Related papers: 13 or 14, Halloween surprise
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
Accounting for the LHCb observation that the reported hidden-charm strange pentaquark $P_{cs}(4459)^0$ can split into two substructures, $P_{cs}(4455)^0$ and $P_{cs}(4468)^0$, with a mass difference of 13 MeV as well as the newly observed…
In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.
We discuss the motivation and the phenomenology of models with either flat or warped extra dimensions. We describe the typical mass spectrum and discovery signatures of such models at the LHC. We also review several proposed methods for…
The paper is devoted to a new direction in SETI. After a general discussion of the field, the authors put forth the hypothesis that the black holes may serve as a physical substratum for intelligent beings. This hypothesis is based on four…
In a previous work we presented a theoretical analysis of the $\Lambda_b \to J/\psi K^- p$ reaction from where a recent experiment by the LHCb collaboration at CERN claimed the existence of two hidden charm pentaquarks, $P_c(4380)^+$ and…
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated solution, which then could be simplified. We discuss some…
These notes are based on the lectures given by the author during Winter Braids IX in Reims in March 2019. We discuss slice knots and why they are interesting, as well as some ways to decide if a given knot is or is not slice. We describe…
Quarks, leptons and heavy vector bosons are suggested to be composed of stable spin-1/2 preons, existing in three flavours, combined according to simple rules. Straightforward consequences of an SU(3) preon-flavour symmetry are the…
A pedagogical overview of strange quark matter and strange stars is presented. After a historical notation of the research and an introduction to quark matter, a major part is devoted to the physics and astrophysics of strange stars, with…
I classify exotic hadrons into two types, "genuine" and "hidden" exotics, and propose that the "hidden" exotics would be interpreted as "chiralons" in the ~U(12)_SF times O(3,1)_L-classification scheme of hadrons. Based upon this conjecture…
I discuss a variety of issues in the physics of excited bottom and charmed hadrons. Recent developments in spectroscopy, strong decays, and production in fragmentation and weak decays are reviewed.
In this paper we introduce the third order Jacobsthal quaternions and the third order Jacobsthal-Lucas quaternions and give some of their properties. We derive the relations between third order Jacobsthal numbers and third order Jacobsthal…
The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.
This is an expanded version of a series of lectures delivered at the 25th Winter School ``Geometry and Physics'' in Srni. After a short introduction to Cartan geometries and parabolic geometries, we give a detailed description of the…
The introduction to this review summarizes chromosphere observation in two figures. The first part showcases the historical emphasis on the eclipse chromosphere in the development of NLTE line formation theory and criticizes 1D modeling.…
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
We give a tree structure on the set of all periodic directions on the golden L, which gives an associated tree structure on the set of periodic directions for the pentagon billiard table and double pentagon surface. We use this to give the…
Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices together with the incidence structure, we investigate variations…
On the 500th anniversary of Albrecht D\"urer's copperplate engraving Melencolia I, we invite readers to join in a time-honored "party game" that has attracted art historians and scientists for many years: guessing the nature and meaning of…