• 대한수학회지
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• 제42권1호
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• pp.135-151
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• 2005

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.

• 대한수학회보
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• 제50권2호
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• pp.659-665
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• 2013

In this note, the $q$-extension of the twisted Lerch Euler zeta functions considered by Jang [Bull. Korean Math. Soc. 47 (2010), no. 6, 1181-1188] is further investigated, and the generalized multiplication theorem for the $q$-extension of the twisted Lerch Euler zeta functions is given. As applications, some well-known results in the references are deduced as special cases.

• 대한수학회보
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• 제50권4호
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• pp.1289-1296
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• 2013

Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb{Z}_p$. From these relationships, we establish some interesting identities.

• 대한수학회지
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• 제39권5호
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• pp.765-773
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• 2002

Let $textsc{k}$＝$F_{q}$(T) be a rational function field. Let $\ell$ be a prime number with ($\ell$, q-1) ＝ 1. Let K/$textsc{k}$ be an elmentary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

• 충청수학회지
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• 제28권4호
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• pp.575-582
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• 2015

The Newton-Raphson method is used to compute the q-th roots of a p-adic number for a prime number q. The sufficient conditions for the convergence of this method are obtained. The speed of its convergence and the number of iterations to obtain a number of corrected digits in the approximation are calculated.

• Journal of information and communication convergence engineering
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• 제7권4호
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• pp.469-474
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• 2009

Q-algorithm is proposed at EPC global Class-1 Generation-2 RFID systems to determine the frame size of next query round. In Q-algorithm, the reader calculates the frame size without estimating the number of tags. But, it uses only the slot conditions: empty, success, or collision. Therefore, it wastes less computational cost and is simpler than other algorithms. However, the constant parameter C value, which is used for calculating the next frame size, is not optimized. In this paper, we propose the optimized C values of Q-algorithm according to the number of tags within the identification range of reader through a lot of computer simulations.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• 대한수학회보
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• 제29권2호
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 한국수학사학회지
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• 제31권4호
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• pp.183-196
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• 2018

In this study, we propose an approximate method to make Jisuguimundo with magic number 93 to 109. In this method, for two numbers p, q with a relationship of M = 2p+q, we use eight pairs of two numbers with sum p and five pairs of two numbers with sum q. Such numbers must be between 1 and 30. Instead of determining all positions of thirty numbers, this method shows that Jisuguimundo with magic number 93 to 109 can be made by determining positions of thirteen numbers $a_i$(i = 1, 2, ${\cdots}$, 8), $b_5$, $c_i$(i = 1, 2, 3, 4). Method 1 is used to make Jisuguimundo with magic number 93 to 108, and method 2 is used to make Jisuguimundo with magic number 109.

• 충청수학회지
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• 제35권3호
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• pp.227-234
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• 2022

Let 𝔽_q be a finite field with odd q elements. In this article, we prove that if E ⊆ 𝔽^d_q, d ≥ 2, and |E| ≥ q, then there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d such that for all y ∈ Y, the number of distances between the point y and the set E is ~ q. As a corollary, we obtain that for each set E ⊆ 𝔽^d_q with |E| ≥ q, there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d so that any set E ∪ {y} with y ∈ Y determines a positive proportion of all possible distances. The averaging argument and the pigeonhole principle play a crucial role in proving our results.