Rellich inequalities with weights

Let Ω be a cone in ${\mathbb {R}^{n}}$ with n ≥? 2. For every fixed ${\alpha \in \mathbb {R}}$ we find the best constant in the Rellich inequality ${\int\nolimits_{\Omega}|x|^{\alpha}|\Delta u|^{2}dx \ge C\int\nolimits_{\Omega}|x|^{\alpha-4}|u|^{2}dx}$ for ${u \in C^{2}_{c}(\overline\Omega\setminus\{0\})}$ . We also estimate the best constant for the same inequality on ${C^{2}_{c}(\Omega)}$ . Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains.     

Polycyclic Phosphorus-Containing Oxaboracyclanes

Abstract

The olygomers consisting of regularly repeating heterocyclic fragments were synthesized by the reaction of polycondensation of the ether of p-phenylenediboric acid and tetraoxymethyloldphosphioes obtained from the different diphosphines and aldehydes. The compounds with endocyclic phosphorus atom (I) were obtained in case of using the aliphatic aldehydes, and the compounds with exocyclic phosphoruscontaining group (II) were obtained when using the hydroxyaldehydes.     

New Biomimetic Catalysts for the Electrochemical Processes on the Basis of Redox-Active Macrocyclic Frame Structures

Abstract

Efficient catalytic systems mimicking the action of metalloenzymes based on cyclic frame structures containing phosphorus, nitrogen, and sulfur coordinating atoms for hydrogen oxidation or reduction under mild conditions are proposed.     

Low‐density polyethylene films doped with europium(III) complex: their properties and applications

Light‐converting polyethylene film containing europium(III) complex with phenanthroline was manufactured under an extrusion process. The film was characterized first by means of time‐of‐flight secondary‐ion‐mass spectrometry (TOF‐SIMS), ultraviolet‐visible‐infrared (UV‐vis‐IR) spectroscopy, then a study of excitation and luminescence spectra, quantum yield and lifetime of luminescence. The quantum yield of luminescence was measured as 5±2%, and the lifetime of luminescence was determined about 470 μsec. TOF‐SIMS surface mapping showed the uniform distribution of europium(III) over the film. Visualization of strong picosecond UV laser beams through the use of the developed film has been demonstrated. Copyright © 2004 John Wiley & Sons, Ltd.     

Modification of fullerene C60 by phosphorylated diazo compounds

New representatives of phosphorylated methanofullerenes were prepared by the reactions of [60]fullerene with O,O-diethyl -diazoethyl- and O,O-diethyl -diazobenzylphosphonates. Electrochemical reduction of the above-mentioned products proceeded stepwise and reversibly.     

Syntheses based on anabasine. Preparation and transformations of N-oxides

The oxidation of N-acetyl-and N-benzoylanabasine with the tert-butyl hydroperoxide (TBHP)— MoCl₅ system or MCPBA proceeds selectively at the nitrogen atom of the pyridine ring. The oxidation of N-methylanabasine under similar conditions gives a mixture of stereo-isomeric N-oxides at the piperidine nitrogen atom, their ratio depending on the reagent used. The oxidation of anabasine by TBHP— MoCl₅ or MCPBA is accompanied by dehydrogenation and results in anabaseine N-oxide. The reactions of anabasine and anabaseine pyridine N-oxides with acetic anhydride were investigated. The substituted 1H-3-pyridin-2-ones were prepared. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 322—328, February, 2006.