• 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.

• 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 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].

• 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.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.

• KIISE Transactions on Computing Practices
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• v.23 no.10
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• pp.594-598
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• 2017

Tremendous quantities of numerical data are generated every day from various sources, including the stock market. Universal codes such as Elias gamma coding, Elias delta coding and Fibonacci coding are generally used to store arrays of integers. Studies have been conducted to support fast access to specific elements in an integer array, while occupying less space. We suggest an improved code system that utilizes the concepts of succinct data structures. This system is based on a data structure that allows compressing a delimiter bit array while supporting queries in constant time. The results of an experiment show that the encoded array uses lower space, while not sacrificing time efficiency.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.481-494
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• 2005

In this study, the goal is to spread profound knowledge and theory through providing with accumulated methods in mathematics education to the students who are relatively neglected in educational benefits. The process is divided into 3 categories: mathematics for obtaining common sense and intelligence, practical math for application, and math as a liberal art to elevate their characters. Furthermore, it includes the reasons for studying math, improving problem-solving skills, machinery application learning, introduction to code(cipher) theory and game theory, utilizing GSP to geometry learning, and mathematical relations to sports and art. Based on these materials, the next step(goal) is to train graduate students to conduct researches in teaching according to the teaching plan, as well as developing interesting and effective teaching plan for the remote high school learners.