Osculation for conic fibrations.

Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior. Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface for k = 2, while their structure plays a significant role for k >= 3. The dimension of the osculating space at any point is studied taking into account the possible existence of curves of low degree transverse to the fibers, and several examples are discussed to illustrate concretely the various situations arising in this analysis. As an application, a complete description of the osculatory behavior of Castelnuovo surfaces is given. The case k = 3 for del Pezzo surfaces is also discussed, completing the analysis done for k = 2 in a previous paper by the authors (2001). Moreover, for conic fibrations X subset of P-N whose k-th inflectional locus has the expected codimension, a precise description of this locus is provided in terms of Chern classes. In particular, for N = 8, it turns out that either X is hypo-osculating for k = 3, or its third inflectional locus is 1-dimensional

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.

Child labor and inadequate family income; preliminary report on a study of the work and welfare of children of agricultural laborers in Hidalgo County, Texas.

Cover title.

Zur geschichte und beschreibung alter und neuer büchersammlungen im königreich Würtemberg, insbesondere der Königlichen öffentlichen bibliothek in Stuttgart und der mit derselben verbundenen münz-, kunst- und alterhümersammlung.

Aus den Würtembergischen jahrbüchern von J.G.D. v. Memminger besonders abgedruckt.

Lucian und die philosophenschulen.

Sonderabdruck aus den Neuen jahrbüchern. Jahrgang 1902. I. abteilung. IX. band.

Topics in differential geometry.

Based on lectures given in the spring of 1949; a few of the latest results of work done since that time have been included.

The way of health insurance

Includes bibliographical references.

Social forces in American history,

Mode of access: Internet.

Griechische elemente in den romanischen sprachen.

Sonderabdruck aus den Neuen jahrbúchern. 1905. I. abteilung. XV. band, 6. heft.

Eidolyzer: a hardware realization of context-guided picture interpretation.

Cover title.

Design of a high speed A/D converter.

"COO-1469-0101."