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Bubble Sort is simple. Yet, it seems a bit difficult for high school students. This paper presents a pedagogical methodology: Using Design Sketch to visualize the concepts in Bubble Sort, and to evaluate how this approach assists students…
By using two different invariants for the Rubik's Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually…
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many different ways. In addition, formulas and identities involving these…
There are many open problems and some mysteries connected to the realizations of the associahedra as convex polytopes. In this note, we describe three -- concerning special realizations with the vertices on a sphere, the space of all…
We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \cite{Lambek} and Johnstone \cite{Johnstone} used for monoid and category emedding results. We show that they are planar…
This is a contribution paper from the Double Chooz experiment to the special issue of NPB on neutrino oscillations. The physics and a history of the reactor theta13 experiments, as well as Double Chooz experiment and its neutrino…
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
A review is given of the theoretical ideas concerning the mysterious pentaquark baryons proposed during the first year after its discovery. We focus on the difficulties involved with the constituent quark models and the discrepancy between…
The molecular picture and the constituent-quark model of exotic hadrons are reviewed, with application to the states recently discovered in the hidden-charm and hidden beauty sectors, and to other configurations.
We review some of the possible models that are able to describe the current Universe which point out the future singularities that could appear. We show that the study of the dark energy accretion onto black- and worm-holes phenomena in…
The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…
Discovery of clusters with high symmetrical geometry, such as C60 fullerene, always attract lots of interest because of their diverse nature. However, most of such interesting cluster were sporadically discovered, is there any systematic…
By taking into light the discovery of pentaquark structures like $P_{\psi s}^\Lambda(4338)^0$, $P_c(4380)$ and $P_c(4450)$, we performed the spectroscopy of hidden-bottom pentaquarks. By utilizing special unitary representations, we…
In this paper we study shells of matter and black holes on the expanding bubbles realizing de Sitter space, that were proposed in arXiv:1807.01570. We construct explicit solutions for a rigid shell of matter as well as black hole like…
A polyhedron $\textbf{P} \subset \mathbb{R}^3$ has Rupert's property if a hole can be cut into it, such that a copy of $\textbf{P}$ can pass through this hole. There are several works investigating this property for some specific polyhedra:…
The spectra of the nucleons and the strange hyperons are well described by a harmonic confinement potential for the constituent quarks and an SU(3) flavor-symmetric interaction mediated by the pseudoscalar octet that is associated with the…
A simple cut-and-patch method is presented for the construction and classification for fullerenes belonging to the octahedral point groups, $O$ or $O_h$. In order to satisfy the symmetry requirement of the octahedral group, suitable numbers…
Data from the Canadian Galactic Plane Survey reveal an abundance of HI shells and arcs in the disk of our galaxy. While their shape is suggestive of stellar winds or supernovae influence, very few of these structures have been examined in…
We study a black hole with a blurred mass density instead of a singular one, which is caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses properties, which…
In this paper, we study the behavior of the pseudo-Newtonian force and potential about a higher dimensional rotating black hole. We obtain conditions for the force character from an attractive to repulsive. We also find the conditions under…