• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.345-370
• /
• 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
• /
• v.45 no.3
• /
• pp.303-338
• /
• 2005

In this paper, we study unitary representations of the group $GL(n,{\mathbb{R}}){\ltimes}{\mathbb{R}}^{(m,n)}$.

• Communications of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.27-41
• /
• 2019

We determine explicit formulas for the number of representations of a positive integer n by quaternary quadratic forms with coefficients 1, 2, 5 or 10. We use a modular forms approach.

• Korean Management Science Review
• /
• v.14 no.1
• /
• pp.205-227
• /
• 1997

Higher level representation splay an important role in model management systems. The role is to make decision makers friendly represent their problem using the representations. In this research, we address higher level representations including five distinctivenesses: Objective, Node, Link, Topological Constraint including five components, and Decision, Therefore, it is developed a system called HLRNET that implements the building procedure of network models using structural knowledge and object data The paper particularly elaborates all components included in each of distinctiveness extracted from structural characteristics of a lot of telecommunication network models. Higher level representations represented with five destinctivenesses should be converted into base level representations which are employed for semantic representations of linear and integer programming problems in a knowledge-assisted optimization modeling system. The system is illustrated with an example of the local access network model.

• Korean Journal of Child Studies
• /
• v.29 no.3
• /
• pp.157-174
• /
• 2008

This study used the person-oriented approach to explore differences in narrative representations of 97 4-, 5- and 6-year old children (30 foster care, 40 biological family, 17 adopted). Using the MacArthur Story Stem Battery (Bretherton et al., 1990), observations were made to obtain children's narrative representations of content themes and performances. Descriptive statistics, ANOV A and hierarchical cluster analyses were performed. The results of this study were that : (1) Biological family children showed more empathy/helping representations. Foster care children and adopted children showed more anxious representations, and foster care children showed more dysregulated aggression. (2) Four clusters of foster care and adopted children and five clusters of family biological children were found.

• East Asian mathematical journal
• /
• v.31 no.1
• /
• pp.41-53
• /
• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.

• Korean Journal of Child Studies
• /
• v.25 no.6
• /
• pp.153-170
• /
• 2004

This study explored age and sex differences in preschoolers' narrative representations of their mothers. Subjects were 120 3-, 4-, 5- and 6-year-old children, with 15 boys and 15 girls in each age group. Using the MacArthur Story Stem Battery(Bretherton et al., 1990), observations were made to obtain children's narrative representations of their mothers. content themes and emotional responses. Boys' representations were more negative and less positive than girls' regardless of their age. Boys talked about more aggressive themes and showed more anxiety and less joy. Five and 6-year-old children had less negative and disciplinary representations of their mothers than 3- and 4-year-olds. Six-year-olds showed less prosocial themes than 3- and 5-years, and fewer aggressive themes than 3-and 4-year while they showed less joy, distress and concern responses than 3-years.

• Journal of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.651-662
• /
• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• Journal of Information Processing Systems
• /
• v.19 no.3
• /
• pp.355-369
• /
• 2023

Since the widespread adoption of deep-learning and related distributed representation, there have been substantial advancements in part-of-speech (POS) tagging for many languages. When training word representations, morphology and shape are typically ignored, as these representations rely primarily on collecting syntactic and semantic aspects of words. However, for tasks like POS tagging, notably in morphologically rich and resource-limited language environments, the intra-word information is essential. In this study, we introduce a deep neural network (DNN) for POS tagging that learns character-level word representations and combines them with general word representations. Using the proposed approach and omitting hand-crafted features, we achieve 90.47%, 80.16%, and 79.32% accuracy on our own dataset for three morphologically rich languages: Uyghur, Uzbek, and Kyrgyz. The experimental results reveal that the presented character-based strategy greatly improves POS tagging performance for several morphologically rich languages (MRL) where character information is significant. Furthermore, when compared to the previously reported state-of-the-art POS tagging results for Turkish on the METU Turkish Treebank dataset, the proposed approach improved on the prior work slightly. As a result, the experimental results indicate that character-based representations outperform word-level representations for MRL performance. Our technique is also robust towards the-out-of-vocabulary issues and performs better on manually edited text.

• Journal of the Korean Chemical Society
• /
• v.56 no.6
• /
• pp.759-767
• /
• 2012

The purpose of this study was to examine the impact of Science Writing Heuristic (SWH) on multiple representations in students' writing and to survey experimental group students' recognition about the use of multiple representations. For this study, Participants of this study were 158 students in 7th grade. 94 students were assigned to the experimental group and 64 students were assigned to the comparative group. The experimental group showed significantly higher mean score than comparative group at utilizing multiple representation in summary writing. Interview analysis indicated that all students who participated in interviews, regardless of solid multi-modal competency, recognized that use of multiple representations with appropriate explanations enable to communicate science information persuasively.