A simple numerical method to study the effect of an applied magnetic field on the energy spectrum of non-periodic superlattice structures is presented. The magnetic field could be either parallel or perpendicular to the growth direction. Our method is based on the transfer matrix technique and on the effective mass approximation. We discuss the advantages and disadvantages of the proposed appro...

In this paper we did a generalization of Hadamard product of Fibonacci Q matrix and Fibonacci Q−n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices. Mathematics Subject Classification: Primary 11B25, 11B37, 11B39, Secondary 11C20

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.

Let us begin by defining a generalized Fibonacci sequence (gn) with all gn in some abelian group as a sequence that satisfies the recurrence gn = gn−1 + gn−2 as n ranges over Z. The Fibonacci sequence (Fn) is the generalized Fibonacci sequence with integer values defined by F0 = 0 and F1 = 1. Recall also the Binet formula: for any integer n, Fn = (α − β)/ √ 5, where α = (1 + √ 5)/2 and β = (1− ...

We study the Fibonacci sets from the point of view of their quality with respect to discrepancy and numerical integration. Let {bn}n=0 be the sequence of Fibonacci numbers. The bn-point Fibonacci set Fn ⊂ [0, 1] is defined as Fn := {(μ/bn, {μbn−1/bn})} μ=1, where {x} is the fractional part of a number x ∈ R. It is known that cubature formulas based on Fibonacci set Fn give optimal rate of error...

Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum of nonconsecutive Fibonacci numbers. This theorem induces a binary numeration system for the positive integers known as Fibonacci coding. Fibonacci code is a variable-length prefix code that is robust against insertion and deletion errors and is useful in data transmission and data compression. In this pape...

The Fibonacci dimension fdim(G) of a graph G is introduced as the smallest integer f such that G admits an isometric embedding into Γf , the f -dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of the isometric and lattice dimension, provide a combinatorial characterization of the Fibonacci dimension using properties of an associated graph, and establish ...

In a recent paper, Kalman [3] derives many interesting properties of generalized Fibonacci numbers. In this paper, we take a different approach and derive some other interesting properties of matrices of generalized Fibonacci numbers. As an application of such properties, we construct an efficient algorithm for computing matrices of generalized Fibonacci numbers. The topic of generalized Fibona...

In this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers. c © 2007 Elsevier Ltd. All rights reserved.