Gabor Frames for Quasicrystals, KK-theory, and Twisted Gap Labeling

We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal $\Lambda,$ and the $K$-theory of the twisted groupoid $C^*$-algebra $\mathcal{A}_\sigma$ arising from a quasicrystal. In particular, we construct a finitely generated projective module \mathcal{H}_\L over $\mathcal{A}_\sigma$ related to time-frequency analysis, and any multiwindow Gabor frame for $\Lambda$ can be used to construct an idempotent in $M_N(\mathcal{A}_\sigma)$ representing \mathcal{H}_\L in $K_0(\mathcal{A}_\sigma).$ We show for lattice subsets in dimension two, this element corresponds to the Bott element in $K_0(\mathcal{A}_\sigma),$ allowing us to prove a twisted version of Bellissard's gap labeling theorem

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Temperature-dependent Raman scattering of DyScO3 and GdScO3 single crystals

We report a temperature-dependent Raman scattering investigation of DyScO3 and GdScO3 single crystals from room temperature up to 1200 {\deg}C. With increasing temperature, all modes decrease monotonously in wavenumber without anomaly, which attests the absence of a structural phase transition. The high temperature spectral signature and extrapolation of band positions to higher temperatures suggest a decreasing orthorhombic distortion towards the ideal cubic structure. Our study indicates that this orthorhombic-to-cubic phase transition is close to or higher than the melting point of both rare-earth scandates (\approx 2100 {\deg}C), which might exclude the possibility of the experimental observation of such a phase transition before melting. The temperature-dependent shift of Raman phonons is also discussed in the context of thermal expansion

Phonon Raman scattering of perovskite LaNiO3 thin films

We report an investigation of perovskite-type LaNiO3 thin films by Raman scattering in both various scattering configurations and as a function of temperature. The room-temperature Raman spectra and the associated phonon mode assignment provide reference data for phonon calculations and for the use of Raman scattering for structural investigations of LaNiO3, namely the effect of strain in thin films or heterostructures. The temperature-dependent Raman spectra from 80 to 900 K are characterized by the softening of the rotational A1g mode, which suggest a decreasing rhombohedral distortion towards the ideal cubic structure with increasing temperature

Evaluation of a new supply strategy based on stochastic programming for a fashion discounter

Fashion discounters face the problem of ordering the right amount of pieces in each size of a product. The product is ordered in pre-packs containing a certain size-mix of a product. For this so-called lot-type design problem, a stochastic mixed integer linear programm was developed, in which price cuts serve as recourse action for oversupply. Our goal is to answer the question, whether the resulting supply strategy leads to a supply that is significantly more consistent with the demand for sizes compared to the original manual planning. Since the total profit is influenced by too many factors unrelated to sizes (like the popularity of the product, the weather or a changing economic situation), we suggest a comparison method which excludes many outer effects by construction. We apply the method to a real-world field study: The improvements in the size distributions of the supply are significant.Comment: 5 pages, 1 tabl