• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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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.

• Honam Mathematical Journal
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• v.26 no.4
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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 $C*_r(N^+){\ncong}C^*(N^+)$.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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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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• v.62 no.4
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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.

• Journal of Digital Convergence
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• v.14 no.6
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• pp.499-511
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• 2016

The aim of this study was to find out effect of the orthographic representation on speech sound segmentation performance. Children's performances of the orthographic representation task and the speech sound segmentation task had positive correlation in words of phoneme-grapheme correspondence and negative correlation in words of phoneme-grapheme non-correspondence. In the case of words of phoneme-grapheme correspondence, there was no difference in performance ability between orthographic representation high level group and low level group, while in the case of words of phoneme-grapheme non-correspondence, the low level group's performance was significantly better than the high level group's. The most frequent errors of both groups were orthographic conversion errors and such errors were significantly more noticeable in the high level group. This study suggests that from the time of learning orthographic knowledge, children utilize orthographic knowledge for the performance of phonological awareness tasks.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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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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• v.53 no.1
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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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• v.21 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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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).

• The Mathematical Education
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• v.44 no.4 s.111
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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.