• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.695-704
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• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.401-411
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• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.

• Theoretical Mathematics and Pedagogical Mathematics
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• v.20 no.3
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• pp.207-221
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• 2013

In this work we study the tribonacci numbers. We find a tribonacci triangle which is an analog of Pascal triangle. We also investigate an efficient method to compute any $n$th tribonacci numbers by matrix method, and find periods of the sequence by taking modular tribonacci number.

• 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 the Korean Mathematical Society
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• v.55 no.2
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• pp.425-445
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• 2018

A set {$a_1,\;a_2,{\ldots},\;a_m$} of positive integers is called a Diophantine m-tuple if $a_ia_j+1$ is a perfect square for all $1{\leq}i$ < $j{\leq}m$. In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs {$F_{k-2}F_{k+1},\;F_{k-1}F_{k+2}$} and {$F_{k-2}F_{k-1},\;F_{k+1}F_{k+2}$}, where $F_n$ is the n-th Fibonacci number.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.48 no.3
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• pp.118-123
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• 1999

This paper describes the finite element procedure including the magnetic hysteresis phenomena. The magnetization-dependent Preisach model is employed to simulate the magnetic hysteresis and applied to each elements. Magnetization is calculated by the Fibonacci search method for the applied field in the implementation of the magnetization-dependent model. This can calculate the magnetization very accurately with small iteration numbers. The magnetic field intensity and the magnetization corresponding to the magnetic flux density obtained by the finite element analysis(FEA) are computed at the same time under the condition that these balues must satisfy the constitutive equation. In order to reduce the total calculation cost, pseudo-permeability is used for the input for the FEA. It is found that the presented method is very useful in combining the hysteresis model with the finite element method.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.549-559
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• 2018

In this paper, we consider the congruences involving harmonic numbers and the terms of the sequences {$U_{kn}$} and {$V_{kn}$}. For example, for an odd prime number p, $${\sum\limits_{i=1}^{p-1}}H_i{\frac{U_{k(i+m)}}{V^i_k}}{\equiv}{\frac{(-1)^kU_{k(m+1)}}{_pV^{p-1}_k}}(V^p_k-V_{kp})(mod\;p)$$, where $m{\in}{\mathbb{Z}}$ and $k{\in}{\mathbb{Z}}$ with $p{\nmid}V_k$.

• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.

• 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.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.745-757
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• 2020

A set {a₁, a₂, …, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves E_k constructed by a Diophantine triple {F_2k, F_2k+2, 4F_2k+1F_2k+2F_2k+3}, and find all integer points on the elliptic curve under assumption that rank(E_k(ℚ)) = 2.