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The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…

Consider an order $n$ abelian group $G$ and a tree $T$ on $n$ vertices. When is it possible to (bijectively) label $V(T)$ by $G$ so that along all edges $xy$ of $T$, the sums $x+y$ are distinct? This problem can be traced back to the work…

We report the discovery of a thin stellar stream found in Pan-STARRS1 photometry near the Galactic bulge in the constellation of Ophiuchus. It appears as a coherent structure in the colour-selected stellar density maps produced to search…

In 1995, Marjorie Rice discovered an interesting tiling by using convex pentagons. The authors discovered novel properties of the tilings of convex pentagon which Rice used in the discovery. As a result, many new convex pentagon tilings…

I outline the history and the original proof of the Arnold conjecture on fixed points of Hamiltonian maps for the special case of the torus, leading to a sketch of the proof for general symplectic manifolds and to Floer homology. This is…

Dynamics reduces the orthorhombicity of magnetic stripes in La_2CuO_4+y. The measured stripe incommensuration can be used to determine the oxygen content of the sample.

We present observations of three protoplanetary disks in visible scattered light around M-type stars in the Upper Scorpius OB association using the STIS instrument on the Hubble Space Telescope. The disks around stars 2MASS…

This paper surveys the theory of multiple packings and coverings. The study of multiple arrangements started in the 60s of the last century, and it was restricted mostly to lattice arrangements on the plane or of general arrangements of…

We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labeled graphs that were used to construct canonical bases in…

In the field of topological insulators, the topological properties of quantum states in samples with simple geometries, such as a cylinder or a ribbon, have been classified and understood during the last decade. Here, we extend these…

Observations of the galactic disk at mid-infrared and longer wavelengths reveal a wealth of structures indicating the existence of complexes of recent massive star formation. However, little or nothing is known about the stellar component…

Aperiodic tiling is a well-know area of research. First developed by mathematicians for the mathematical challenge they represent and the beauty of their resulting patterns, they became a growing field of interest when their practical use…

This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions,…

In 1985, physicists Dixon, Harvey, Vafa and Witten studied string theories on Calabi-Yau orbifolds (cf. [DHVW]). An interesting discovery in their paper was the prediction that a certain physicist's Euler number of the orbifold must be…

MUSE observations of the cluster of galaxies CGr32 ($M_{200}$ $\simeq$ 2 $\times$ 10$^{14}$ M$_{\odot}$) at $z$ = 0.73 reveal the presence of two massive star forming galaxies with extended tails of diffuse gas detected in the…

Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.

We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications…

An hieroglyph on n letters is a cyclic sequence of the letters 1,2, . . . , n of length 2n such that each letter appears in the sequence twice.Take an hieroglyph H. Take a convex polygon with 2n sides. Put the letters in the sequence of…

We present two unusual observations of Saturn recorded during the early years of the twentieth century

These are expository notes in which we explain how one can see some exceptional surgeries connecting the suspension of the cat-bat map and the unit tangent bundles to some hyperbolic orbispheres.