• 대한수학회보
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• 제52권2호
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• pp.627-647
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• 2015

In this paper, we construct the Schr$\ddot{o}$dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m and find covariant maps for the Schr$\ddot{o}$dinger-Weil representation.

• 호남수학학술지
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• 제26권4호
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• pp.483-507
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• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• 대한수학회지
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• 제34권2호
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• pp.345-370
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• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.689-697
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• 2022

In this paper, we study dual integrable representations of locally compact commutative hypergroups and give a sufficient and necessary condition for a dual integrable representation to have an admissible vector.

• 디지털융복합연구
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• 제14권6호
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• pp.499-511
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• 2016

음운인식은 구어의 기본 단위인 말소리를 지각하고 조작하는 능력으로, 이것은 이후 문자습득에 영향을 주는 것으로 알려져 있다. 그러나 몇몇 연구에서는 문자의 기본 단위인 철자에 대한 지식이 반대로 음운인식에 영향을 준다고 주장한다. 본 연구에서는 5, 6세 아동을 대상으로 철자표상 과제와 말소리분절 과제를 실시한 후, 두 과제 수행력 간 상관관계, 철자표상 상위집단과 하위집단 간 말소리분절 과제의 정반응 점수, 그리고 오류유형을 비교 분석하였다. 그 결과 철자표상 과제와 말소리분절 과제 수행력은 자소-음소 일치 단어에서는 양의 상관, 불일치 단어에서는 음의 상관을 보였다. 자소-음소 일치 단어의 경우 두 집단 간 말소리분절 수행력에 차이가 없었지만, 자소-음소 불일치 단어의 경우 하위집단이 상위집단보다 말소리분절 수행력이 유의하게 좋았다. 두 집단 모두에서 가장 많이 나타난 오류는 철자화 오류였고, 이러한 경향은 상위집단에서 두드러졌다. 본 연구는 철자를 배우기 시작한 직후부터는 아동들이 말소리분절 과제 수행에 철자지식을 활용하고 있음을 시사한다.

• 대한수학회논문집
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• 제32권4호
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• pp.999-1008
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• 2017

By mainly using certain properties arising from the semisimple Lie group SO(2, 1), we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.143-148
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• 2013

The theory of generalized Bessel functions is reformulated within the framework of an operational formalism using the multiplier representation of the Lie group $T_3$ as suggested by Miller. This point of view provides more efficient tools which allow the derivation of generating functions of generalized Bessel functions. A few special cases of interest are also discussed.

• East Asian mathematical journal
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• 제21권2호
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• pp.151-161
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• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.

• 대한수학회지
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• 제45권2호
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• 한국수학교육학회지시리즈A:수학교육
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• 제44권4호
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• pp.627-651
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• 2005

This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.