A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).     

Study of Interactions in the CuInS2-FeS System

Russian Journal of General Chemistry - The CuInS2-FeS section of the ternary Cu2S-In2S3-FeS system has been studied by means of differential thermal, X-ray diffraction, and microstructural...     

Crystal Structure and Hirshfeld Surface Analysis of (E)-1-(4-Bromophenyl)-2-(2,2-Dichloro-1-(4-Fluorophenyl)vinyl)diazene

Crystallography Reports - The CuCl-catalyzed olefination with CCl4 in the presence of tetramethylethylenediamine in DMSO leads to the formation of...     

Heterocyclization of cycloalkenes with di(2-pyridyl) diselenide in the presence of antimony pentachloride

Cycloalkenes react with di(2-pyridyl) diselenide in the presence of antimony pentachloride with the formation of products of the selenenylating electrophile cycloaddition at the multiple bond. The final products of heterocyclization, chloroantimonates(III) of 2,3-dihydro[1,3]selenazolo[3,2-a]pyridinium derivatives were isolated.     

Effect of Organic Counterions on the Properties of N-Lauryl Diisopropanolamine Surfactants

The influence of counterions on the surface properties of N-lauryl diisopropanolamine surfactants is delineated using conductometry and surface tension measurements. Twelve types of organic counterions have been studied: C₁–C₁₂ monocarboxylic acids anions. The surface properties of the synthesized surfactants, including surface tension, critical micelle concentration (CMC), effectiveness (π_CMC), efficiency (pC₂₀), maximum surface excess (Γ_max), minimum surface area (A_min), Gibbs energy of micellization (ΔG_mic), and adsorption (ΔG_ad) processes in the aqueous. The biodegradability of the prepared surfactants was tested in river water using the die-away method. Petroleum-collecting and petroleum-dispersing capacities of the synthesized compounds on the surface of water of varying mineralization degree have been studied.     

The Weak Convergence Theorem for the Distribution of the Maximum of a Gaussian Random Walk and Approximation Formulas for its Moments

In this study, asymptotic expansions of the moments of the maximum (M(β)) of Gaussian random walk with negative drift (???β), β?>?0, are established by using Bell Polynomials. In addition, the weak convergence theorem for the distribution of the random variable Y(β)?≡?2?β?M(β) is proved, and the explicit form of the limit distribution is derived. Moreover, the approximation formulas for the first four moments of the maximum of a Gaussian random walk are obtained for the parameter β?∈?(0.5, 3.2] using meta-modeling.     

Cycloaddition of 2-pyridinetellurenyl chloride to alkenes

The action of 2-pyridinetellurenyl chloride on alkenes results in the polar cycloaddition of the tellurium-centered electrophile at the multiple bond with the formation of 2,3-dihydro[1,3]tellurazolo[3,2-a]pyridinium derivatives.