Cyclotomic shuffles

Analogues of 1-shuffle elements for complex reflection groups of type $G(m,1,n)$ are introduced. A geometric interpretation for $G(m,1,n)$ in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group $G(m,1,n)$. Considering shuffling as a random walk on the group $G(m,1,n)$, we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra $H(m,1,n)$ for $m=2$ and small $n$

Vladislav Ardzinba – the first president of Abkhazia (biographical sketch

The article is a biographical sketch, telling about the first president of Abkhazia Vladislav Ardzinba, who was one of the originators of Abkhazia independence and new political elite formation

Enantioselective Total Synthesis of (+)-Cassiol

An enantioselective total synthesis of (+)-cassiol is reported. The complex derived from Pd-2(pmdba)(3) and enantiopure t-BuPHOX ligand catalyzes enantioconvergent decarboxylative alkylation to generate the quaternary carbon stereocenter at an early stage. The overall synthetic strategy involves a convergent late-stage coupling of two fragments. The synthesis features a longest linear sequence of eight steps

Formation of speech culture primary school teachers in today's language situation

The article considers the problems associated with the formation and perfection of speech culture of future primary school teachers. In this paper identifies the main features characteristic of the modern linguistic situation, the working methods aimed at the formation of linguistic and communicative competence of future teachers of primary school. Modeling speech situations is one of their effective exercise in the development of communication skills and mastery of the rules of modern literary languag

Caucasus Geopolitics: Modern Trends Conflicts and Development

The article studies major trends of Caucasus geopolitical situation development in terms of modern global politics, indicates major parties, settling conflicts in the region and their immediate interests in the Caucasus

Geoethnopolitical Aspect of the Caucasus Development in terms of Sochi Preparation for Winter Olympic Games

The article is concerned with geopolitical problems within the Caucasus Region in terms of modern regional processes, indicates major features of the region and their impact on Sochi preparation for Winter Olympic Games

Study of olivines from Omolon and Seymchan meteorites using X-ray diffraction and Mössbauer spectroscopy with a high velocity resolution

Study of olivine from Omolon and Seymchan meteorites was performed using X-ray diffraction and Mössbauer spectroscopy with a high velocity resolution. X-ray diffraction patterns were measured at room temperature while Mössbauer spectra were measured at 295 and 90 K. The orthorhombic crystal lattice parameters were evaluated for olivine from Omolon and Seymchan. These parameters appeared to be different for olivines from both meteorites. Mössbauer spectral components related to 57Fe in crystallographically non-equivalent sites M1 and M2 in both olivines were determined and its Mössbauer hyperfine parameters were evaluated. Some differences in the tendencies of temperature dependence of spectral parameters and small variations of 57Fe quadrupole splitting in both M1 and M2 sites of olivines from Omolon and Seymchan were found. On the basis of Mössbauer parameters and chemical data, the temperatures of equilibrium cation distribution were evaluated for both olivines. © 2012 American Institute of Physics

Theoretical and experimental study of high-pressure synthesized B20-type compounds Mn1−x_{1-x}(Co,Rh)x_xGe

The search and exploration of new materials not found in nature is one of modern trends in pure and applied chemistry. In the present work, we report on experimental and \textit{ab initio} density-functional study of the high-pressure-synthesized series of compounds Mn$_{1-x}$(Co,Rh)$_x$Ge. These high-pressure phases remain metastable at normal conditions, therewith they preserve their inherent noncentrosymmetric B20-type structure and chiral magnetism. Of particular interest in these two isovalent systems is the comparative analysis of the effect of $3d$ (Co) and $4d$ (Rh) substitution for Mn, since the $3d$ orbitals are characterized by higher localization and electron interaction than the $4d$ orbitals. The behavior of Mn$_{1-x}$(Co,Rh)$_x$Ge systems is traced as the concentration changes in the range $0 \leq x \leq 1$. We applied a sensitive experimental and theoretical technique which allowed to refine the shape of the temperature dependencies of magnetic susceptibility $\chi(T)$ and thereby provide a new and detailed magnetic phase diagram of Mn$_{1-x}$Co$_x$Ge. It is shown that both systems exhibit a helical magnetic ordering that very strongly depends on the composition $x$. However, the phase diagram of Mn$_{1-x}$Co$_x$Ge differs from that of Mn$_{1-x}$Rh$_x$Ge in that it is characterized by coexistence of two helices in particular regions of concentrations and temperatures.Comment: 12 pages, 11 figure