A family of coupled nanostrips with varying dimensions is demonstrated exhibiting optical magnetic responses across the whole visible spectrum, from red to blue. We refer to such a phenomenon as rainbow magnetism. The experimental and analytical studies of such structures provide us with a universal building block and a general recipe for producing controllable optical magnetism for various pra...

We have investigated infinitely long, monostrand Pt nanowires theoretically, and found that they exhibit Hund’s rule magnetism. We find a spin moment of 0.6 μB per atom, at the equilibrium bond length. Its magnetic moment increases with stretching. The origin of the wire magnetism is analyzed and its effect on the conductance through the wire is discussed.

In 1600, William Gilbert of Colchester published the standard treatise on the difference between magnetism and electricity. He died a few years later, and his analysis was the canon of European thinking on the subject for 300 years. In 1894, Pierre Curie suggested that electricity and magnetism might be coupled in materials, but theoretical and experimental validation only came at the end of th...

The paper shows that there is no finite set of forbidden minors which characterizes classes of independence models that are representable by Gaussian, discrete and binary distributions, respectively. In addition, a way to prove the nonexistence of a finite characterization for any other class of independence models is suggested. MSC 2000: 60A99, 68T30, 94A15

The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of Centers Program in the interest of information exchange. UCF and the U.S. Government assumes no liability for the contents or use thereof.

In this paper, we obtain a forbidden-minor characterization of the class of binary gammoids M such that, for every pair of elements x, y of M, both the splitting matroid Mx,y and the element splitting matroid M ′ x,y are binary gammoids.

A connected edge-colored graphG is said to be rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors, and the rainbow connection number rc(G) ofG is the minimum number of colors that can make G rainbow-connected. We consider families F of connected graphs for which there is a constant kF such that every connected F-free graph G with...

Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.

We characterize graphs that have intersection representations using unit intervals with open or closed ends such that all ends of the intervals are integral in terms of infinitely many minimal forbidden induced subgraphs. Furthermore, we provide a quadratic-time algorithm that decides if a given interval graph admits such an intersection representation.