Related papers: Trigonometric inequalities for Fibonacci chains
The aim of this paper is to show both analytically and numerically the existence of a subwavelength phononic bandgap in bubble phononic crystals. The key is an original formula for the quasi-periodic Minnaert resonance frequencies of an…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
In this paper, we bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to $m$-extensions. It allows us to identify gapsets and, in general, $m$-extensions with tilings of boards. As…
We consider fermionic and bosonic quantum chains where a defect separates two subsystems and compare the corresponding entanglement spectra. With these, we calculate their R\'enyi entanglement entropies and obtain analytical formulae for…
Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci…
The millimeter wave (mmWave) band will be exploited to address the growing demand for high data rates and low latency. The higher frequencies, however, are prone to limitations on the propagation of the signal in the environment. Thus,…
We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and…
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average…
Phononic crystals exhibit Bragg bandgaps, frequency regions within which wave propagation is forbidden. In solid continua, bandgaps are the outcome of destructive interferences resulting from periodically alternating layers. Under certain…
The spectral evolution from periodic structure to random structure has always been an interesting topic in solid state physics, the generalized n-component Fibonacci sequences (n- CF) provide a convenient tool to investigate such process…
We study theoretically the transmission spectra in one-dimensional photonic quasicrystals, made up of SiO$_2$($A$) and TiO$_2$($B$) materials, organized following the Octonacci sequence, where the $n$th-stage of the multilayer $S_{n}$ is…
The star-triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular and hexagonal lattices. Among the consequences are box-crossing (RSW)…
We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $\theta=45^\circ$ and a pair of hexagonal lattices with…
Millimeter wave (mm-wave) communications is considered a promising technology for 5G networks. Exploiting beamforming gains with large-scale antenna arrays to combat the increased path loss at mm-wave bands is one of its defining features.…
Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal…
The phenomenon of bound state in the continuum (BIC) with infinite quality factor and lifetime has emerged in recent years in photonics as a new tool of manipulating light-matter interactions. However, most of the investigated structures…
We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between…
Fibonacci word fractals are a class of fractals that have been studied recently, though the word they are generated from is more widely studied in combinatorics. The Fibonacci word can be used to draw a curve which possesses…
We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…