the problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. we seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. we assume that the work content required by the activities follows an exponential distribution. the decision variables of the model are the allocated resourc...

Knuth [12, Page 417] states that “the (program of the) Fibonaccian search technique looks very mysterious at first glance” and that “it seems to work by magic”. In this work, we show that there is even more magic in Fibonaccian (or else Fibonacci) search. We present a generalized Fibonacci procedure that follows perfectly the implicit optimal decision tree for search problems where the cost of ...

The Fibonacci secant function is constructed in this paper. Fibonacci tan-sec method is presented to search for the exact traveling wave solutions of nonlinear differentialdifference equations (DDEs). This method is essentially equivalent to the classical hyperbolic method. The discrete mKdV lattice and some other lattice equations are chosen to illustrate the efficiency and effectiveness of th...

In this paper, an adaptive step size auto focus search algorithm and a reduced zoom tracking algorithm are proposed. Many different auto focus search algorithms exist, such as global search, binary search, Fibonacci search, and so on. Global search can ensure the global peak is found correctly, but the search time is too long. The search time of binary or Fibonacci search is shortened, but the ...

The golden ratio has fascinated people of diverse interests for at least 2,400 years (see e.g. [24]). In mathematics (and the arts) two quantities a and b are in the golden ratio if the ratio of the sum of the quantities a+b to the larger quantity a is equal to the ratio of the larger quantity a to the smaller quantity b . This amounts to setting (a+b)/a = a/b =: φ and solving φ2−φ−1 = 0 which ...

The Fibonacci numbers are defined, as usual9 by the recurrence F0 = 0, F1 = 1, Fk = Fk_x +Fk.z, k> 1. The Fibonacci tree of order k, denoted Tk, can be constructed inductively as follows: If k = 0 or k = 1, the tree is simply the root 0. If k > 15 the root is Fk ; the left subtree is Tjc_1; and the right subtree is Tk_2 with all node numbers increased by Fk . TG is shown in Figure 1. For an ele...

For an optimal binary search tree T with a subtree S(d) at a distance d from the root of T, we study the ratio of the weight of S(d) to the weight of T. The maximum possible value, which we call ρ(d), of the ratio of weights, is found to have an upper bound of 2/Fd+3 where Fi is the ith Fibonacci number. For d = 1, 2, 3, and 4, the bound is shown to be tight. For larger d, the Fibonacci bound g...

For a finitely generated group G = 〈A〉 where A = {a1, a2, . . . , an} the sequence xi = ai+1, 0 ≤ i ≤ n − 1, xi+n = ∏n j=1 xi+j−1, i ≥ 0, is called the Fibonacci orbit of G with respect to the generating set A, denoted FA(G). If FA(G) is periodic, we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). We examine the Fibonacci lengths of al...