• The Pure and Applied 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.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.4
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• pp.586-593
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• 1994

This paper suggests the algorithm for on-line efficiency control of permancent magnet synchronous motors driving the electric vehicles. The existance of unigue d-axis current is verified, which generates the maximum efficiency at operating points of motor. Using the Fibonacci search method, d-axis current converges to the minimization of inverter input power, and to prevent the variation of motor speed in process of the efficiency control, the voltage decoupled control strategy is introduced. Through the experiments, the effects of an efficiency control algorithm are verified.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.731-752
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• 2020

We introduce the p-deformation of generalized Humbert polynomials. For these polynomials, we derive the differential equation, generating function relations, Fibonacci-type representations, and recurrence relations and state the companion matrix. These properties are illustrated for certain polynomials belonging to p-deformed generalized Humbert polynomials.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• 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.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.418-432
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• 2023

In this study, we consider the Hankel and Gram matrices which are defined by the elements of special number sequences. Firstly, the eigenvalues, determinant, and norms of the Hankel matrix defined by special number sequences are obtained. Afterwards, using the relationship between the Gram and Hankel matrices, the eigenvalues, determinants, and norms of the Gram matrices defined by number sequences are given.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.137-159
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• 2012

In this paper, we deal with recent researches on Ying N$\ddot{u}$ and Ying Buzu(盈不足) which were addressed in the book Jiu Zhang Suan Shu(九章算術, The Nine Chapters on the Mathematical Art). Ying N$\ddot{u}$(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(盈不足術, the method of excess and deficit) represents an algorithm which has been used for solving many mathematical problems. It is known as a rule of double false position in the West. We show the importance of Ying Buzu Shu via an analysis of some problems in 'Ying Buzu' chapter. In 1202, Fibonacci(c.1170-c.1250) used Ying Buzu Shu in his book. This shows some of Asian mathematics were introduced to the West even before the year 1200. We present the origin of Ying Buzu Shu, and its relationship with Cramer's Rule. We have discovered how Asia's Ying Buzu Shu spread to Europe via Arab countries. In addition, we analyze some characters of Ying N$\ddot{u}$(Ying Buzu) in the book Suan Xue Bao Jian(算學寶鑑).

• Proceedings of the Korean Society of Applied Pharmacology
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• 1994.04a
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• pp.187-187
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• 1994

선경인더스트리 연구소에서 개발된 100 여종의 새로운 백금착체 항암제 중 그 동안의 전임상연구를 통해 항암효과가 우수하고 안정성이 확인된 항암제인 SKI 2053R의 인체내 최대내약용량을 결정하고 부작용 및 항암효과를 평가하고 약제의 인체내 약동학적 특성을 검토하기 위해 각종 악성종양 환자들을 대상으로 제 1상 임상연구를 시행하였다. 약제의 투여는 500m1의 5% 포도당용액에 용해하여 1시간에 걸쳐 정주하였으며 병의 악화나 심한 독성이 없으면 치료를 매 4주마다 반복하였다. SKI 2053R의 초기용량은 생쥐에서의 LD$_{10}$의 1/10에 해당하는 40 mg/$m^2$로 하였고, 용량의 단계별 증가는 modified Fibonacci법에 따랐다. 각 단계별로 3명이상의 환자를 치료하여 WHO 기준상 3도 이상의 부작용이 2/6 이상에서 나타날 때의 용량을 최대내약용량으로 설정하였다.

• 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.