• 대한수학회보
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• 제48권2호
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.

• 대한수학회논문집
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• 제37권4호
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• pp.1181-1197
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• 2022

We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

• 대한수학회지
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• 제32권4호
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.233-249
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• 2015

This paper is concerned with applications of representations of the Lie group of class $D_4$ to PDE. A realization of all irreducible finite-dimensional representations of $D_4$ is found and their application to a study of solutions of some systems of partial differential equations is given.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.503-521
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• 2013

지난 20여 년간 선형대수학 교수학습과정에서 공학적 도구의 필요성이 지속적으로 제기되어 왔으며 실제 선형대수학 교재를 통하여 관련된 다양한 도구가 소개되었다. 그러나 한국 대학의 선형대수학 교육에서는 다양한 현실적인 이유로 도구 활용이 미진하였다. 따라서 오랜 기간 선형대수학의 이론 교육에만 치중한 경향이 있다. 본 논문에서는 한국의 대학수학교육 부분 중 공학적 도구 도입에서 제기되는 문제점과 어려움을 모두 해결할 수 있는 대안을 구체적으로 제시한다. 그리고 실제 대학수학교육에서 공학적 도구의 활용이 이루어진 모델의 하나로 Sage를 이용하여 개발한 선형대수학 웹 콘텐츠와 행렬계산기를 소개한다. 이를 활용하면 교육현장에서 선형대수학의 대부분의 개념을 언제, 어디서나 사용가능한 무료 도구와 함께 직관적으로 이해하고, 시각화 및 대용량 계산을 수시로 편리하게 수행하며 학습할 수 있다. 더구나 다루는 행렬의 크기를 자연스럽게 변형 및 확대할 수 있다. (http://sage.skku.edu/static/mc.html)

• 한국수학교육학회지시리즈A:수학교육
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• 제47권1호
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• pp.75-89
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• 2008

Internet has been widely spread out and the need of convenient mathematical expression in the internet has been in need. In this paper, we discvss how MathML and JAVA have been developed for mathematical expressions in the internet. And we introduce our JAVA applet tools that adapted the object oriented programming techniques of the MathML and JAVA. Most of our JAVA toots have been developed for linear algebra course whose method can be applied to other subject as well. Then we discuss how we use those tools and output from the use of them in our class.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1047-1067
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• 2016

In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denoted by ${\overrightarrow{D}}_{r,s}(x)$, where $r,s{\in}{\mathbb{N}}$ and x is an indeterminate are introduced. A presentation of walled signed Brauer algebras in terms of generators and relations is given. The cellularity of a walled signed Brauer algebra is established. Finally, ${\overrightarrow{D}}_{r,s}(x)$, is quasi- hereditary if either the characteristic of a field, say p, p = 0 or p > max(r, s) and either $x {\neq}0$ or x = 0 and $r{\neq}s$.

• 대한수학회보
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• 제55권4호
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• pp.1037-1049
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• 2018

In this paper, we have first presented the construction of the linear characters of a finite Coxeter group $G_n$ of type $B_n$ by lifting all linear characters of the quotient group $G_n/[G_n,G_n]$ of the commutator subgroup $[G_n,G_n]$. Also we show that the sets of distinguished coset representatives $D_A$ and $D_{A^{\prime}}$ for any two signed compositions A, A' of n which are $G_n$-conjugate to each other and for each conjugate class ${\mathcal{C}}_{\lambda}$ of $G_n$, where ${\lambda}{\in}\mathcal{BP}(n)$, the equality ${\mid}{\mathcal{C}}_{\lambda}{\cap}D_A{\mid}={\mid}{\mathcal{C}}_{\lambda}{\cap}D_{A^{\prime}}{\mid}$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.283-294
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• 2007

By a near ${\lambda}$-lattice is meant an upper ${\lambda}$-semilattice where is defined a parti binary operation $x{\Lambda}y$ with respect to the induced order whenever $x$, $y$ has a common lower bound. Alternatively, a near ${\lambda}$-lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near ${\lambda}$-lattices is a quasivariety. A ${\lambda}$-semilattice $\mathcal{A}=(A;{\vee})$ is said to have sectional (antitone) involutions if for each $a{\in}A$ there exists an (antitone) involution on [$a$, 1], where 1 is the greatest element of $\mathcal{A}$. If this antitone involution is a complementation, $\mathcal{A}$ is called an ortho ${\lambda}$-semilattice. We characterize these near ${\lambda}$-lattices by certain identities.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권1호
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• pp.59-68
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• 2005

We are introducing a new learning environment for linear algebra at Sungkyunkwan University, and this is changing our teaching methods. Korea's e-Campus Vision 2007 is a program begun in 2003, to equip lecture rooms with projection equipment, View cam, tablet PC and internet D-base. Now our linear algebra classes at Sungkyunkwan University can be taught in a modem learning environment. Lectures can easily being recorded and students can review them right after class. At Sungkyunkwan University almost $100\%$ of all large and medium size lecture rooms have been remodeled by Mar. 2005 and are in use. We introduce this system in detail and how this learning environment changed our teaching method. Analysis of the positive effect will be added.