Related papers: M\"obius strips before M\"obius: Topological hints…
In recent archaeological investigations of Pompeii Regio V houses, a series of new, rather enigmatic images on the floors of the entrance and of the Tablinium of the so called House of Orion have been unearthed. These images are presented…
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
We present the first results of a comprehensive census of the stellar content of the nearby OB associations based on Hipparcos positions, proper motions and parallaxes for 12842 candidate member stars distributed over 21 fields on the sky.…
Signed graphs are studied since the middle of the last century. Recently, the notion of homomorphism of signed graphs has been introduced since this notion captures a number of well known conjectures which can be reformulated using the…
In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.
We investigate the structure of the tri-pants graph, a simplicial graph introduced by Maloni and Palesi, whose vertices correspond to particular collections of homotopy classes of simple closed curves of the twice-punctured torus, called…
The Ophiuchus stellar stream presents a dynamical puzzle: its old stellar populations ($\sim 12$ Gyr) cannot be reconciled with (1) its orbit in a simple model for the Milky Way potential and (2) its short angular extent, both of which…
The discovery and characteristics of transneptunian binaries are reviewed. In the 20 years since their first discovery, a wealth of detail has emerged including the frequency of binaries in different populations, their relative sizes and…
Grid homology for MOY graphs is immediately defined from grid homology for transverse spatial graphs developed by Harvey and O'Donnol in 2017. We studied some properties of grid homology for MOY graphs such as the oriented skein relation,…
We present the results of detailed N-body simulations of clusters moving in a realistic Milky Way (MW) potential. The strong interaction with the bulge and the disk of the Galaxy leads to the formation of tidal tails, emanating from…
We derive, from the work of M. Ratner on joinings of time-changes of horocycle flows and from the result of the authors on its cohomology, the property of orthogonality of powers for non-trivial smooth time-changes of horocycle flows on…
Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ (LSCO) is an archetype with static spin stripes at low…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
This review is devoted to open strings, and in particular to the often surprising features of their spectra. It follows and summarizes developments that took place mainly at the University of Rome ``Tor Vergata'' over the last decade, and…
We prove that strictly mean convex toroids contain infinitely many (geometrically distinct) embedded free boundary minimal M\"obius bands as well as infinitely many embedded free boundary minimal annuli. The surfaces in both families are…
We show that from historical record and mathematic analysis, "fractal expressions" may have been a conscious pursuit at least one thousand years ago as an element of beauty in ancient Chinese calligraphy.
Recent observations of HL Tau revealed remarkably detailed structure within the system's circumstellar disc. A range of hypotheses have been proposed to explain the morphology, including, e.g., planet-disc interactions, condensation fronts,…
This article is a translation of Michael Sadowsky's original paper "Die Differentialgleichungen des M\"obiusschen Bandes." in Jahresbericht der Deutschen Mathematiker-Vereinigung 39 (2. Abt. Heft 5/8, Jahresversammlung vom 16. bis 23.…
An edge-on debris disk was detected in 2015 around the young, nearby A0V star HD 110058. The disk showed features resembling those seen in the disk of beta Pictoris that could indicate the presence of a perturbing planetary-mass companion…
This manuscript introduces Diophantine labeling, a new way of labeling of the vertices for finite simple undirected graphs with some divisibility condition on the edges. Maximal graphs admitting Diophantine labeling are investigated and…