We present some binomial identities for sums of the bivariate Fi-bonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.

This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures IPLS in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch ED problem studied in the field of power system...

What are generally referred to as the Fibonacci numbers and the method for their formation were given by Virahanka (between A.D. 600 and X00). Gopala (prior to A.D. 1135) and Hemacandra (c. A.D. 1150). all prior to L. Fibonacci (c. A.D. 1202). Narayana Pandita (A.D. 13Sh) established a relation between his srftcisi~ci-pcrirLfi. which contains Fibonacci numbers as a particular case. and “the mul...

Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are: (i) robustness, manifesting itself by the local containment of errors; (ii) simple encoding and and decoding. The main applica· tiOD explored is the transmission of binary strings whose length is in aD. unknown range, using robust Fibonacci representations instead of the conventional errorsensitive...

After defining a class of generalized Fibonacci numbers and Lucas numbers, we characterize the Fibonacci pseudoprimes of the mth kind. In virtue of the apparent paucity of the composite numbers which are Fibonacci pseudoprimes of the mth kind for distinct values o f the integral parameter m , a method, which we believe to be new, for finding large probable primes is proposed. An efficient compu...

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made about the Fibonacci sequence. It will then go into specific cases of the CRT and how to calculate Fibonacci numbers with reduced forms of the CRT equations. For each of the cases, algorithms and ana...

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...

This paper deals with a practical transportation model known as the Vehicle Routing Problem with Backhauls (VRPB), which aims at designing the minimum cost route set for satisfying both delivery and pick-up demands. In methodological terms, we propose a local search metaheuristic which explores rich solution neighborhoods composed of exchanges of variable-length customer sequences. To efficient...