In this paper we did a generalization of Hadamard product of Fibonacci Q matrix and Fibonacci Q−n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices. Mathematics Subject Classification: Primary 11B25, 11B37, 11B39, Secondary 11C20

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.

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...

The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.

Let {ai,j} be real numbers for 0 6 i 6 r 1 and 1 6 j 6 2, and define a sequence {vn} with initial conditions v0, v1 and conditional linear recurrence relation vn = at,1vn 1 + at,2vn 2 where n ⌘ t (mod r) (n > 2). The sequence {vn} can be viewed as a generalization of many well-known integer sequences, such as Fibonacci, Lucas, Pell, Jacobsthal, etc. We find explicitly a linear recurrence equati...

This paper proposes a method of combining the concepts of recursive algorithms and functional programming in hardware design. Though recursion is readily available in functional programming languages, a translation step is required to convert the recursion in such functional program to a synthesizable hardware specification. This proposal uses the idea of Finite State Machines used in [5], comb...