Related papers: Graphene nanocones and Pascal matrices

One of the aims of this paper is to provide a short survey on the Z2-graded, the symmetric and the left (right) generalizations of the classical determinant theory for square matrices with entries in an arbitrary (possibly non-commutative)…

Graphene and some graphene like two dimensional materials; hexagonal boron nitride (hBN) and silicene have unique mechanical properties which severely limit the suitability of conventional theories used for common brittle and ductile…

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function…

In this work we argue that it is important to make a proper choice of the unit cell within tight-binding theory if one aims to compute the optical matrix elements. By considering zigzag graphene nanoribbons, we demonstrate that the band…

Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be…

We prove that the maximum determinant of an $n \times n $ matrix, with entries in $\{0,1\}$ and at most $n+k$ non-zero entries, is at most $2^{k/3}$, which is best possible when $k$ is a multiple of 3. This result solves a conjecture of…

Let $G$ be a connected graph on $n$ vertices and $D(G)$ its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or {a} unicyclic graph. In…

The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like…

The objective of this paper is to develop a general algebraic theory of supertropical matrix algebra, extending [11]. Our main results are as follows: * The tropical determinant (i.e., permanent) is multiplicative when all the determinants…

A (global) determinantal representation of hypersurface in P^n is a matrix, whose entries are linear forms in homogeneous coordinates and whose determinant defines the hypersurface. We study the properties of such representations for…

Understanding the adhesion between graphene and other materials is crucial for achieving more reliable graphene-based applications in electronic devices and nanocomposites. The ultra-thin profile of graphene, however, poses significant…

We establish the $\#P$-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing $\lambda$-immanants of $0$-$1$ matrices is $\#P$-hard whenever the…

We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency…

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

We investigate the reflectionlessness and invisibility properties in the transverse electric (TE) mode solution of a linear homogeneous optical system which comprises the $\mathcal{PT}$-symmetric structures covered by graphene sheets. We…

Two-dimensional graphene, carbon nanotubes and graphene nanoribbons represent a novel class of low dimensional materials that could serve as building blocks for future carbon-based nanoelectronics. Although these systems share a similar…

There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…

An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…