• East Asian mathematical journal
• /
• 제32권1호
• /
• pp.77-84
• /
• 2016

We explicitly derive diagrams representing (1,1)-decompositions of rational pretzel knots $K_{\beta}=M((-2,\;1),\;(3,\;1),\;({\mid}6{\beta}+1{\mid},{\beta}))$ from four unknotting tunnels for ${\beta}=1,\;-2$ and 2.

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.1-15
• /
• 2022

In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

• East Asian mathematical journal
• /
• 제33권1호
• /
• pp.67-74
• /
• 2017

Let k, m and t be positive integers with $m{\geq}4$ and even. It is shown that $K_{km+1(2t)}$ has a decomposition into gregarious m-cycles. Also, it is shown that $K_{km(2t)}$ has a decomposition into gregarious m-cycles if ${\frac{(m-1)^2+3}{4m}}$ < k. In this article, we make a remark that the decompositions can be circulant in the sense that it is preserved by the cyclic permutation of the partite sets, and we will exhibit it by examples.

• 대한수학회보
• /
• 제55권5호
• /
• 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.

• 대한수학회보
• /
• 제52권1호
• /
• pp.85-103
• /
• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• 대한수학회지
• /
• 제45권4호
• /
• pp.965-976
• /
• 2008

In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제27권1호
• /
• pp.1-22
• /
• 2023

In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial Xa00 Xa11··· Xann over a field k. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end.

• 대한수학회지
• /
• 제5권1호
• /
• pp.23-24
• /
• 1968

• 대한수학회지
• /
• 제5권1호
• /
• pp.7-10
• /
• 1968

• East Asian mathematical journal
• /
• 제15권1호
• /
• pp.135-146
• /
• 1999