Affine Deligne-Lusztig varieties in affine flag varieties

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.Comment: 44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of

Optical study of orbital excitations in transition-metal oxides

The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R=La, Sm, Y), LaMnO3, Y2BaNiO5, CaCu2O3, and K4Cu4OCl10, ranging from early to late transition-metal ions, from t_2g to e_g systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yield good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g., the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular in case of the orbital excitations at about 0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing.Comment: published version, discussion of TiOCl extended to low T, improved calculation of orbital excitation energies in TiOCl, figure 16 improved, references updated, 33 pages, 20 figure

Posterior vitreous detachment following intravitreal drug injection

BACKGROUND: To evaluate the incidence of posterior vitreous detachment (PVD) induced by intravitreal injection of different intravitreal drugs. METHODS: This prospective observational study included 61 patients (61 eyes) with different underlying retinal diseases: exudative age-related macular degeneration (n = 47), cystoid macular edema (CME) after retinal vein occlusion (n = 8), and CME of other origin (n = 6). Bevazicumab (1.25 mg) was injected into 25 eyes, ranibizumab (0.5 mg) into 27 eyes, triamcinolone (4 mg) into six eyes, and a combination of bevacizumab and triamcinolone into three eyes. Patients with initial PVD were excluded. Patients were followed for at least 4–6 weeks after their last injection by Fourier-domain OCT, fundus biomicroscopy and ultrasound B-examination. RESULTS: Overall, 15 of 61 eyes developed a PVD after intravitreal injection (n = 6 after ranibizumab, n = 7 after bevacizumab and n = 2 after triamcinolon) within a mean follow-up period of 11.1 weeks. PVD occurred in three eyes after the first injection, in three eyes after the second, and in seven eyes after the third injection. Incidence of PVD correlated with increasing age. CONCLUSION: Intravitreal injection of commonly-used drugs seems to induce posterior vitreous detachment, which may thus influence the outcome of the underlying disease