Related papers: Trigonometric inequalities for Fibonacci chains
We study graphene on a photonic crystal operating in the terahertz (THz) spectral range. We show that the absorption of graphene becomes a modulated function of frequency and can be enhanced by more than three times at specific frequency…
Chiral quasi-bound states in the continuum (q-BICs) have recently emerged in metaphotonics as resonances that combine ultrahigh quality factors with near-unity circular polarization. However, these states are typically confined to the…
We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental designs and radial basis function approximation. However, it…
New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit $q \to 1$, they reduce to the para-Racah polynomials which are orthogonal with respect to a quadratic…
We study the relationship between the electronic spectrum structure and the configurational order of one-dimensional quasiperiodic systems. We take the Fibonacci case as an specific example, but the ideas outlined here may be useful to…
Terahertz wireless communications offer abundant untapped spectrum and are regarded as a promising playground for next-generation high-throughput links. Yet oscillator phase noise becomes the dominant impairment at such high frequencies,…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
We show that strong pairing correlations in Fermi gases lead to the appearance of a gap-like structure in the RF-spectrum, both in the balanced superfluid and in the normal phase above the Clogston-Chandrasekhar limit. The average RF-shift…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches…
We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and…
We suggest the statistical spectral theory of oscillations in quasi-optical cavity resonator filled with random inhomogeneities. It is shown that inhomogeneities in the resonator result in intermode scattering leading to the shift and…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
We report theoretical electronic structure of Fibonacci superlattices of narrow-gap III-V semiconductors. Electron dynamics is accurately described within the envelope-function approximation in a two-band model. Quasiperiodicity is…
We consider the problem of finding quasiperiodicities in a Fibonacci string. A factor u of a string y is a cover of y if every letter of y falls within some occurrence of u in y. A string v is a seed of y, if it is a cover of a superstring…
The Fibonacci cube of dimension n, denoted as $\Gamma$ n , is the subgraph of n-cube Q n induced by vertices with no consecutive 1's. In this short note we prove that asymptotically all vertices of $\Gamma$ n are covered by a maximum set of…
The sequence of partial sums of Fibonacci numbers, beginning with $2$, $4$, $7$, $12$, $20$, $33,\dots$, has several combinatorial interpretations (OEIS A000071). For instance, the $n$-th term in this sequence is the number of length-$n$…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…