• 대한수학회보
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• 제56권5호
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• pp.1143-1157
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• 2019

Let $T_aD_b(n)$ and $T_aD^{\prime}_b(n)$ denote respectively the number of representations of a positive integer n by $a(x^2-x)/2+b(4y^2-3y)$ and $a(x^2-x)/2+b(4y^2-y)$. Similarly, let $S_aD_b(n)$ and $S_aD^{\prime}_b(n)$ denote respectively the number of representations of n by $ax^2+b(4y^2-3y)$ and $ax^2+b(4y^2-y)$. In this paper, we prove 162 formulas for these functions.

• 대한수학회지
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• 제57권6호
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• pp.1373-1388
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• 2020

In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

• 한국수학사학회지
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• 제13권2호
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• pp.151-160
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• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• 대한수학교육학회지:학교수학
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• 제17권1호
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• pp.19-33
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• 2015

본 연구는 일반계 고등학교 1학년 학생들을 대상으로 컴퓨터 대수시스템(Computer Algebra Systems, CAS), 즉 CAS 공학을 사용한 수학수업을 교사의 표상 전환 중심으로 살펴보았다. 이 수업에서 수학교과 내용별로 어떤 표상 전환이 일어났는지를 한 달 진행된 CAS 공학을 사용한 15차시 수업 중 합성함수의 개념 도입부분에 해당하는 두 차시의 수학 수업을 중심으로 분석하였다. 특히 Lesh, Behr, & Post(1987)의 투명 표상과 불투명 표상 사이의 전환과 Kosslyn(1994)의 설명 표상과 묘사 표상 사이의 전환을 중심으로 살펴보았다. 본 연구의 결과 CAS 공학은 일반계 고등학교 수학 수업에서 표상 전환을 도와주었으며 교사 개인의 표상을 만들어내는 기회를 제공하였다. 그러나 표상 전환의 기회가 모두 교수-학습의 목적에 맞게 사용되지는 않았다. 이러한 결과는 수학 수업에서 CAS 공학에 의한 표상 전환의 새로운 역할의 중요성과 교사 역할의 중요성을 재고하는 기회를 제공할 것으로 기대된다.

• 한국초등과학교육학회지:초등과학교육
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• 제39권1호
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• pp.26-39
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• 2020

Visual Representation Competence Taxonomy (VRC-T) was developed in previous study(Yoon, 2018) to provide a framework conducive to assess visual representation competence and to devise appropriate educational activities for it. This study is an extension of the previous study. It aimed to explore the usefulness of VRC-T and revise it by analyzing the patterns of visual representation use in science lessons. The researcher collected lesson plans on shadow principle from 11 pre-service and 13 in-service elementary teachers and conducted individual interviews regarding what visual representations they considered and how they tried to use them in science lessons. VRC-T was used as an analytical framework to examine the types and cognitive processes of visual representations. As a result, new categories were added and the revised VRC-T was completed (VRC-TR). It was also found that both pre- and in-service teachers mainly focused on 'interpreting' the 'descriptive representation' while designing their lesson plans. Additionally, in-service teachers showed more limited use of visual representations compared to pre-service teachers. In-service teachers largely relied on the national science textbooks, while pre-service teachers reflected their own learning experiences in their teacher-training program. These results showed that teachers' use of visual representations heavily relied on their prior learning and teaching experiences. The VRC-TR presented in this study and examples of class activities in each category can be helpful for teachers and researchers who want to use visual representations more effectively.

• 대한수학회보
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• 제40권3호
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• pp.537-544
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• 2003

The non-existence is proved of continuous irreducible representations p : Gal(Q/Q) \longrightarrow GL$_2$(F$_{p}$) with Artin conductor N outside p for a few small values of p and N.N.

• 대한수학회보
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• 제44권1호
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• pp.173-176
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• 2007

The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\=\mathbb{Q}/\mathbb{Q}$) which are unramified outside 2.

• 대한수학회지
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• 제36권2호
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• pp.421-430
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• 1999

In this paper we investigate representation groups of wreathed 2-groups and explicitly determine all the linearly inequivalent irreducible projective representations of wreathed 2-groups.

• 대한수학회보
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• 제33권2호
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• pp.213-219
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• 1996

In this note we study the representations on Hilbert space of involutive semigroups, i.e., semigroups endowed with an involutive antiautomorphism. This subject is studied by K. H. Neeb, and some interesting results are ivestigated ([3]).

• International Journal of CAD/CAM
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• 제3권1_2호
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• pp.13-17
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• 2003

Hybrid method of representing geometric entities as combination of boundary (B-rep) and functional (F-rep) representations is presented which can be used as a basis of solid modeling kernel. It contains whole functionality of classic B-rep kernel, and also supports enveloping (sweep of solid body). Principles and keysolutions are considered. Example of a real task that comes from gearing is provided.