• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.107-113
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• 2010

In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k ($k\;{\in}\;\mathbb{Z}$>0). We also give several relations between the roots on g(A).

• 한국수학사학회지
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• 제31권1호
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• pp.1-17
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• 2018

In this expository paper, we present an abridged report on the max-plus eigenspaces of max-plus matrices with its brief history. At the end of our work, a number of examples are presented with maple codes, and then we make a claim from the observation of these examples, which is on the euclidean dimension of the max-plus eigenspaces of strongly definite matrices.

• 한국철도학회:학술대회논문집
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• 한국철도학회 1998년도 추계학술대회 논문집
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• pp.137-143
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• 1998

Numerical simulation is conducted to clarify the heat transfer and fluid flow characteristics of traction motor for electric car SIMPLE algorithm based on finite volume method is used to make linear algebra equation. The governing equations are solved by TDMA(TriDiagonal Matrix Algorithm) with line-by-line method and block correction. From the results of simulation, the characteristics of cooling pattern is strongly affected by the size of hole in stator core. In the case of high rotational speed of rotor, temperature difference along the axial direction is more decreased than that of low rotational speed.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• 대한수학회논문집
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• 제20권3호
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• pp.443-456
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• 2005

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $L(G){\rightarrow}G$ denote the exponential mapping. For $S{\subseteq}G$, we define the tangent set of S by $L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras

• Korean Journal of Mathematics
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• 제27권2호
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• 대한수학회보
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• 제58권4호
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• 대한수학회지
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• 제59권4호
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• pp.789-804
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• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• 대한수학회보
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• 제60권1호
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• pp.83-91
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• 2023

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring M_n(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

• 한국학교수학회논문집
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• 제13권1호
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• pp.125-141
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• 2010

본 연구의 목적은 컴퓨터대수시스템(CAS)를 활용하여 개인 적응용 이산수학 학습을 가능케하는 웹기반 가상 학습용 콘텐츠를 개발하는 것이다. 중등과정과 대학과정의 이산수학에서 공통적으로 등장하는 집합, 관계, 행렬, 그래프 등의 내용 요목을 중심으로 콘텐츠를 구성하였다. 이산수학의 특성상 컴퓨터를 사용한 이산구조를 즉각적으로 처리하여 그 결과를 시각적으로 제시하는 가상 학습용 콘텐츠 제작 환경을 제시하였다. 각 단원마다 동영상 기반의 강의 콘텐츠를 제공하였으며 강의 기반의 개념을 구체화할 수 있는 Mathematica 기반의 실습하기 기능을 추가하였다. 특히 행렬 단원 학습에서 학습구조도식을 이용한 콘텐츠 설계와 이에 따른 내용 요소별 베이지언 추론망 기반의 진단학습 모듈을 추가함으로써 구체적인 피드백을 통한 개인 적응형 학습이 가능하도록 설계하였다. 개발된 행렬 학습용 콘텐츠 중심으로 10명의 이공계 대학생이 실제 사용해 본 반응을 형성평가의 일환으로 분석하여 향후 수정 방향을 도출하였다.