Photonic synthetic materials provide an opportunity to explore the role of microscopic
quantum phenomena in determining macroscopic material properties. There are, however …

During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …

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 …

Materials science and the study of the electronic properties of solids are a major field of
interest in both physics and engineering. The starting point for all such calculations is single …

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive
interference of Bloch wave functions encoded in only lattice symmetry. Here, we develop a …

We study the spectral properties of Schrödinger operators on perturbed lattices. We shall
prove the non-existence or the discreteness of embedded eigenvalues, the limiting …

Determining and analyzing the spectra of graphs is an important and exciting research topic
in mathematics science and theoretical computer science. The eigenvalues of the …

We introduce the notion of “fractafold”, which is to a fractal what a manifold is to a Euclidean
half-space. We specialize to the case when the fractal is the Sierpinski gasket SG. We show …

This is an expository article on discrete geometric analysis based on the lectures which the
author gave at Gregynog Hall, University of Wales, as an activity of the Project “Analysis on …

This paper is to point out that proposition 3.3 and some results from'Some physical and
chemical indices of clique-inserted lattices'(Zhang 2013 J. Stat. Mech. P10004) are incorrect …