• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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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.

• Journal for History of Mathematics
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• v.13 no.2
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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.

• School Mathematics
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• v.17 no.1
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• pp.19-33
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• 2015

This study examined mathematics class using the CAS(Computer Algebra Systems, CAS) targeted for high school first grade students. We examined what kind of transforming of representations got up according to mathematics subject contents at this classroom. This study analyzed 15 math lessons during one month and the focus of analysis was on the classroom teacher. In particular, for transformations among representations this study mainly investigated from theoretical frameworks such as transparent and opaque representation of Lesh, Behr & Post(1987), descriptive and depictive representation of Kosslyn(1994). According to the results of this study, CAS technology affected the transforming of representations in high school math class and this transforming of representations improved the students' thinking and understanding of mathematical concepts and provided the opportunity to create the representation of individual student. Such results of this study suggest the importance of CAS technology's role in transforming of representations. and they offer the chance to reconsider the fact that CAS technology could be used to improve students' ability of transforming representations at the mathematics class.

• Journal of Korean Elementary Science Education
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• v.39 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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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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• v.3 no.1_2
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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.