• Title/Summary/Keyword: Fibonacci sequence

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The design of interconnection network using inorder traversal on Fibonacci tree (피보나치 트리에서 중위순회를 이용한 상호연결망 설계)

  • 김현주;김용석
    • Proceedings of the IEEK Conference
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    • 2000.11c
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    • pp.59-62
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    • 2000
  • In this paper, We propose the new interconnection network which is designed to edge numbering method using inorder traversal a Fibonacci trees and its jump sequence is Fibonacci numbers. It has a simple (shortest path)routing algorithm, diameter, node degree. It has a spaning subtree which is Fibonacci tree and it is embedded Fibonacci tree. It is compared with Hypercube. We improve diameter compared with Hypercube on interconnection network measrtes.

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A COMPLETENESS ON GENERALIZED FIBONACCI SEQUENCES

  • Lee, Gwang-Yeon
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.239-249
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    • 1995
  • Let $V = (v_1, v_2, \cdots)$ be a sequence of positive integers arranged in nondecreasing order. We define V to be complete if every positive integer n is the sum of some subsequence of V, that is, $$ (1.1) n = \sum_{i=1}^{\infty} a_i v_i where a_i = 0 or 1.

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ON THE INTERSECTION OF k-FIBONACCI AND PELL NUMBERS

  • Bravo, Jhon J.;Gomez, Carlos A.;Herrera, Jose L.
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.535-547
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    • 2019
  • In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.

REPRESENTING NATURAL NUMBERS AS UNIQUE SUMS OF POSITIVE INTEGERS

  • Laohakosol, Vichian;Chalermchai, Jiraporn
    • The Pure and Applied Mathematics
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    • v.11 no.1
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    • pp.63-72
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    • 2004
  • It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, $\cal{l}\geq2$, of repetitions. It is shown that the $(\cal{l}+1)$-adic expansion is the only such representation possible.

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A COMPLETE FORMULA FOR THE ORDER OF APPEARANCE OF THE POWERS OF LUCAS NUMBERS

  • Pongsriiam, Prapanpong
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.447-450
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    • 2016
  • Let $F_n$ and $L_n$ be the nth Fibonacci number and Lucas number, respectively. The order of appearance of m in the Fibonacci sequence, denoted by z(m), is the smallest positive integer k such that m divides $F_k$. Marques obtained the formula of $z(L^k_n)$ in some cases. In this article, we obtain the formula of $z(L^k_n)$ for all $n,k{\geq}1$.

NEW BANACH SPACES DEFINED BY THE DOMAIN OF RIESZ-FIBONACCI MATRIX

  • Alp, Pinar Zengin;Kara, Emrah Evren
    • Korean Journal of Mathematics
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    • v.29 no.4
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    • pp.665-677
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    • 2021
  • The main object of this study is to introduce the spaces $c_0({\hat{F}^q)$ and $c({\hat{F}^q)$ derived by the matrix ${\hat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the 𝛼-, 𝛽-, 𝛾- duals of these spaces and give the characterization of matrix classes (${\Lambda}({\hat{F}^q)$, Ω) and (Ω, ${\Lambda}({\hat{F}^q)$) for 𝚲 ∈ {c0, c} and Ω ∈ {ℓ1, c0, c, ℓ}.

Maximum Power Point Tracking Control Employing Fibonacci Search Algorithm for Photovoltaic Power Generation System

  • Miyatake Masafumi;Kouno Tooru;Nakano Motomu
    • Proceedings of the KIPE Conference
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    • 2001.10a
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    • pp.622-625
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    • 2001
  • Photovoltaic generation systems need MPPT (Maximum Power Point Tracking) control because the output power depends on the operating voltage and current. Therefore, many researchers propose various types of MPPT control methods. A new MPPT control scheme is proposed in this paper in order to realize higher efficiency with simple calculation. The line search algorithm with fibonacci sequence which is one of the optimizing method is employed for the MPPT. The line search method is modified for real-time operation. The method is verified by simulations and experiments. It is concluded that the scheme can respond fast variation of irradiance.

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Study on Visual Patterns about Spatial Dimensions - Centered on the Golden Ratio, Fibonacci Sequence, and Fractal Theory - (공간 차원에 관한 시각적 패턴 연구 - 황금비, 피보나치 수열, 프랙털 이론을 중심으로 -)

  • Kim, Min-Suk;Kim, Kai-Chun
    • Korean Institute of Interior Design Journal
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    • v.23 no.1
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    • pp.88-95
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    • 2014
  • This study intended arousal of other viewpoints that deal with and understand spaces and shapes, by describing the concept of 'dimensions' into visual patterns. Above all, the core concept of spatial dimensions was defined as 'expandability'. Then, first, the 'golden ratio', 'Fibonacci sequence', and 'fractal theory' were defined as elements of each dimension by stage. Second, a 'unit cell' of one dimension as 'minimum unit particles' was set. Next, Fibonacci sequence was set as an extended concept into two dimensions. Expansion into three dimensions was applied to the concept of 'self-similarity repetition' of 'Fractal'. In 'fractal dimension', the concept of 'regularity of irregularity' was set as a core attribute. Plus, Platonic solids were applied as a background concept of the setting of the 'unit cell' from the viewpoint of 'minimum unit particles'. Third, while 'characteristic patterns' which are shown in the courses of 'expansion' of each dimension were embodied for the visual expression forms of dimensions, expansion forms of dimensions are based on the premise of volume, directional nature, and concept of axes. Expressed shapes of each dimension are shown into visually diverse patterns and unexpected formative aspects, along with the expression of relative blank spaces originated from dualism. On the basis of these results, the 'unit cell' that is set as a concept of theoretical factor can be defined as a minimum factor of a basic algorism caused by other purpose. In here, by applying diverse pattern types, the fact that meaning spaces, shapes, and dimensions can be extracted was suggested.

The Fibonacci Edge Labelings on Fibonacci Trees (피보나치트리에서 피보나치 에지 번호매김방법)

  • Kim, Yong-Seok
    • Journal of KIISE:Computer Systems and Theory
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    • v.36 no.6
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    • pp.437-450
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    • 2009
  • In this paper, we propose seven edge labeling methods. The methods produce three case of edge labels-sets of Fibonacci numbers {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} and {$F_{3k+2}|k\;{\geq}\;0$}. When a sort of interconnection network, the circulant graph is designed, these edge labels are used for its jump sequence. As a result, the degree is due to the edge labels.