Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Spectrophotometric Study of Interaction of Comenic Acid with Cetylpyridinium Chloride

The interaction of comenic acid with cetylpyridinium chloride in aqueous solutions was studied by spectrophotometry. Compositions of ionic associates formed depending on cetylpyridinum chloride concentration were found, and logarithms of equilibrium constants of corresponding association reactions were determined.     

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejér's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejér's average. The quantum uncertainty is then demonstrated to have a classical counterpart.     

Degradation of Metal 2-Acrylamido-2-methylpropanesulfonate-N-Vinylpyrrolidine Copolymers in Aqueous Solutions Containing Different Cations

The influence of single- and double-charged cations on degradation of metal 2-acrylamido-2-methylpropanesulfonate-N-vinylpyrrolidine copolymers in aqueous solutions in the presence of potassium peroxodisulfate, K₂S₂O₈, at 50 and 70°C was studied by viscosimetry.     

Intramolecular 1,5-Hydride Shift in Products of Stevens 3,2-Rearrangement of Ammonium Salts Containing 3-Phenyl-2-propynyl Group

In products of Stevens 3,2-rearrangement of ammonium salts containing alongside alkoxycarbon- ylmethyl also 3-phenyl-2-propynyl group an intramolecular 1,5-hydride shift is observed resulting in immonium salts which transform into aminoesters of enamine structure. The hydrolysis of the latter provides the lower aliphatic aldehydes and the corresponding aminoesters. An acid treatment of the reaction mixture affords a mixture of hydrogenated and nonhydrogenated esters of α-ketoacids originating from the mixture of 1,3-diene aminoesters. At treating with concn. HCl of the obtained mixture the nonhydrogeneted ketoester undergoes cyclization into 4-methyl-3-phenyl-2-buten-1,4-olide.     

Preparation and Characteristics of a Cation Exchanger Based on Oxidized Anthracite

The features of anthracite oxidation as influenced by temperature and time were determined. Physicochemical and sorption characteristics of the resulting cation exchanger were studied.     

Heat Kernel and Hardy’s Theorem for Jacobi Transform

In this paper, the authors obtain sharp upper and lower hounds for the heat kernel associated with Jacobi transform, and get some analogues of Hardy‘s Theorem for Jacobi transform by using the sharp estimate of the heat kernel.