The article surveys the main topics, techniques, and results of the theory of periodic
operators arising in mathematical physics and other areas. Close attention is paid to …

Small-radius tubular structures have attracted considerable attention in the last few years,
and are frequently used in different areas such as Mathematical Physics, Spectral Geometry …

This paper outlines a program in what one might call spectral sheaf theory—an extension of
spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the …

The purpose of this text is to set up a few basic notions concerning quantum graphs, to
indicate some areas addressed in the quantum graph research, and to provide some …

In Generalized Barycentric Coordinates in Computer Graphics and Computational
Mechanics, eminent computer graphics and computational mechanics researchers provide …

We study the spectrum of the normalized Laplace operator of a connected graph $\Gamma
$. As is well known, the smallest nontrivial eigenvalue measures how difficult it is to …

This article builds upon the techniques developed within our previous investigation of the
relativistic and gravitational properties of the Wolfram Model-a new discrete spacetime …

Denoising diffusion (score-based) generative models have become a popular choice for
modeling complex data. Recently, a deep connection between forward-backward stochastic …

With remarkable stability and exceptional optoelectronic properties, two-dimensional (2D)
halide layered perovskites hold immense promise for revolutionizing photovoltaic …

We establish a connection between the stability of an eigenvalue under a magnetic
perturbation and the number of zeros of the corresponding eigenfunction. Namely, we …