The combinatorial properties of the Fibonacci innnite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity , quasicrystals etc. In this note, we introduce the singular words of the Fibonacci innnite word and discuss their properties. We establish two decompositions of the Fibonacci word in singu...

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...

In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.

In this paper, we define (h(x), g(y))-extension of the Fibonacci p-numbers. We also define golden (p, h(x), g(y))-proportions where p (p = 0, 1, 2, 3, · · · ) and h(x)(> 0), g(y)(> 0) are polynomials with real coefficients. The relations among the code elements of a new Fibonacci matrix, Gp,h,g, (p = 0, 1, 2, 3, · · · ), h(x) (> 0), g(y) (> 0) coincide with the relations among the code matrix f...

We give the bicomplex Gaussian Fibonacci and Lucas numbers establish generating functions Binet’s formulas related to these numbers. Also, we present summation formula, matrix representation Honsberger identity their relationship between Finally, show relationships among Fibonacci, Lucas,

A simple algebraic approach to synthesis Fibonacci Switched Capacitor Converters (SCC) is analyzed and the expected losses are estimated. The proposed approach reduces the power losses by increasing the number of target voltages. The synthesized Fibonacci SCC is compatible with the binary SCC and uses the same switch network. This feature is extremely beneficial since it provides the option to ...