• Journal of the Korean Society of Costume
• /
• v.58 no.5
• /
• pp.102-117
• /
• 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
• /
• v.2 no.2
• /
• pp.27-30
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.849-856
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.277-287
• /
• 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 $x,\;y{\in}{\tau}_{\infty}(F)$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1587-1598
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1317-1329
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1503-1514
• /
• 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.

• Journal of KIISE:Computer Systems and Theory
• /
• v.36 no.4
• /
• pp.283-290
• /
• 2009

The rank/select data structure is a basic tool of succinct representations for several data structures such as trees, graphs and text indexes. For a given string sequence, it is used to answer the occurrence of characters up to a certain position. In previous studies, theoretical rank/select data structures were proposed, but they didn't support practical operational time and space. In this paper, we propose a simple solution for implementing rank/select data structures efficiently. According to experiments, our methods without complex encodings achieve nH$_0$ + O(n) bits of theoretical size and perform rank/select operations faster than the original HSS data structure.

• Journal of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.223-241
• /
• 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.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.46 no.5
• /
• pp.15-24
• /
• 2009

Compressed sensing addresses the recovery of a sparse vector from its few linear measurements. Recently, the success for the vector case has been extended to the matrix case. Compressed sensing of low-rank matrices solves the ill-posed inverse problem with fie low-rank prior. The problem can be formulated as either the rank minimization or the low-rank approximation. In this paper, we survey recently proposed efficient algorithms to solve these two formulations.