In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties these polynomials—among others, a graph interpretation matrix generators. Moreover, present connections with Pascal’s triangle.

Hypergeometric functions are an important tool in many branches of pure and applied mathematics, and they encompass most special functions, including the Chebyshev polynomials. There are also well-known connections between Chebyshev polynomials and sequences of numbers and polynomials related to Fibonacci numbers. However, to my knowledge and with one small exception, direct connections between...

In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between k-step Fibonacci numbers. addition, study sequence modulo m periods of Hperbolic-type sequences for any k which are related m. Furthermore, extend to groups. Finally, obtain 2-Fibonacci in dihedral group D2m, (m ? 2) with respect generating pairs (x,y) (y, x).

Our aim in this paper is to focus on some applications in differential geometry of the metallic means family (a generalization of the golden mean) and generalized Fibonacci sequences, using a class of polynomial structures defined on Riemannian manifolds. We search for properties of the induced structure on a submanifold by metallic Riemannian structures and we find a necessary and sufficient c...

This paper presents a new object oriented framework DAMPVM/DAC which is implemented on top of DAMPVM and provides automatic partitioning of irregular divide-andconquer (DAC) applications at runtime. The processes are then mapped dynamically to processors taking into account their speeds and even loads by other user processes. The paper presents the programming interface (API) of the framework, ...

The global structural optimization is carried out for off-lattice protein AB models in two and three dimensions by conformational space annealing. The models consist of hydrophobic and hydrophilic monomers in Fibonacci sequences. To accelerate the convergence, we have introduced a shift operator in the internal coordinate system, and effectively reduced the search space by forming a quotient sp...

This paper presents a Coq library that lifts an abstract yet precise notion of running-time into the type of a function. Our library is based on a monad that counts abstract steps, controlled by one of the monadic operations. The monad’s computational content, however, is simply that of the identity monad so programs written in our monad (that recur on the natural structure of their arguments) ...

Image scrambling is used to make images visually unrecognizable such that unauthorized users have difficulty decoding the scrambled image to access the original image. This article presents two new image scrambling algorithms based on Fibonacci p-code, a parametric sequence. The first algorithm works in spatial domain and the second in frequency domain (including JPEG domain). A parameter, p, i...

Complex biological patterns are often governed by simple mathematical rules. A favourite botanical example is the apparent relationship between phyllotaxis (i.e. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci number sequence (1, 2, 3, 5, 8, 13 . . .). It is frequently alleged that leaf primordia adopt Fibonacci-related pa...