Schur rings over a Galois ring of odd characteristic

It is proved that any Schur ring over a Galois ring of odd characteristic is either normal, or of rank 2, or a non-trivial generalized wreath product. The normal Schur rings are characterized as a special subclass of the cyclotomic Schur rings.     

Invariant Functions on Simple Orders

It is shown that any continuous invariant function on a doubly homogeneous simple order is a polynomial with respect to supremum and infimum operations.     

Lost heat capacity and entropy in the helical magnet MnSi

The heat capacity of MnSi at B = 0 and B = 4 T was measured in the temperature range 2.5-100 K. To analyze the data, calculations of the phonon spectrum and phonon density of states in MnSi were performed. The calculated phonon frequencies were confirmed by means of inelastic neutron scattering. The analysis of the data suggests the existence of negative contributions to the heat capacity and entropy of MnSi at T > T(c) that may imply a specific ordering in the spin subsystem in the paramagnetic phase of MnSi.     

Link Homologies and the Refined Topological Vertex

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R ₁, R ₂). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.     

Raman investigation of hydrostatic and nonhydrostatic compressions of OH‐ and F‐apophyllites up to 8 GPa

Layer silicates F‐ and OH‐apophyllites, KCa₄Si₈O₂₀(F, OH)·8H₂O, have been investigated by Raman spectroscopy at hydrostatic and nonhydrostatic pressures up to ~8 GPa in diamond anvil cells using a 4 : 1 methanol–ethanol mix as pressure‐transmitting medium. Our experiments show that at hydrostatic compression, apophyllites retain their crystalline states (i.e. no amorphization) up to 5 GPa. The wavenumbers of most bands exhibit linear dependences on pressure, except for a few ones, e.g. at 162 and 3565 cm^–1 in OH‐form (160.5 and 3558 cm^–1 in F‐form) that show nonlinear dependences. Nonhydrostatic compression with additional uniaxial loading induces amorphization of apophyllites. The majority of the bands in OH‐apophyllite decreases markedly in intensity and shows considerable broadening under nonhydrostatic compression up to 3–6 GPa. In addition, the wavenumbers of several bands at nonhydrostatic compression exhibit considerable nonlinear dependences on pressure with strong hysteresis. These bands are mainly associated with vibrations of the interlayer ions and molecules and also of stretching and bending silicate sheets, hence being highly sensitive to the interlayer distance. Finally, we have calculated the lattice dynamics of F‐apophyllite and interpreted the majority of bands, and these data are used to explain the complex baric behavior of the bands. Copyright © 2011 John Wiley & Sons, Ltd.     

A model for the dissociative adsorption of N2O on Cu(1 0 0) using a continuous potential energy surface

For the first time, a continuous ab initio potential energy surface (PES) taking into account all molecular degrees of freedom is built and used to model the reaction of a polyatomic molecule with a surface. DFT slab calculations are used to sample the configuration space of the system N₂O/Cu(1 0 0), and the PES function is built with a method of Manzhos and Carrington [J. Chem. Phys. 127 (2007) 014103] using dimensionality reduction from only 4300 single-point energies. Molecular dynamics simulations are performed on the PES to calculate the probability of dissociative adsorption.     

Expansion of analytic functions in q-orthogonal polynomials

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.      

Optically active Babinet planar metamaterial film for terahertz polarization manipulation

A planar Babinet‐inverted dimer metamaterial possessing strong optical activity is proposed and characterized. An original fabrication method to produce large area (up to several cm²) freely suspended flexible metallic membranes is implemented to fabricate the metamaterial. Its optical properties are characterized by terahertz time‐domain spectroscopy, revealing anisotropic transmission with high optical activity. A simple coupled resonator model is applied to explain the principal optical features of the dimers, with predictive power of positions and number of resonances through a parametrical model. The model is validated for correct polarization‐dependent quantitative results on the optical activity in transmission spectra. The fabrication method presented in this work as well as the slit dimer design has great potential for exploitation in terahertz optics.