Search results

article

Properties and applications of some special integer number sequences

Cristina Flaut, Diana Savin, Geanina Zaharia

Mathematical Methods in the Applied Sciences > 44 > 9 > 7442 - 7454

In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in cryptography and applications of some quaternion elements.

article

On some combinatorial properties of bihyperbolic numbers of the Fibonacci type

Dorota Bród, Anetta Szynal‐Liana, Iwona Włoch

Mathematical Methods in the Applied Sciences > 44 > 6 > 4607 - 4615

In this paper, we give some properties of the bihyperbolic Fibonacci, Jacobsthal and Pell numbers, among others the Binet formula, Catalan, Cassini, and d'Ocagne identities. Moreover, we present the generating function and summation formulas for these numbers.

article

On metallic ratio in $Z_{p}$

Seda Yamaç Akbiyik, Mücahit Akbiyik, Salim Yüce

Mathematical Methods in the Applied Sciences > 42 > 16 > 5535 - 5550

Metallic ratio is a root of the simple quadratic equation x² = kx + 1 for k is any positive integer which is the characteristic equation of the recurrence relation of k‐Fibonacci (k‐Lucas) numbers. This paper is about the metallic ratio in

Z_{p}

. We define k‐Fibonacci and k‐Lucas numbers in

Z_{p}

, and we show that metallic ratio can be calculated in

Z_{p}

if and only if p≡ ± 1 mod (k² + 4), which is...

article

Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

Merve İlkhan

Mathematical Methods in the Applied Sciences > 42 > 16 > 5143 - 5153

Norm of an operator T:X→Y is the best possible value of U satisfying the inequality and lower bound for T is the value of L satisfying the inequality where ‖.‖_X and ‖.‖_Y are the norms on the spaces X and Y, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space ℓ_p(w) into a new space called as Fibonacci weighted difference...

article

Prevalence of Fibonacci numbers in orbital period ratios in solar planetary and satellite systems and in exoplanetary systems

Vladimir Pletser

Astrophysics and Space Science > 2019 > 364 > 9 > 1-15

It is shown that orbital period ratios of successive planets in the Solar System, of satellites in giant planet systems and of exoplanets in exoplanetary systems are preferentially closer to irreducible fractions formed with Fibonacci numbers between 1 and 8 than to other fractions, in a ratio of approximately 60% vs 40%. Furthermore, if sets of minor planets are chosen with gradually smaller inclinations...

article

On Generalized Pell and Pell–Lucas Numbers

Lucyna Trojnar-Spelina, Iwona Włoch

Iranian Journal of Science and Technology, Transactions A: Science > 2019 > 43 > 6 > 2871-2877

In this paper, we introduce and study a new one-parameter generalization of Pell numbers. We describe their distinct properties also related to matrix representation.

article

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

Vakeel A. Khan, Emrah E. Kara, Henna Altaf, Nazneen Khan, more

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-7

Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c0I(Fˆ) $c_{0}^{I}(\hat{F})$, cI(Fˆ) $c^{I}(\hat{F})$ and l∞I(Fˆ) $l_{\infty }^{I}(\hat{F})$. In this paper, we give the ideal convergence of Fibonacci...

article

Transpose of Nörlund matrices on the domain of summability matrices

Gholamreza Talebi

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-5

Let E=(En,k)n,k≥0 $E=(E_{n,k})_{n,k\geq 0}$ be an invertible summability matrix with bounded absolute row sums and column sums, and let Ep $E_{p}$ denote the domain of E in the sequence space ℓp $\ell _{p}$ (1≤p<∞) $(1\le p<\infty )$. In this paper, we consider the transpose of Nörlund matrix associated with a nonnegative and nonincreasing sequence as an operator mapping ℓp $\ell _{p}$ into the...

article

Some family of Diophantine pairs with Fibonacci numbers

Jinseo Park, June Bok Lee

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 2 > 367-384

A set {a₁, a₂, …, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we prove that if {F_2k, F_2k+4, c} is a Diophantine triple then there is a unique positive integer d such that c < d and {F_2k, F_2k+4, c, d} is a Diophantine quadruple.

article

Proper strong-Fibonacci games

Flavio Pressacco, Laura Ziani

Decisions in Economics and Finance > 2018 > 41 > 2 > 489-529

We define proper strong-Fibonacci (PSF) games as the subset of proper homogeneous weighted majority games which admit a Fibonacci representation. This is a homogeneous, type-preserving representation whose ordered sequence of type weights and winning quota is the initial string of Fibonacci numbers of the one-step delayed Fibonacci sequence. We show that for a PSF game, the Fibonacci representation...

article

Norm inequalities involving upper bounds for certain matrix operators in Orlicz-type sequence spaces

