• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.507-524
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• 2013

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.945-959
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• 2008

n-ary $H_v$-structures is a generalisation of both n-ary structures and $H_v$-structures. A wide class of n-ary $P-H_v$-groups is the n-ary $P-H_v$-groups that is concidered in this paper. In this paper the notion of a normal subgroup of an n-ary $P-H_v$-groups is introduced and the isomorphism theorems for n-ary $P-H_v$-groups are stated and proved. Also some examples and related properties are investigated.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.175-192
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• 2010

In this paper, we introduced the notion of T-vague n-ary subgroups on n-ary subgroups (G, f) and have studied their related properties.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.495-502
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• 2013

Let $\mathcal{T}^{(p)}_n$ be the set of p-ary labeled trees on $\{1,2,{\ldots},n\}$. A maximal decreasing subtree of an p-ary labeled tree is defined by the maximal p-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{T}^{(p)}_{n,k}$ of $\mathcal{T}^{(p)}_n$, which is the set of p-ary labeled trees whose maximal decreasing subtree has k vertices.

• The Transactions of the Korea Information Processing Society
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• v.4 no.11
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• pp.2732-2744
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• 1997

This paper is based on multicasting model in k-ary n-cubes, and Proposes an adaptive wormhole routing algorithm which allows faults and channel contention. The proposed algorithm only requires $2{\times}n$ virtual channels per physical channel which is proportional to the dimension n in order to allow (n-1) faults in a k-ary n-cube. This method uses smaller number of virtual channels than the previously Proposed adaptive routing algorithms [5, 18]. Through a chaos simulator, we have measured message delay considering fault-tolerant as well as message traffic to our adaptive routing algorithm.

• The Korean Journal of Applied Statistics
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• v.13 no.1
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• pp.179-188
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• 2000

본 논문에서는 반복된 블록으로 구성된 부분적으로 균형된 삼각형계획을 이용하여 블록이 반복된 균형 n-ary 이면교배 실험을 설계하고 효율에 대해서 연구하였다. 또한 설계 가능한 계획을 나열하였다.

• East Asian mathematical journal
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• v.21 no.2
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• pp.241-248
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• 2005

Properties of congruences on n-ary groups are investigated.

• Journal of the Korea Society of Computer and Information
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• v.18 no.4
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• pp.123-129
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• 2013

The performance and practicality of cryptosystem for encryption, decryption, and primality test are primarily determined by the implementation efficiency of the modular exponentiation of $a^b$ (mod m). To compute $a^b$ (mod m), the standard binary squaring (square-and-multiply) still seems to be the best choice. However, in large b bits, the preprocessed n-ary, ($n{\geq}2$ method could be more efficient than binary squaring method. This paper proposes a square-and-divide and unpreprocessed n-ary square-and-divide modular exponentiation method. Results confirmed that the square-and-divide method is the most efficient of trial number in a case where the value of b is adjacent to $2^k+2^{k-1}$ or to. $2^{k+1}$. It was also proved that for b out of the beforementioned range, the unpreprocessed n-ary square-and-divide method yields higher efficiency of trial number than the general preprocessed n-ary method.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.5
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• pp.908-915
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• 2001

In this paper, it is analyzed theoretically that the performance degradation, caused by carrier frequency offset, in an OFDM/M-ary PSK system. Then, when Turbo coding is adopted to an OFDM/M-ary PSK system, the degree of performance enhancement is evaluated. Finally, the maximum frequency offset is calculated to satisfy the BER performance required in a Turbo coded OFDM/M-ary PSK system. As results of analysis, it is shown that the more the number of M-ary is, the worse the BER performance is. Moreover, 7dB, 9dB, and 17dB of $E_b/N_o$ are required in QPSK, 8PSK and 16PSK systems, respectively in order to satisfy the error performance, $BER=10^{-3}$ for voice communication. If $E_b/N_o$ are 10㏈ and 15㏈, the frequency offset should be below 0.05 and 0.075, respectively, for voice communication. When Turbo coding is adopted to an OFDM/M-ary PSK system, the less the number of M-ary is, the greater the performance enhancement of Turbo coding is. If the number of a M-ary system of the system is below 16, it is found that required $E_b/N_o$ is about 8dB to satisfy $BER=10^{-5}$ Moreover, in the system the Turbo coding scheme, voice communication is available with greatly low$E_b/N_o$, and 8dB of $E_b/N_o$ is enough for data communication regardless of the permission range of frequency offset.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.2
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• pp.41-47
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• 2016

The times of multiplication for encryption and decryption of cryptosystem is primarily determined by implementation efficiency of the modular exponentiation of $a^b$(mod m). The most frequently used among standard modular exponentiation methods is a standard binary method, of which n-ary($2{\leq}n{\leq}6$) is most popular. The n-ary($1{\leq}n{\leq}6$) is a square-and-multiply method which partitions $b=b_kb_{k-1}{\cdots}b_1b_{0(2)}$ into n fixed bits from right to left and squares n times and multiplies bit values. This paper proposes a variable-length partition algorithm that partitions $b_{k-1}{\cdots}b_1b_{0(2)}$ from left to right. The proposed algorithm has proved to reduce the multiplication frequency of the fixed-length partition n-ary method.