• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.971-997
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• 2018

The parity of cyclotomic numbers of order 2, 4 and 6 associated with 4-cyclotomic cosets modulo an odd prime p are obtained. Hence the explicit expressions of primitive idempotents of minimal cyclic codes of length $p^n$, $n{\geq}1$ over the quaternary field $F_4$ are obtained. These codes are observed to be subcodes of Q codes of length $p^n$. Some orthogonal properties of these subcodes are discussed. The minimal cyclic codes of length 17 and 43 are also discussed and it is observed that the minimal cyclic codes of length 17 are two weight codes. Further, it is shown that a Q code of prime length is always cyclotomic like a binary duadic code and it seems that there are infinitely many prime lengths for which cyclotomic Q codes of order 6 exist.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.245-250
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• 1992

In this paper, we present a nev algorithm for the fast computation of the discrete cosine transform(DCT). This algorithm consists of the three dimensional prime factor-decomposed algorithm(PFA) and three dimensional common factor-decomposed algorithm(CFA). We can compute N-point DCT for the number N decomposable Into three relative prime numbers using PFA and into three common numbers using CFA. We also show input and output index mapping for the three decomposition. it results in requiring fever multiplicaions than the previous algorithms. Particularly, for the large number N, it is more powerful in reducing the number of multiplication.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.719-726
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• 1998

In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.1-84
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• 2017

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.649-658
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• 2019

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo $p^2$, one of which is $$\sum\limits_{k=1}^{p-1}k^2B_{p,k}B_{p,k-d}{\equiv}4(-1)^d\{{\frac{1}{3}}d(2d^2+1)(4pH_d-1)-p\({\frac{26}{9}}d^3+{\frac{4}{3}}d^2+{\frac{7}{9}}d+{\frac{1}{2}}\)\}\;(mod\;p^2)$$, where a prime number p > 3 and $1{\leq}d{\leq}p$.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.89-94
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• 2003

Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06b
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• pp.272-275
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• 2011

본 논문에서는 수학에서 사용하는 소수(Prime number)를 찾는 원리에 대한 학습을 위한 게임 기반 학습(Game based learning) 콘텐츠인 Prime Miner라는 게임을 제안한다. Prime Miner는 게임이 가지고 있는 장점과 소수의 원리를 결합하여 게임을 통해 학습자의 흥미를 이끌어 학습에 몰입할 수 있도록 도우며, 학습자가 게임 규칙을 통해 소수의 원리를 합리적으로 배울 수 있도록 유도한다. 본 논문에서는 Prime Miner의 게임 원리와 학습자가 Prime Miner를 통해 소수 학습을 하는 방법을 설명한다. 또한 퍼즐게임에서 종종 발생하는 더 이상 게임을 진행할 수 없는 상태인 교착상태(Deadlock)를 피하기 위한 숫자 타일의 배치에 관한 방법도 제시한다.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.2 no.3
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• pp.188-198
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• 1990

Turbulent characteristics of turbulent pulsating flows were studied experimentally in a square duct. Velocity waveforms, velocity profiles, and turbulent intensity of turbulent pulsating flow were investigated by using a hot-wire anemometer with data acquisition and a processing system in a square duct with a ratio of 1 ($40mm{\times}40mm$) to 4,000mm long. Turbulent components were shown to be larger in decelerating than in accelerating regions and also larger for a large phase of velocity and U'rms distribution of turbulent flow. The effect of velocity amplitude ratio does not exist for specified time [${\theta}(z^{\prime})$], amplitude ratio (${\mid}U^{\prime}_{rms.os.1}{\mid}/{\mid}U_{m.os.1}{\mid}$), and phase difference (${\Delta}U^{\prime}_{rms.os.1}-{\Delta}U_{m.os.1}$) in either turbulent oscillating or cross-sectional mean velocity components. The effect of dimensionless angular frequency for specified time [${\theta}(z^{\prime})$] can be disregarded because the dimensionless angular frequency does not affect the specified time. The velocity distributions of turbulent pulsating flows for various time-averaged Reynolds numbers are in approximate agreement with the velocity distributions for equivalent Reynolds numbers and 1/7th power law of steady flow.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.111-113
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• 1990

We apply Bredikhin's theorem to the distribution of prime numbers in arithmetic progressions.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.27-32
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• 2000

The quadratic fields generated by $x^2$=ax+1($\alpha\geq$1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=$\alpha^2$+4 is a prime in $\mathbb{Z}$, such that $\mathbb{Q}(\sprt{p})$ has class numbers 1, 3 and 5.