About a Group That Acts Freely on an Abelian Group

Siberian Mathematical Journal -     

Thermodynamic and kinetic characteristics of the adsorption of acetone on the KU-23 sulfo-cation exchanger in the absence and presence of palladium

The thermodynamic and kinetic parameters of the adsorption of acetone on the sulfo-cation exchanger KU-23 and Pd/KU-23 have been determined. It has been found that application of palladium to the sulfo-cation exchanger strengthens the bond between acetone and the surface and increases the degree of localization of the adsorbed molecules.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 1, pp. 87–91, January–February, 1986.     

Modulation of the Casimir force by laser pulses: Influence of oxide films on the silicon surface

The possibility of modulating the Casimir force that acts in an air medium between a gold sphere and a silicon plate irradiated by laser pulses has been studied. It has been demonstrated that the oxide film that is formed on the silicon surface in air hardly affects the possibility of modulating the Casimir force when the distances between interacting bodies are of the order of 100 nm. With an increase in the distance, the modulation depth decreases; however, this region is of less practical interest, because the Casimir forces become too weak.     

On a Free Action of a Group on an Abelian Group

Let x be an element of order 3 in a group G acting freely on a nontrivial abelian group. If for every gG the order of the commutator [x,g] is finite then x belongs to a finite normal subgroup of G.     

Kinetics of decomposition of isopropylbenzene hydroperoxide catalyzed by dodecamolybdophosphoric acid

Using the NMR method, the kinetics of decomposition of isopropylbenzene hydroperoxide catalyzed by dodecamolybdophosphoric acid has been invertigated in acetone at 22–50°C. The reaction is first order with respect to both the hydroperoxide and the catalyst, the activation energy is 14 kcal/mol. The data obtained are in agreement with the reaction mechanism suggested by Kharasch /1/.

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, , 22–50°C. , 1 1 ; 14 /. , (1).

     

Matrix representation of Lie algebras over rings

Over the principal ideal ring k, the Lie k-algebras which are free k-modules of finite rank are, to within isomorphism, the Lie subalgebras of the full matrix algebra M(n, k).Translated from Matematicheskii Zametki, Vol.10, No. 6, pp. 671–678, December, 1971.The author takes this opportunity to thank M. I. Kargapolov for the formulation of the problem, attention, and discussion.     

Frequency tuning and doubling in Yb-doped fiber lasers

A compact Yb-doped fiber laser (YDFL) based on a tunable fiber Bragg grating (FBG) with ～6 W output power and ～45 nm tuning around 1080 nm has been developed. The laser output power and its spectral width (～0.15 nm) do not change significantly at the tuning, while the FBG reflection coefficient increases with an increase in FBG compression. It has been shown that this increase is due to stress-induced changes in the FBG’s refractive-index modulation amplitude. Intracavity frequency doubling in the YDFL has also been performed. About 0.4 W of green radiation with tuning in the range 540–548 nm has been achieved with a KTP nonlinear crystal.     

Coulomb broadening of the peak of electromagnetically induced transparency in plasma

We have measured the shape of the Autler-Townes doublet and the peak of electromagnetically induced transparency (EIT) under plasma conditions. We compare the experimental results with the calculated spectrum of the probe field of a three-level ArII Λ-scheme by taking into account Coulomb collisions. We show that the Coulomb broadening of the EIT peak is small (less than 40%), while the saturation resonance is broadened under the experimental conditions by a factor of 3. In contrast to the saturation resonance attributable to the Bennett dip in the velocity distribution of the population, the EIT peak is a coherent effect and is broadened mainly through Coulomb dephasing.