• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.297-309
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• 2001

White noise distribution theory over the complex Gaussian space is established on the basis of the recently developed white noise operator theory. Unitarity condition for a white noise operator is discussed by means of the operator symbol and complex Gaussian integration. Concerning the overcompleteness of the exponential vectors, a coherent sate representation of a white noise function is uniquely specified from the diagonal coherent state representation of the associated multiplication operator.

• Journal of the Korean Chemical Society
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• v.58 no.6
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• pp.580-589
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• 2014

The concepts used to explain specific phenomenon can be influenced by context or coherent regardless of context. The purpose of this study is to understand middle school students' concept of particles in particular context and to investigate the effects of context on concept of particles. A conceptual questionnaire was developed to find out how students represented particles in two contexts: solid and solution states of electrolytes, and ion precipitation reaction. The questionnaire was administered to $9^{th}$ grade students after classes of 'electrolyte and ions' unit. The responses of students were analyzed using framework developed for categorization of students' concepts. The results are as follows: First, it was found that students used various concepts on particles when they explained solid and solution state of electrolytes, respectively. Second, we identified students' concepts of particles used to explain ion precipitation reaction. In addition, we recognized that majority of students failed to write correct chemical symbols. Third, approximately 79% of students showed coherent responses for explanation of particles in solution state of both electrolytes and ion precipitation reaction. About 57% of students had scientific concepts. Some suggestions were made based on results for acquisition of scientific concepts on particles in different contexts.