Functional analysis proofs of Abel's theorems

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

     

Rückbezüge des Mathematikunterrichts und der Methodik des Mathematikunterrichts in der DDR auf historische Vorausentwicklungen

The author discusses at some examples exemplarily, how the pedagogy of mathematics education in the GDR from curricular and educational/psychological knowledge from the time before 1945 has developed scientifically.     

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.     

Security Applications of Optical Face Recognition System: Access Control in E-Learning

The educational system has gradually shifted from a face-to-face to an e-learning system, which has become prevalent in advanced countries with the advance of information technology, and connection of global networks. Accordingly, a growing demand is emerging for more reliable individual certification with technical precision in order to measure and record learning achievements and credentials of participants. The present system has a limit in terms of registration capacity, therefore, its accuracy has often been questioned. Against this background, an individual certification system is proposed particularly for access control in e-learning. Under our proposed system, a compact optical correlator for facial recognition is employed. This correlator was previously tested for of biometrics authentication accuracy and proved highly reliable, having recorded remarkably low error rates (below 1%). The recorded error rate is sufficiently robust that the system itself can be regarded as a valid and practical viable attestation system.     

The Dual Properties of Lk-UR and k-SS Space

In this paper, we get some properties in the dual space of Lk-UR and k-SS Banach space.AMS Subject Classification: 46B09     

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.