• 복식
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• 제58권5호
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• pp.102-117
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• 2008

This study shows the badge system for military officials of Joseon dynasty. The badge system for military officials of the 15th century consists of rank badges with tiger and leopard for the first and second ranks and rank badges with bear for the third rank. According to the code of laws, military officials are supposed to wear the rank badges with four different kinds of animals in Joseon dynasty. However, the badge system shown in the code of laws sometimes does not match with the badges in practices. Based on the literature, remaining badges and the badges in portraits, six different kinds of badges with animals are found : First, rank badges with tiger and leopard were used until the late 16th century. Second, rank badges with tiger were found in the period between the early 17th century and the latter 18th century. Third, rank badges with Haechi were found in the early 17th century. Fourth, rank badges with lions can be found in remains of the mid 17th century, the literature and the portrait of the late 18th century. Finally, the rank badges with double leopards or with single leopard were found from a portrait dated the late of 18th century to the last period of Joseon dynasty.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.27-30
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• 1998

Let A and B be $m{\times}n$ matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A+B) = rank(A)+rank(B) implies that rank(T(A) + T(B)) = rankT(A) + rankT(B). We characterize the set of all linear operators which preserve the set of pairs of $n{\times}n$ matrices on which the rank is additive.

• 대한수학회지
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• 제32권4호
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• pp.849-856
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• 1995

There are some papers on structure theorems for the spaces of matrices over certain semirings. Beasley, Gregory and Pullman [1] obtained characterizations of semiring rank 1 matrices over certain semirings of the nonnegative reals. Beasley and Pullman [2] also obtained the structure theorems of Boolean rank 1 spaces. Since the semiring rank of a matrix differs from the column rank of it in general, we consider a structure theorem for semiring rank in [1] in view of column rank.

• 대한수학회보
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• 제54권1호
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• pp.277-287
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• 2017

We consider ${\tau}_{\infty}(F)$ - the space of upper triangular infinite matrices over a field F. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps ${\phi}$ such that rank(x + y) = rank(x) + rank(y) implies rank(${\phi}(x+y)$) = rank(${\phi}(x)$) + rank(${\phi}(y)$) for all $x,\;y{\in}{\tau}_{\infty}(F)$.

• 대한수학회보
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• 제55권5호
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• pp.1587-1598
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• 2018

We study additive decompositions (and generalized additive decompositions with a zero-dimensional scheme instead of a finite sum of rank 1 tensors), which are not of minimal degree (for sums of rank 1 tensors with more terms than the rank of the tensor, for a zero-dimensional scheme a degree higher than the cactus rank of the tensor). We prove their existence for all degrees higher than the rank of the tensor and, with strong assumptions, higher than the cactus rank of the tensor. Examples show that additional assumptions are needed to get the minimally spanning scheme of degree cactus +1.

• 대한수학회지
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• 제54권4호
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• pp.1317-1329
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• 2017

A Boolean rank one matrix can be factored as $\text{uv}^t$ for vectors u and v of appropriate orders. The perimeter of this Boolean rank one matrix is the number of nonzero entries in u plus the number of nonzero entries in v. A Boolean matrix of Boolean rank k is the sum of k Boolean rank one matrices, a rank one decomposition. The perimeter of a Boolean matrix A of Boolean rank k is the minimum over all Boolean rank one decompositions of A of the sums of perimeters of the Boolean rank one matrices. The arctic rank of a Boolean matrix is one half the perimeter. In this article we characterize the linear operators that preserve the symmetric arctic rank of symmetric Boolean matrices.

• 대한수학회지
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• 제56권6호
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• pp.1503-1514
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• 2019

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.

• 한국정보과학회논문지:시스템및이론
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• 제36권4호
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• pp.283-290
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• 2009

Rank/select 자료구조는 트리, 그래프, 문자열 인덱스 등의 다양한 자료구조를 간결하게 표현하는 기본 도구이다. Rank/select 자료구조는 주어진 문자열에 어느 위치까지 나타난 문자 개수를 세는 연산을 처리한다. 효율적인 rank/select 자료구조를 위해 이론적인 압축 방식들이 제안되었으나, 실제 구현에 있어 연산 시간 및 저장 공간의 효율을 보장할 수 없었다. 본 논문은 간단한 방법으로 이론적인 압축 크기를 보장하면서 연산 시간도 효율적인 rank/select 자료구조 구현 방법을 제시한다. 본 논문의 실험을 통해, 복잡한 인코딩 방법 없이도 이론적인 nH$_0$ + O(n) 비트 크기에 근접하면서 기존의 HSS 자료구조보다 빠른 rank/select 연산을 지원하는 구현 방법임을 보인다.

• 대한수학회지
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• 제42권2호
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• pp.223-241
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• 2005

Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.

• 대한전자공학회논문지SP
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• 제46권5호
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• pp.15-24
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• 2009

Compressed sensing은 소수의 선형 관측으로부터 sparse 신호를 복원하는 문제를 언급하고 있다. 최근 벡터 경우에서의 성공적인 연구 결과가 행렬의 경우로 확장되었다. Low-rank 행렬의 compressed sensing은 ill-posed inverse problem을 low-rank 정보를 이용하여 해결한다. 본 문제는 rank 최소화 혹은 low-rank 근사의 형태로 나타내질 수 있다. 본 논문에서는 최근 제안된 여러 가지 효율적인 알고리즘에 대한 survey를 제공한다.