• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 추계종합학술대회 논문집(3)
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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.

• 대한수학회보
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• 제32권2호
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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.

• 대한수학회보
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• 제56권2호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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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.

• 호남수학학술지
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• 제40권1호
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• pp.139-153
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• 2018

Let $P{\geq}3$ be an integer and let ($U_n$) denote generalized Fibonacci sequence defined by $U_0=0$, $U_1=1$ and $U_{n+1}=PU_n-U_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equation $U_n=11x^2+1$. We show that only $U_1$ and $U_2$ may be of the form $11x^2+1$.

• 대한수학회논문집
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• 제31권3호
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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 $n,k{\geq}1$.

• Korean Journal of Mathematics
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• 제29권4호
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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_∞}.

• 전력전자학회:학술대회논문집
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• 전력전자학회 2001년도 Proceedings ICPE 01 2001 International Conference on Power Electronics
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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.

• 한국실내디자인학회논문집
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• 제23권1호
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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.

• 한국정보과학회논문지:시스템및이론
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• 제36권6호
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• pp.437-450
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• 2009

본 논문에서는 임의의 피보나치 트리에 에지번호매김을 하여 피보나치 수들의 집합 {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} 그리고 {$F_{3k+2}|k\;{\geq}\;0$}인 세가지 경우의 에지번호 집합을 얻는 7가지의 에지번호매김방법들을 제안한다. 이러한 에지번호들의 집합은 상호연결망의 일종인 원형군의 설계시 점프열로 사용할 수 있으므로 망척도 중 하나인 분지수를 결정한다.