Atanu Manna

The Journal of Analysis > 2019 > 27 > 3 > 761-779

In this paper, upper bounds of certain matrix operator norms are estimated in Orlicz-type weighted sequence spaces. Three spaces, namely, weighted Orlicz–Euler $$e_{\lambda , \varphi }^{\alpha }$$ e λ , φ α , weighted Orlicz–Fibonacci $$F_{\lambda , \varphi }$$ F λ , φ and weighted Orlicz $$l_\varphi (\lambda )$$ l φ ( λ ) are considered. Denote $$\Vert A\Vert _{X,...

article

Robust audio watermarking algorithm based on DWT using Fibonacci numbers

Ali Akbar Attari, Ali Asghar Beheshti Shirazi

Multimedia Tools and Applications > 2018 > 77 > 19 > 25607- 25627

This paper presents a blind and robust audio watermarking algorithm developed based on Fibonacci numbers properties and the discrete wavelet transform (DWT) advantages. The method embeds watermark bits in the 6th level approximation subband of DWT at which there is less sensitivity of the human auditory system. The key idea is dividing the 6th level approximation coefficients into small frames and...

article

Fibonacci and Telephone Numbers in Extremal Trees

Urszula Bednarz, Iwona Włoch

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 121-133

In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.

article

Some special number sequences obtained from a difference equation of degree three

Cristina Flaut, Diana Savin

Chaos, Solitons & Fractals > 2018 > 106 > C > 67-71

In this paper we present applications of special numbers obtained from a difference equation of degree three. As a particular case of this difference equation of degree three, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the generalized quaternion algebras. Using properties of these quaternion elements, we can define a set with an interesting algebraic structure,...

article

On generalized Mersenne numbers, their interpretations and matrix generators

Paweł Ochalik, Andrzej Włoch

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica > 2018 > 72 > 1

In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining identities.

article

An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers

J. Sokół, S. İlhan, H. Ö. Güney

Journal of Mathematics and Applications > 2018 > Vol. 41 > 195--206

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel...

article

From golden to unimodular cryptography

Sergiy Koshkin, Taylor Styers

Chaos, Solitons & Fractals > 2017 > 105 > C > 208-214

We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q matrices, and prove that it preserves the original error correction properties of the encryption. Moreover, the additional parameters involved in generating the coding matrices make this unimodular cryptography resilient to the chosen plaintext attacks that worked...

article

Variable-Length Non-Overlapping Codes

Stefano Bilotta

IEEE Transactions on Information Theory > 2017 > 63 > 10 > 6530 - 6537

We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in the literature, called, respectively, fix-free code and non-overlapping code. In this paper we present constructive algorithms for such codes and some numerical results about their...

article

Fibonacci statistical convergence and Korovkin type approximation theorems

Murat Kirişci, Ali Karaisa

Journal of Inequalities and Applications > 2017 > 2017 > 1 > 1-15

The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, we provide various approximation results concerning the classical Korovkin theorem via Fibonacci type statistical convergence.

article

Counting exceptional points for rational numbers associated to the Fibonacci sequence

Charles L. Samuels

Periodica Mathematica Hungarica > 2017 > 75 > 2 > 221-243

If $$\alpha $$ α is a non-zero algebraic number, we let $$m(\alpha )$$ m ( α ) denote the Mahler measure of the minimal polynomial of $$\alpha $$ α over $$\mathbb Z$$ Z . A series of articles by Dubickas and Smyth, and later by the author, develop a modified version of the Mahler measure called the t-metric Mahler measure, denoted $$m_t(\alpha )$$ m t ...

INFONA - science communication portal

Search results

Properties and applications of some special integer number sequences

On some combinatorial properties of bihyperbolic numbers of the Fibonacci type

On metallic ratio in $Z_{p}$

Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

Prevalence of Fibonacci numbers in orbital period ratios in solar planetary and satellite systems and in exoplanetary systems

On Generalized Pell and Pell–Lucas Numbers

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

Transpose of Nörlund matrices on the domain of summability matrices

Some family of Diophantine pairs with Fibonacci numbers

Proper strong-Fibonacci games

Norm inequalities involving upper bounds for certain matrix operators in Orlicz-type sequence spaces

Robust audio watermarking algorithm based on DWT using Fibonacci numbers

Fibonacci and Telephone Numbers in Extremal Trees

Some special number sequences obtained from a difference equation of degree three

On generalized Mersenne numbers, their interpretations and matrix generators

An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers

From golden to unimodular cryptography

Variable-Length Non-Overlapping Codes

Fibonacci statistical convergence and Korovkin type approximation theorems

Counting exceptional points for rational numbers associated to the Fibonacci sequence

Filter options

Publication date

Content availability

Publication type

Publication language

Keywords

Data set

INFONA - science communication portal

Search results

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Content availability

Publication type

Publication language

Keywords

Data set

Reporting an error / abuse

Sending the report failed

Accessibility options