₄ aliphatic alcohols. The conversions of ethanol, propanol- 1, propanol-2, butanol-1, butanol-2, and tert-butanol on carbon nanotubes, nanoflakes, and nanoflakes doped with nitrogen are investigated. Oxidized and nonoxidized multiwalled carbon nanotubes, nanoflakes, and nanoflakes doped with nitrogen are synthesized. X-ray diffraction analysis, X-ray photoelectron spectroscopy, scanning and transmission electronic microscopies, Brunauer–Emmett–Teller method, derivatographic analyses, and the pulsed microcatalytic method are used to characterize comprehensively the prepared catalysts. It was established that all of the investigated carbon nanomaterials (with the exception of nondoped carbon nanoflakes) are bifunctional catalysts for the conversion of aliphatic alcohols, and promote dehydration reactions with the formation of olefins and dehydrogenation reactions with the formation of aldehydes or ketones. Nanoflakes doped with nitrogen are inert with respect to secondary alcohols and tert-butanol. The role of oxygen-containing and nitrogen-containing surface groups, and of the geometrical structure of the carbon matrix of graphene nanocarbon materials in the catalytic conversion of aliphatic alcohols, is revealed. Characteristics of the conversion of aliphatic alcohols that are associated with their structure are identified.     

Using gold nanoparticles in spectrophotometry

Published data on the use of gold nanoparticles in spectrophotometry are summarized. Data on methods for preparing gold nanoparticles and their optical properties are presented. The main approaches on which spectrophotometic methods of substance determination using gold nanoparticles are based are discussed. Examples of determining of metal ions, anions, and organic compounds are presented.     

Synthesis of N-substituted amides by the Ritter reaction with heteropoly acids as catalysts

Reactions of a number of nitriles with camphene in the presence of the heteropoly acids H₃PW₁₂O₄₀, H₇PMo₁₂O₄₂, and H₄SiW₁₂O₄₀ as catalysts were studied. In all cases, N-substituted amides were obtained in sufficiently high yields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 374–376, February, 2006.     

Number of lattice points in a sphere

A new estimate is obtained for the residue R in the asymptotics of the number of integer points in a ball of radius a. The estimate has the form R ? a ^{17/14 + ?} .     

Synthesis of 3-tetradecylpentane-2,4-dione and investigation of its compression isotherms by the Lengmuir-Blodgett method

By alkylation of acetylacetone in anhydrous methanol 3-tetradecylpentane-2,4-dione was prepared. Its individuality and structure were confirmed by IR and NMR spectroscopy and mass-spectrometry. Compression isotherms of the Lengmuir monolayers on water subphase surface depending on the tautomeric form of 3-tetradecylpentane-2,4-dione were studied.     

Photocatalytic activity and physicochemical characteristics of modified potassium polytitanates in the reaction of decomposition of aqueous-alcoholic solutions

Study of the photocatalytic activity of nanomaterials based on potassium polytitanate modified with transition metal ions (Ni²⁺, Cr³⁺, Cu²⁺) demonstrated that the cation composition, morphology of photocatalyst particles, and their size strongly affect the photocatalytic activity. The rate of the photoinduced hydrogen evolution from the aqueous-alcoholic solution grows in the series of potassium polytitanates modified with Cu²⁺, Ni²⁺, Cr³⁺ ions, and that from pure water, for potassium polytitanates modified with Ni²⁺,Cr³⁺, Cu²⁺ ions. The capacity for intercalation of water into the interlayer space does not strongly affect the rate of the photoinduced hydrogen evolution. It was shown that potassium polytitanate modified with Cr³⁺ ions has the maximum quantum efficiency (30%).     

Chemistry of modified flavonoids 17. Imidazole analogs of flavonoids

Summary Imidazole analogs of chalcones were synthesized by the reaction of 1-methyl-2 formyl-5-chloroimidazole with o-hydroxyacetophenones. Isomerization and oxidative cyclization of chalcones yielded imidazole analogs of flavonones and flavones. These compounds were used in the synthesis of pyrazolines, pyrazoles, and isoxazoles.Taras Shevchenko Kiev University, Kiev 252017. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1063-1070, August, 1994.For Communication 16 see [1].