• ETRI Journal
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• v.40 no.1
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• pp.111-121
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• 2018

To find the emerging patterns (EPs) in streaming transaction data, the streaming is first divided into some time windows containing a number of transactions. Itemsets are generated from transactions in each window, and then the emergence of itemsets is evaluated between two windows. In the tilted-time windows model (TTWM), it is assumed that people need support data with finer accuracy from the most recent windows, while accepting coarser accuracy from older windows. Therefore, a limited array's elements are used to maintain all support data in a way that condenses old windows by merging them inside one element. The capacity of elements that accommodates the windows inside is modeled using a particular number sequence. However, in a stream, as new data arrives, the current array updating mechanisms lead to many null elements in the array and cause data incompleteness and inaccuracy problems. Two models derived from TTWM, logarithmic TTWM and Fibonacci windows model, also inherit the same problems. This article proposes a novel push-front Fibonacci windows model as a solution, and experiments are conducted to demonstrate its superiority in finding more EPs compared to other models.

• Journal of the KSME
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• v.31 no.1
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• pp.43-50
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• 1991

로봇의 설계시 고려하여야 하는 여러가지 면을 기술하였다. 평면 3자유도 링크의 경우 길이비를 "Fibonacci Sequence"를 따라가도록 결정하였으며 여유자유도를 갖는 직접구동로봇의 설계 및 제작시 유의하여야 할 사항을 정리하였다. 몸체설계후 POSTECH DD 로봇을 위한 실시간 제 어환경이 구성되었으며 VME버스의 MC68020/68882 프로세서를 탑재한 "one board" 컴퓨터에서 모든 로봇제어 소프트웨어가 수행되었다.든 로봇제어 소프트웨어가 수행되었다.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.593-605
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• 2015

In this study, we define r-circulant, circulant, Hankel and Toeplitz matrices involving the integer sequence with recurrence relation U_n = pU_n-1 + U_n-2, with U₀ = a, U₁ = b. Moreover, we obtain special norms of above mentioned matrices. The results presented in this paper are generalizations of some of the results of [1, 10, 11].

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1069-1080
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• 2017

The Tribonacci sequence ${\{T_n}\}_{n{\geq}0}$ resembles the Fibonacci sequence in that it starts with the values 0, 1, 1, and each term afterwards is the sum of the preceding three terms. In this paper, we find all integers c having at least two representations as a difference between a Tribonacci number and a power of 2. This paper continues the previous work [5].

• East Asian mathematical journal
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• v.23 no.3
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• pp.371-380
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• 2007

It is well known that the solutions of the Diophantine equation $x^2+xy-y^2=1$ is related to the Fibonacci sequence. In this study, we generalize the above fact to the tribonacci sequence and its generalized from using the group structure of solutions of some Diophantine equations.

• KSBB Journal
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• v.29 no.5
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• pp.336-342
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• 2014

Asexual benthic polyp reproduction plays a major role in the jellyfish bloom. Recent studies found that temperature is the most important factor to regulate the budding rate of the polyps. We established a simple dynamic model to count the number of polyps depending on the variation of temperature with two data sets from different places. The population of polyps was counted through the budding rate and the number of budding times by Fibonacci sequence. It is assumed that the budding rate depends on the temperature only. The budding rate of the asexual reproduction shows very sensitive to the distribution of the seawater temperature. The model was tested to the temperature data of Ansan located in the west sea of Korea. The results indicate that this model can be useful to predict the blooms of Aurelia aurita polyps, which may have considerable influence on the bloom of medusa. The shape of temperature curve plays a key role in the predicting the bloom of Aurelia aurita polyps.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1439-1443
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• 2010

For a positive integer k $\geq$ 2, the k-bonacci sequence {$g^{(k)}_n$} is defined as: $g^{(k)}_1=\cdots=g^{(k)}_{k-2}=0$, $g^{(k)}_{k-1}=g^{(k)}_k=1$ and for n > k $\geq$ 2, $g^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n-2}+{\cdots}+g^{(k)}_{n-k}$. And the k-Lucas sequence {$l^{(k)}_n$} is defined as $l^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n+k-1}$ for $n{\geq}1$. In this paper, we give a representation of nth k-Lucas $l^{(k)}_n$ by using determinant.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.433-442
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• 2022

Let N^(q) be an arithmetic table of a negative exponent polynomial with q-commuting variables. We study sequential properties of diagonal sums of N^(q). We first device a q-coefficient table $\hat{N}$ of N^(q), find sequences of diagonal sums over $\hat{N}$, and then retrieve the findings of $\hat{N}$ to N^(q). We also explore recurrence rules of s-slope diagonal sums of N^(q) with various s and q.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.711-732
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• 2018

In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide "concrete" necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.733-740
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• 2021

Let (F_n)_n≥0 be the Fibonacci sequence and p be a prime number. For 1≤k≤m, the Fibonomial coefficient is defined as $$\[\array{m\\k}\]_F=\frac{F_{m-k+1}{\ldots}{F_{m-1}F_m}}{{F_1}{\ldots}{F_k}}$$ and $\[\array{m\\k}\]_F=0$ whan k>m. Let a and n be positive integers. In this paper, we find the conditions of prime number p which divides Fibonomial coefficient $\[\array{P^{a+n}\\{p^a}}\]_F$. Furthermore, we also find the conditions of p when $\[\array{P^{a+n}\\{p^a}}\]_F$ is not divisible by p.