To parallelize applications that require the use of random numbers, an efficient and good quality parallel random number generator is required. In this paper, we study the parallelization of lagged Fibonacci generators for distributed memory parallel computers. Two popular ways of generating a random sequence in parallel are studied: the contiguous subsequence technique and the leapfrog techniq...

The Fibonacci sequence {Fn} is defined by the recurrence relation Fn = Fn−1+ Fn−2, for n ≥ 2 with F0 = 0 and F1 = 1. The Lucas sequence {Ln} , considered as a companion to Fibonacci sequence, is defined recursively by Ln = Ln−1 + Ln−2, for n ≥ 2 with L0 = 2 and L1 = 1. It is well known that F−n = (−1)Fn and L−n = (−1)Ln, for every n ∈ Z. For more detailed information see [9],[10]. This paper pr...

We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, Kagome artificial spin ice (ASI). The number strong modes in FMR depend on orientation applied DC magnetic field. In addition, discontinuities observed field-frequency dispersion curves also field orientation, and signal a multi-step magnetization reversal, which is caused by reduced energy...

The aim of this paper is to construct general forms ordinary generating functions for special numbers and polynomials involving Fibonacci type polynomials, Lucas Chebyshev Sextet Humbert-type chain anti-chain rank the lattices, length any alphabet words, partitions, other graph polynomials. By applying Euler transform Lambert series these functions, many new identities relations are derived. us...

In this paper we consider the class of binary trees and present the results of a comprehensive experimental study on the four most representative algorithms for drawing trees, one for each of the following treedrawing approaches: Separation-Based, Path-based, Level-based, and Ringed Circular Layout. We establish a simpler, more intuitive format for storing binary trees in files and create a lar...

Double Fibonacci sequences (xn,k) are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.

The propagation of light in nonperiodic quasicrystals is studied by ultrashort pulse interferometry. Samples consist of multilayer dielectric structures of the Fibonacci type and are realized from porous silicon. We observe mode beating and strong pulse stretching in the light transport through these systems, and a strongly suppressed group velocity for frequencies close to a Fibonacci band gap...

Abstract In this letter, we show a connection between the random Fibonacci recurrence and the visible points of the plane. In particular, we show that by suitably modifying the rules of the random Fibonacci map, there is a unique correspondence between the visible points (points with relative prime coordinates) of the first quadrant and the vertices of a self-similar graph (what we call the Fib...

This paper proposes a novel metaheuristic Child Drawing Development Optimization (CDDO) algorithm inspired by the child's learning behavior and cognitive development using golden ratio to optimize beauty behind their art. The was first introduced famous mathematician Fibonacci. of two consecutive numbers in Fibonacci sequence is similar, it called ratio, which prevalent nature, art, architectur...