Finite groups with two noncomplemented subgroups

Mathematical Notes - The finite groups containing exactly two noncomplemented subgroups are described.     

CsCl effect on the optical properties of the 80GeS2–20Ga2S3 base glass

Optical properties of chalcogenide glasses belonging to the series (80GeS₂–20Ga₂S₃)_100−x (CsCl) _x with x=0;5;10;15;20 were investigated. The linear refractive indices (n ₀) were determined by prism measurements at four wavelengths: 633 nm, 825 nm, 1311 nm, and 1511 nm. Z-scan experiments were performed at 800 nm to measure the non-linear indices (n ₂) and the absorption coefficients (β). CsCl additions in the base glass (80GeS₂–20Ga₂S₃) are characterized by a white shift of the transmission in the visible range and a strong decrease of both n ₀ and n ₂. As the same time, β is also decreasing and this results in a figure of merit FOM=2βλ/n ₂ that remains relatively low at 800 nm, meaning that this series of highly non-linear glasses should be very suitable for optical switching applications at telecommunication wavelengths.     

Evolution of the commensurate and incommensurate magnetic phases of the S = 3/2 kagome staircase Co?V?O? in an applied field

Single crystal neutron diffraction studies have been performed on the S = 3/2 kagome staircase compound Co(3)V(2)O(8) with a magnetic field applied along the magnetization easy-axis ([Formula: see text]). Previous zero-field measurements (Chen Y et al 2006 Phys. Rev. B 74 014430) reported a rich variety of magnetic phases, with a ferromagnetic ground state as well as incommensurate, transversely polarized spin density wave (SDW) phases (with a propagation vector of [Formula: see text]) interspersed with multiple commensurate lock-in transitions. The magnetic phase diagram with [Formula: see text] adds further complexity. For small applied fields, μ(0)H ≈ 0.05 T, the commensurate lock-in phases are destabilized in favor of the incommensurate SDW ones, while slightly larger applied fields restore the commensurate lock-in phase with δ = 1/2 and yield a new commensurate phase with δ = 2/5. For measurements in an applied field, higher-order scattering is observed that corresponds to the second harmonic.