Showing papers on "Fibonacci number published in 1981"

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

Abstract: We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ1, and akth neighboranti-ferromagnetic interactionJk. WhenJk/J1=−1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k−1)th term in a generalized Fibonacci sequence defined by,FN(k)=FN−1(k)+FN−k(k). In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2×∞ strip of the square lattice, and (c) “directed” self-avoiding walks on finite lattice strips.

On the application of the golden ratio in the visual arts

Abstract: The Golden Ratio or Section or Mean for a line divided into a shorter length a and a longer length b is determined by alb = b/(a + b). The value of the Ratio is the irrational number (/ 5-1)/2 = 0.618.... A Golden Rectangle is one in which the Ratio applies to its sides of length a and b. The ratios of the successive Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21, 34, ... oscillate rapidly to the limiting value 0.618, the Golden Ratio [1]. There are two aspects of the Golden Ratio that are of interest to contemporary artists: (1) whether it should be used as a theoretical basis for their own works of art

Complement representations in the Fibonacci computer

Abstract: Two complement representations and a sign-magnitude one are introduced which allow for handling negative numbers using only binary coefficients in Fibonacci base expansions. These are developed for practical implementation in Fibonacci computers.

A non-fibonacci search plan with fibonacci-like results

Abstract: This article describes a nondeterministic search plan, hereinafter called the mid-point technique. While not optimal in the minimax sense, the plan offers several possible advantages over the Fibonacci technique. Further, the expected value of the reduction ratio at each stage is identical to the reduction ratio achieved by the minimax optimal Fibonacci method. IMTROVUCTWhl