• 대한수학회보
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• 제51권4호
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• pp.1055-1062
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• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• 대한수학회논문집
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• 제37권3호
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• pp.669-679
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• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• 경영과학
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• 제25권2호
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• pp.81-88
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• 2008

This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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• pp.60-66
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• 2006

This paper presents a new algorithm for the K shortest path problem in a directed network. After a shortest path is produced with Dijkstra algorithm, detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set, this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated for the K-1 st path of the set. This algorithm can be applied to a problem of generating the detouring paths in the navigation system for ITS and also for vehicle routing problems.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• 대한디지털의료영상학회논문지
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• 제12권2호
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• pp.97-101
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• 2010

This experimental study is carried out one of the General Hospital in Kyungbok providence. Abdomen Phantom being located Anterior-posterior(AP) position on portable bed, and the portable X-ray generating device was placed the phantom at $-90^{\circ}$ direction. The experiment were set 65 kVp, 10 mAs, $10{\times}10\;cm^2$, 100 cm(FOD) for the measurement. Digital proportional counting tube survey meter was used for measuring the space scatter dose. Measurement points of horizontal distribution was set up at $30^{\circ}$ interval by increasing 50 cm radius of upside, downside, left and right. Vertical distribution of measurement points were set up for the vertical plane with a radius of at $30^{\circ}$ intervals with 50cm increments. It is concluded that longer distance from the soure of X-ray significantly decrease radiation dose to the patient and use of the radiation protection device should be applied in clinical practice to reduce dose to the patient.

• 대한수학회보
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• 제51권6호
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• pp.1841-1850
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• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.

• 대한수학회보
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• 제46권5호
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• pp.867-871
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• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• 디지털융복합연구
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• 제12권6호
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• pp.223-229
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• 2014

대용량의 지식베이스 시스템에서 유용한 정보를 추출하여 효율적인 의사결정을 수행하기 위해서는 정제된 특징추출이 필수적이고 중요한 부분이다. 러프집합이론에 있어서 최적의 리덕트의 추출과 효율적인 객체의 분류에 대한 문제점을 극복하고 자, 본 연구에서는 조건 및 결정속성의 효율적인 특징추출을 위한 러프엔트로피 기반 퀵리덕트 알고리듬을 제안한다. 제안된 알고리듬에 의해 유용한 특징을 추출하기 위한 조건부 정보엔트로피를 정의하여 중요한 특징들을 분류하는 과정을 기술한다. 또한 본 연구의 적용사례로써 실제로 UCI의 5개의 데이터에 적용하여 특징을 추출하는 시뮬레이션을 통하여 본 연구의 모델링이 기존의 방법과 비교결과, 제안된 방법이 효율성이 있음을 보인다.

• 대한전자공학회논문지
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• 제12권4호
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• pp.21-27
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• 1975

본 논문에서는 분기가 있는 일반조합논리회로의 다중결함을 검출할 수 있는 테스트집합을 구하는 절차를 유도하였다. 일반논리회로를 우선 내부분기점을 전후하여 이를 분기가 없는 부분회로로 분리하고 각 부분회로에 대한 최소테스트집합을 구한다. 다음에 각 부분테스트를 최대한으로 병립시켜 합성테스트를 구하여 종합적인 일차입력벡터를 정한다. 이러날 수 있는 모든 결함을 빠짐없이 피복할 수 있는 최소테스트집합을 구해가는 과정에 대해서는 각 를 들어 상세히 설명하였다. In this paper, a procedure for deriving of multiple fault detection test sets is presented for fan-out reconvergent combinational logic networks. A fan-out network is decomposed into a set of fan-out free subnetworks by breaking the internal fan-out points, and the minimal detecting test sets for each subnetwork are found separately. And then, the compatible tests amonng each test set are combined maximally into composite tests to generate primary input binary vectors. The technique for generating minimal test experiments which cover all the possible faults is illustrated in detail by examples.