- Book Chapter
- 10.1142/9789819825448_0009
Proper Actions and Representation Theory
- Mar 01, 2026
- Toshiyuki Kobayashi
Publications from 2021 to 2026
Showing 5 of 5 papers
Proper Actions and Representation Theory
A generating operator for Rankin–Cohen brackets
Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on “generating operators” for a family of differential operators between two manifolds. We prove a novel formula of the generating operators for the Rankin–Cohen brackets by using higher-dimensional residue calculus. Various results on the generating operators are also explored from the perspective of infinite-dimensional representation theory.
Read moreA Short Proof for Rankin–Cohen Brackets and Generating Operators
Exploring Fear of Oral Presentation: A Look at The Origin and Strategies for Reduction
In a language learning course, there are four skills that students must master, and communication is one of the essential skills. Lately, with the adaption of alternative assessment, an oral presentation has been a favourite assessment tool for educators to evaluate students. The main reason for students’ inability to succeed in this assessment is the fear or anxiety faced in the evaluation. Educators should educate students on ways or methods to overcome these negative feelings, as oral presentation is an essential skill that students should acquire before entering the working world. The research aims to investigate whether 1) The origins of fear influence students’ oral presentation. 2) Fear reduction strategies influents learners’ oral presentation. 3) The relationship between origins of oral presentation and fear reduction strategies. The quantitative study was contacted in several faculties in a Malaysian public university. One hundred seventy-six respondents were involved in answering a five-Likert scale survey of three sections designed to facilitate the research findings. The findings show that students’ oral presentations do influent by internal and external factors of fear. Students do implement strategies to overcome their fear of oral presentation. However, the relationship between the origins of oral presentation and fear reduction strategies was weak. The reduction strategies applied by the students did not overcome the fear of oral presentation. This study found that other issues might be the course of the fear of oral presentation.
Read moreLearning Environment: What are the University Students’ Perceptions?
Research worldwide continues to prove that the quality of the learning environment is very important in determining learning success. This study replicated the study by Hassan, Majid & Hassan (2020). A quantitative survey was distributed using Google Forms. The survey has 5 sections with a demographic profile and 30 items using a 5-Likert scale. In the context of this study, the university students are exposed to four basic types of learning environments, which are learner-centred environment, community-centred environment, assessment-centred environment and knowledge-centred environment. Questionnaires were answered by 102 students from three levels of Japanese language studies in a public university in Malaysia. Findings revealed that the students' perceptions of the learning environment were positive. The findings also showed that all four approaches; learner-centred, community-centred, assessment-centred and knowledge-centred are significant and influenced the learning environment. The learner-centred approach has the highest mean scores, which indicates that the students feel comfortable in this learning environment where they are allowed to have their own language practices. The results also showed that there are strong positive relationships between learner and community-centred, learner and assessment-centred, learner and knowledge-centred, knowledge and community-centred, knowledge and assessment-centred, and assessment and community-centred.
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