• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.921-932
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• 2003

A number of variants of Hofstadter's original sequence have been investigated. Here we investigate a collection of similarly defined such sequences which give rise to intriguingly different results.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.475-490
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• 2019

Let C^(q) be the q-commuting arithmetic table of (x + y)ⁿ with noncommuting variables. We study sequential properties of diagonal sums of C^(q) with various q > 0. One of our results shows that each diagonal sum plays like Fibonacci number with some minor conditions.

• 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.

• 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.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.357-367
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• 2013

It is important to make students do research for oneself. But the practice of inquiry activity is not easy in the mathematics education field. Intellectual curiosities of students are unpredictable. It is important to meet intellectual curiosities of students. We could get a sequence in the process solving a problem. This sequence was expressed in a form of the recurrence relation $a_n=a_{n-1}+a_{n-3}$ ($n{\geq}4$), $a_1=a_2=a_3=1$. We tried to look for the general terms of this sequence. This sequence is similar to Fibonacci sequence, but the process finding the general terms is never similar to Fibonacci sequence. We can get two general terms expressed in different form after our a great deal of effort. We hope that this study will give the spot of education energy.

• 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].

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.539-554
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• 2020

A set {a₁, a₂, …, a_m} of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two elements in the set decreased by one is a perfect square. In this paper, we find a solution of Pellian equations which is constructed by D(-1)-triples and using this result, we prove the extendibility of D(-1)-pair with some conditions.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.691-694
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• 2002

The most unstable situation of laminar plane Poiseuille flow for transition to turbulence is investigated by using a pseudo-spectral method. A number of various disturbance modes are tested and it is found that the flow is the most unstable when it is disturbed by an oblique wave with an angle of $29.7^{\circ}$.

• 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.