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Stability analysis of bursting models
이의우 대한수학회 2005 대한수학회지 Vol.42 No.4
In this paper, we present a general method for the stability analysisof some bursting models.Our method is geometric in the sense that we consider a flow-defined return map definedon a section and determine when the map is a contraction.We find that there are three different stability types in the codimension-1 planar bursters.
이의우 崇實大學校 1999 論文集 Vol.29 No.1
In this paper, we consider one class of bursting models that are so-called square wave bursting. One of the typical models which give rise to square wave bursting is simplified Chay-keizer model for the electrical activities of pancreatic β-cells. We describe the underlying mathematical mechanism for the bursting and present some recent mathematical resu1ts concerning the model.
Romey의 方法에 따른 高等學校 地球科學 敎科書의 分析
禹榮均,李義雨,金熙洙 공주대학교 사범대학 과학교육연구소 1993 과학교육연구 Vol.24 No.1
Science Ⅰ(2) and Earth Science, the high school textbooks by the 5th curriculu, were analyzed by Romey`s method and analytic results were compard. The results of Science Ⅰ(2) textbooks are as follows: In the contents, the index of students involvement ranges from 0.16 to 0.02. The average indices in each chapter of 8 different textbooks are 0.08, 0.10, 0.09, 0.08 and 0.05. The maximum index is in chapter Ⅱ and the maximum index chapter Ⅴ. In the figures and tables, the index of students involvement ranges from 1.00 to 0.00. The average indices in each chapter of 8 different textbooks are 0.29, 0.25, 0.21, 0.25 and 0.14. The maximum index is in chapter Ⅰ and the minimum index in chapterⅤ. In the exrecises, the index of student involvement ranges from 1.50 to 0.00. The average indices in each chapter of 8 different textbooks are 0.45, 0.23, 0.33, 0.25 and 0.31. The maximum index is in chapter Ⅰ and the minimum index in chapterⅡ. The results of Earth Science textbooks are as follows: In the contents, the index of student involvement ranges from 0.15 to 0.00. The average indices in each chapter of 7 different textbooks are 0.07, 0.06, 0.04 and 0.04. The maximum index is in chapter Ⅰ and the minimum index in chapter Ⅲ and Ⅵ. In the figures and tables, the index of student involvement ranges from 0.67 to 0.00. The average in each chapter of 7 different textbooks are 0.17, 0.21, 0.15 and 0.04. The maximum index is in chapter Ⅱ and the minimum index in chapter Ⅵ. In the exercises, the index of student ranges from 1.00 to 0.00. The average indices in each chapter of 7 different textbooks are 0.23, 0.32, 0.40 and 0.35. The maximum index is in chapter Ⅲ and the minimum index in chapter Ⅰ. The suitable involvement index for inquiry learning should be over 0.40(Romey, 1968), but the indices shown above are below 0.40. Therefore, as a whole, it is considered that Science Ⅰ(2) and Earth Science textbooks by the 5th curriculum are not suitable for inquiry learning. But, partly, ordering contents, figures and tables, and exercises index of student involvement is seen the progressive tendency to 0.40. Therefore, figures and tables than contents, and exercises than figures and tables, and Science Ⅰ(2) than Earth Science are more inquiring. And, according to the textbooks, or chapters, or contents, figures and tables, exercises, index of student involvement are partly higher than 0.40. There would be the possibility of raising the index value of the textbooks if the writer would pay more times, attentions and endeavors in editing new textbooks.