Related papers: M\"obius strips before M\"obius: Topological hints…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we…
We introduce the crisscross and the cup, both of which are immersed $3$-twist polygonal paper Moebius band of aspect ratio $3$. We explain why these two objects are limits of smooth embedded paper Moebius bands having knotted boundary. We…
N=(2,1) heterotic string theory provides clues about hidden structure in M-theory related to string duality; in effect it geometrizes some aspects of duality. The program whereby one may deduce this hidden structure is outlined, together…
The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of…
We generalize an identity, first found by Bremner, for the action of three nested Nambu brackets.
It is shown that every complete n-vertex simple topological graph has at least Omega(n^{1/3}) pairwise disjoint edges, and these edges can be found in polynomial time. This proves a conjecture of Pach and T\'oth.
The spectrum of any star viewed through a sufficient quantity of diffuse interstellar material reveals a number of absorption features collectively called diffuse interstellar bands (DIBs). The first DIBs were reported 90 years ago, and…
Using a recent result of Bowden, Hensel and Webb, we prove the existence of homeomorphisms with positive stable commutator length in the groups of homeomorphisms of the real projective plane and M\"obius strip which are isotopic to the…
Spiral arms in protoplanetary discs are thought to be linked to the presence of companions. We test the hypothesis that the double spiral arm morphology observed in the transition disc MWC 758 can be generated by an $\approx 10$ M$_{\rm…
The B fields in OB stars (BOB) survey is an ESO large programme collecting spectropolarimetric observations for a large number of early-type stars in order to study the occurrence rate, properties, and ultimately the origin of magnetic…
Cross-identifications for 14,574 intrinsically luminous galactic stars (mostly OB stars) to objects in the 2MASS survey have been determined using a search box of +/-0.0015 degrees (+/- 5.4 arcsec) in both RA and Dec. Instructions on…
We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.
First, we consider order-$n$ ribbon tilings of an $M$-by-$N$ rectangle $R_{M,N}$ where $M$ and $N$ are much larger than $n$. We prove the existence of the growth rate $\gamma_n$ of the number of tilings and show that $\gamma_n \leq (n-1)…
Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mirror cut surface. By using a surface-link group of a mirror…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
Our recent discoveries of magnetic fields in a small number of Herbig Ae/Be (HAeBe) stars, the evolutionary progenitors of main sequence A/B stars, raise new questions about the origin of magnetic fields in the intermediate mass stars. The…
When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a…
A conjecture regarding the structure of expander graphs is discussed.
We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a…