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We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…

Well-graded families, extremal systems and maximum systems (the last two in the sense of VC-theory and Sauer-Shelah lemma on VC-dimension) are three important classes of set systems. This paper aims to study the notion of duality in the…

In this article, we use concepts and methods from the theory of simplicial sets to study discrete Morse theory. We focus on the discrete flow category introduced by Vidit Nanda, and investigate its properties in the case where it is defined…

We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere $\mathbb{S}^2$ depending on the length of an ellipse determined by the indexes of its singularities. In addition, for minimizing…

Conventional magnetic flux concentrators (MFCs) are typically designed with solid structures, which may not be optimal for applications requiring lightweight design or material efficiency. In this study, we investigate the feasibility of…

Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…

We introduce two common divisor graphs associated with a finite skew brace, based on its $\lambda$- and $\theta$-orbits. We prove that the number of connected components is at most two and the diameter of a connected component is at most…

Let A be a union of smooth plane curves C_i, such that each singular point of A is quasihomogeneous. We prove that if C is a smooth curve such that each singular point of A U C is also quasihomogeneous, then there is an elementary…

Spinor--Vector Duality (SVD) has been observed in worldsheet constructions of heterotic--string compactifications. Recently, its realisation in the effective field theory limit of string vacua in six and five dimensions has been…

A versatile and portable magnetically shielded room with a field of (700 \pm 200) pT within a central volume of 1m x 1m x 1m and a field gradient less than 300 pT/m is described. This performance represents more than a hundred-fold…

The contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal…

We show how the low-energy properties of the 2-leg XXZ spin-1/2 ladders with general anisotropy parameter $\Delta $ on closed geometries can be accounted for in the framework of the m-reduction procedure developed in [1]. In the limit of…

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational…

Chiral multifold fermions in solids exhibit unique band structures and topological properties, making them ideal for exploring fundamental physical phenomena related to nontrivial topology, chirality, and symmetry breaking. However, the…

Let M denote a compact, oriented 3-manifold and let a denote a contact 1-form on M. This article proves that the vector field that generates the kernel of the 2-form da has at least one closed, integral curve.

We show that for every complete Riemannian surface $M$ diffeomorphic to a sphere with $k \geq 0$ holes there exists a Morse function $f:M \rightarrow \mathbb{R}$, which is constant on each connected component of the boundary of $M$ and has…

Given a geometric structure on $\mathbb{R}^{n}$ with $n$ even (e.g. Euclidean, symplectic, Minkowski, pseudo-Euclidean), we analyze the set of points inside the domain of definition of an arbitrary given $\mathcal{C}^1$ vector field, where…

It is highly desirable to modify and improve the Dirac electron system of graphene for novel electronic properties and promising applications. For this purpose, we study 2D heterostructures consisting of graphene and monolayer TMDs by means…

We study linearly independent complex line fields on almost-complex manifolds, which is a topic of long-standing interest in differential topology and complex geometry. A necessary condition for the existence of such fields is the vanishing…

In neutral graphene dots the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped…