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In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…

This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complete in the context of finite partial orders, as general as…

In these two lectures I will discuss some outstanding problems in the standard model of cosmology, concentrating on the physics that might be related to the title of this school, ``Searching for the totally unexpected in the LHC era.'' In…

We highlight topical issues in hyperon spectroscopy that will be accessible when a secondary beam of neutral kaons is created in Hall D at Jefferson Lab as proposed to the JLab Program Advisory Committee. The new beam will have a flux of…

We describe some three-dozen curious phenomena manifested by parabolas inscribed or circumscribed about certain Poncelet triangle families. Despite their pirouetting motion, parabolas' focus, vertex, directrix, etc., will often sweep or…

We report a small advance on a question raised by Robertson, Schweitzer, and Wagon in [RSW02]. They constructed a genus-13 polyhedron built from bricks without corners, and asked whether every genus-0 such polyhedron must have a corner. A…

In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them.

In this proceedings report, we discuss unique features of charmed, or in general heavy, baryons with one heavy quark. A well and long-term known phenomena, the distinction of the two modes of the rho and lambda type of a three-quark system…

A fake octagon is a genus two translation surface with only one singular point and the same periods as the octagon. Existence of infinitely many fakes was first established by McMullen in 2007, and more generally follows from dynamical…

This resource letter is designed to guide students, educators, and researchers through (some of) the literature on black holes. Both the physics and astrophysics of black holes are discussed. Breadth has been emphasized over depth, and…

Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…

Dedicated to Solomon Marcus, the current paper continues a recent series about our meetings. Trying to recreate the spirit of those meetings, we first propose a discussion which started as a high-school problem. The main part of the current…

Link homology theories (such as knot Floer homology and Khovanov homology) have become indispensable tools for studying knots and links, including powerful 4-dimensional obstructions. These notes, based on lectures given at the 2024 Georgia…

The aim of this paper is two-fold. First, the study of $C_{12}$-structure (called by us corner structure) is extended to the general case without any condition, unlike our previous papers (see, \cite{BB, BG2, BG, BBB}). Second, starting…

The study is about a basic shadow experiment, which was enriched with a simulation to understand the reasoning of participants when we use a trick. Two light sources create an umbra and penumbra behind the objects. With this experiment, we…

The possibility to determine the axial strange form factor of the nucleon from elastic neutrino-nucleon scattering experiments is studied. The existing experimental information is shortly mentioned and several observables which could be…

This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to…

We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial…

Wormholes are extremely attractive objects for research, and although many mathematical and physical properties of these objects have been discovered and studied in the recent decades, there remain many unsolved problems and opportunities…

Dark matter is one of the most intriguing scientific mysteries of our time and offers exciting instructional opportunities for physics education in high schools. The topic is likely to engage and motivate students in the classroom and…