نتایج جستجو برای: fibonacci functional equation
تعداد نتایج: 806225 فیلتر نتایج به سال:
Optical vortex beams, generated by Diffractive Optical Elements (DOEs), are capable of creating optical traps and other multi-functional micromanipulators for very specific tasks in the microscopic scale. Using the Fibonacci sequence, we have discovered a new family of DOEs that inherently behave as bifocal vortex lenses, and where the ratio of the two focal distances approaches the golden mean...
For an Erdős-Surányi sequence it is customary to consider its signum equation. Based on some classical heuristic arguments, we conjecture the asymptotic behavior for the number of solutions of this signum equation in the case of the sequence {n}n (k 2) and the sequence of primes. Surprisingly, we show that this method does not apply at all for the Fibonacci sequence. By computing the precise nu...
The role of the topological index, ZG, proposed by the present author in 1971, in various problems and topics in elementary mathematics is introduced, namely, (i) Pascal’s and asymmetrical Pascal’s triangle, (ii) Fibonacci, Lucas, and Pell numbers, (iii) Pell equation, (iv) Pythagorean, Heronian, and Eisenstein triangles. It is shown that all the algebras in these problems can be easily obtaine...
In this paper, we provide an explicit upper bound on the absolute value of solutions n < m 0 to Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes k-generalized Fibonacci sequence. The depends only k.
A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...
Using a tight-binding model and transfer-matrix technique, as well as Lanczos algorithm, we numerically investigate the nature of the electronic states and electron transmission in site, bond and mixing Fibonacci model chains. We rely on the Landauer formalism as the basis for studying the conduction properties of these systems. Calculating the Lyapunov exponent, we also study the localization...
In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with Fibonacci, Jacobsthal, Pell Padovan numbers give their structural properties by matrix methods. Then obtain new relationships between numbers.
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.
can be reduced to a relation of form (1), between xn and xn+1. Consequently, the relation's two consecutive terms of Fibonacci, Lucas, and Pell sequences are given in [2]. S. Roy [6] finds this relation for the Fibonacci sequence using hyperbolic functions. In this paper we shall prove that if a sequence (xn)n>1 satisfies a linear recurrence of order r > 2, then there exists a polynomial relati...
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