• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.773-782
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• 1994

Investigation of the number of representations as well as of projective representations of a finite group has been important object since the early of this century. The numbers are very related to the number of conjugacy classes of G, so that this gives some informations on finite groups and on group characters. A generally well-known fact is that the number of non-equivlaent irreducible representations, which we shall write as n.i.r. of G is less than or equal to the number of conjugacy classes of G, and the equality holds over an algebraically closed field of characteristic not dividing $\mid$G$\mid$. A remarkable result on the numbers due to Reynolds can be stated as follows.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1187-1237
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• 2020

Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.527-538
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• 2014

Let K be a compact Hausdorff space, $\mathfrak{A}$ a commutative complex Banach algebra with identity and $\mathfrak{C}(\mathfrak{A})$ the set of characters of $\mathfrak{A}$. In this note, we study the class of functions $f:K{\rightarrow}\mathfrak{A}$ such that ${\Omega}_{\mathfrak{A}}{\circ}f$ is continuous, where ${\Omega}_{\mathfrak{A}}$ denotes the Gelfand representation of $\mathfrak{A}$. The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology ${\sigma}(\mathfrak{A},\mathfrak{C}(\mathfrak{A}))$, are discussed. We also provide some results on its completeness under the norm defined by ${\mid}{\parallel}f{\parallel}{\mid}={\parallel}{\Omega}_{\mathfrak{A}}{\circ}f{\parallel}_{\infty}$.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1239-1252
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• 2010

The structure of V(Ƶ($ZA_n$)) is known when $n\leq6$. If n = 5 or 6, then a complete set of generators of V (Ƶ($ZA_n$)) has been deter-mined. In this study, it was shown that V (Ƶ($ZA_n$)) is trivial when n = 7, 8 or 9 and it is generated by a single unit u when n = 10 or 11: This unit u is characterized explicitly for n = 10 or 11 by using irreducible characters of $A_n$.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.915-931
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• 2009

The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• Biotechnology and Bioprocess Engineering:BBE
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• v.8 no.1
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• pp.23-31
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• 2003

A mathematical model was formulated to simulate the long-term performance of an anaerobic bioreactor designed to digest Korean food wastes. The system variables of various decomposition steps were built into the model, which predicts the temporal characters of Solid waste, and volatile fatty acid (VFA) in the reactor, and gas production in response to various input loadings and temperatures. The predicted values of VFA and gas production were found to be in good agreement with experimental observations in batch and repeated-input systems. Finally, long-term reactor performance was simulated with respect to the seasonal temperature changes from 5C in winter to 25C in Summer at different food waste input loadings. The simulation results provided us with information concerning the success or failure of a process during long-term operation .

• Journal for History of Mathematics
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• v.28 no.5
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• pp.263-278
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• 2015

As intuition is more unreliable than logic or reason, its studies in mathematics and mathematics education have not been done that much. But it has played an important role in the invention and development of mathematics with logic. So, it is necessary to recognize and explore the value of intuition in mathematics education. In this paper, I investigate the function and role of intuition in terms of mathematical learning and problem solving. Especially, I discuss the positive and negative aspects of intuition with its characters. The intuitive acceptance is decided by self-evidence and confidence. In relation to the intuitive acceptance, it is discussed about the pedagogical problems and the role of intuitive thinking in terms of creative problem solving perspectives. Intuition is recognized as an innate ability that all people have. So, we have to concentrate on the mathematics education via intuition and the complementary between intuition and logic. For further research, I suggest the studies for the mathematics education via intuition for students' mathematical development.

• The Mathematical Education
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• v.40 no.1
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• pp.67-75
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• 2001

Since performance assessment was introduced in Korea in the middle of 1990, many problems which include its definition, characters, methods and scorings etc., raised in mathematics education worlds. Therefore this paper presents the theoretical background of performance assessment in mathematics education. Contemporary teaching and loaming theories reject stimulus-response theory which emphasizes outcome. Performance assessment emphasizes the assessment which reveal learning process and various strategies. And it bases on constructivism and socio-cultural perspective. This paper presents paradigms which guide the roles and purposes of assessment. The paradigms include conventional paradigm, constructivist paradigm and critical paradigm. There is a close correlation between constructivist paradigm and performance assessment. Assessment has to grasp the development of present and the possibility of development of future of the students. Performance assessment must be fixed the new paradigm of education for this purpose.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1392-1394
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• 1996

This paper presents an algorithm to separate vowels from consonants in Korean characters captured in noisy images and to recognize them. The algorithm has been originally developed for the recognition of the usage code (which is represented by a single Korean character) in the license plates or Korean vehicles. It, however, could be easily adopted to other applications with minor changes, in which character recognition is needed and the environment is noisy. The key ideas or the algorithm are to localize the vowels utilizing the Hough transformation and to separate the vowels from consonants utilizing mathematical morphology. We observed that the presented algorithm effectively separates vowels even if the vowels and consonants are joined together after thresholding. We also observed that our algorithm outperforms some conventional algorithms especially when the input images are noisy. The details of the comparison study are presented in the paper.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.