The Kleinfeld identities in generalized accessible rings

It is proved that the identities ([x, y]⁴, z, t) = ([x, y]², z, t) [x, y] = [x, y] ([x, y]², z, t) = 0, known in the theory of alternative rings as the Kleinfeld identities, are fulfilled in every generalized accessible ring of characteristic different from 2 and 3. These identities allow us to construct central and kernel functions in the variety of generalized accessible rings. It is also proved that in a free generalized accessible and a free alternative ring with more than three generators the Kleinfeld element ([x, y]², z, t) is nilpotent of index 2.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 291–297, February, 1976.     

Losses in an open microwave resonator with an ultrathin cylinder

Two methods are used to calculate the losses introduced in an open resonator by an ultrathin cylindrical sample placed in the antinode of the electric field of the main oscillation mode. It is demonstrated that the dependence of the losses on the cylinder parameters for wires is ambiguous in character, which must be considered when developing methods for measuring and control of characteristics of such objects placed in open quasioptical resonators. In special cases, some parameters of the examined samples can be determined only from measurements of the losses introduced in the open resonator.     

Capillary finite-amplitude waves with Tolman’s nonlinearity

Capillary finite-amplitude waves on a fluid surface are analyzed numerically by means of the conformal mapping method with allowance for Tolman’s nonlinearity which reflects the dependence of the surface tension coefficient on the surface curvature. The dependence of the wave profile and the wave velocity on the Tolman length is analyzed. Keywords: capillary waves, Tolman’s nonlinearity.     

Unusual reaction of 3-amino-1,2,4-triazole with 1,3-diiodopropan-2-one

3-Amino-1,4-bis(2-oxopropyl)-4H-1,2,4-triazolium triiodide is the product of the reaction of 3-amino-1,2,4-triazole with 1,3-diiodopropan-2-one in acetone in the absence of bases and phase-transfer catalysts. In dimethyl sulfoxide, conversely, a water soluble polyionene consisting of three aminotriazole rings bound by 1,3-dimethylenecarbonyl bridges is formed. The effect of the solvent on the alkylation of 3-amino-1,2,4-triazole with 1,3-diiodopropan-2-one was studied.     

Mechanism and kinetics of mechanical alloying in an immiscible Fe-Mg system

Mössbauer spectroscopy, X-ray diffraction, Auger spectroscopy, secondary ion mass-spectrometry and chemical analysis were used to study mechanical alloying of Fe and Mg powder mixture with the atomic ratio of 93:7. It has been shown that the process of mechanical alloying involves the formation of nanostructure in α-Fe particles, penetration and segregation of Mg atoms along the α-Fe grain boundaries, formation of the α-Fe(Mg) supersaturated solid solution.