Application of Algebraic Combinatorics to Finite Spin Systems with Dihedral Symmetry

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic with the dihedral group D_N. In this paper group-theoretical `parameters' of such groups are determined, especially decompositions of transitive representations into irreducible ones and double cosets. These results are necessary to construct matrix elements of any operator commuting with G in an efficient way. The approach proposed can be usefull in many branches of physics, but here it is applied to finite spin systems, which serve as models for mesoscopic magnets.Comment: 3 eps figs, 24 page

International observational campaign of the 2014 eclipse of EE Cephei

Context. EE Cep is one of few eclipsing binary systems with a dark, dusty disc around an invisible object similar to ε Aur. The system is characterised by grey and asymmetric eclipses every 5.6 yr that have significant variations in their photometric depth, ranging from ${\sim}0{{\overset{\text{ m}}{.}}}5$ to ${\sim}2{{\overset{\text{ m}}{.}}}0$. Aims. The main aim of the observational campaign of the EE Cep eclipse in 2014 was to test the model of disc precession. We expected that this eclipse would be one of the deepest with a depth of ${\sim}2{{\overset{\text{ m}}{.}}}0$. Methods. We collected multicoloured observations from almost 30 instruments located in Europe and North America. These photometric data cover 243 nights during and around the eclipse. We also analyzed low- and high-resolution spectra from several instruments. Results. The eclipse was shallow with a depth of $0{{\overset{\text{ m}}{.}}}71$ in the V band. The multicoloured photometry illustrates small colour changes during the eclipse with a total amplitude of order ${\sim}{+}0{{\overset{\text{ m}}{.}}}15$ in the B − I colour index. We updated the linear ephemeris for this system by including new times of minima, measured from the three most recent eclipses at epochs E = 9, 10, and 11. We acquired new spectroscopic observations, covering orbital phases around the eclipse, which were not observed in the past and increased the data sample, filling some gaps and giving better insight into the evolution of the Hα and Na