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Polynomial growth harmonic maps on complete Riemannian manifolds
이영하 대한수학회 2004 대한수학회보 Vol.41 No.3
In this paper, we give a sharp estimate on the cardinality of the set generating the convex hullcontaining the image of harmonic mapswith polynomial growth rate on a certain class of manifoldsinto a Cartan-Hadamard manifold with sectional curvature boundedby two negative constants.We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifoldinto a regular ball in terms of massive subsets,in the case when the space of bounded harmonic functions on the manifold is finite dimensional.
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이영하 韓國體育大學校 1995 論文集 Vol.18 No.-
After analyzing data obtained from 145 athlete skaters, the following results were obtained in this study : 1. Upon analyzing the ratio of injury that occurred during a whole season, 60% of the injuries occurred during the winter. This implies that most injuries occur during the winter. 2. The injuries occurred most during competitions rather than during practice. There appears to be a high correlation between the number of years an athlete has participated in competitions and the likelihood of an athlete injuring oneself. Thus, in order to prevent injury, it appears that the development of certain skills are very importantly needed. 3. The victory and loss of important skating competitions depend much on corner gliding. 45% of the total injuries occurred in the corner. At the time of collision, the safety measures, as reported by 12% of the respondents, are generally insufficient. 4. The greatest cause of injury was reported by 50% and is said to be body collision during competitions. 18% reported that the insufficiency of the facillity was another cause. 5. Many injured athletes were often not given first and before being taken to a hospital. 6. Analysis of the time of injury and the rate of injury indicates that most injuries(39%) occur during the night time. The study shows that it is important to match warm up time to the time of a competition. 7. The number of days for which an athlete was treated was at least 1 week, as reported by 40%, It appears that despite a poor health condition, participation in competition was still high at 23%, This requires come attention. 8. The most occurred type of injury was reported by 41% as being contusion, Head injury was reported by 22%. 9. Awareness of the importance of injury prevention and safety os lacking such that it is important that coaches give much attention to athletes' warm-up and cool down periods. 10. The athletes' preparedness for injury is low. Wearing one's uniform and the safety features required during competitions may be necessary during the practice sessions. 11. Injury can be prevented by systematic training, the improvement of certain skill at appropriate times, and sufficient amount of preparation right before a competition.
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Rhodopseudomonas sp. KCTC1437에서의 Polyhydroxyalkanoates와 5-Aminolevulinic Acid의 생합성
이영하,기형석,최강국,문명님,양영기 한국미생물학회 2002 미생물학회지 Vol.38 No.2
For elucidating the relationship between the biosynthetic pathways for polyhydroxyslkanoates (PHAs) and 5-aminolevulinic acid (ALA), culture conditions for the production of these two biomaterials by Rhodopseudomonas sp. KCTC 1437 were investigated. Of the carbon substrates tested, acetic acid was the best carbon source for cell growth and PHA biosynthesis. When succinic acid was added as a co-substrate into culture medium, cell growth and PHA production were greatly increased up to 2.5 g/ι and 73% of dry cell weight, respectively. The PHA obtained from the carbon substrates tested was homopolyester of 3-hydroxybutyrate, while valeric acid was only effective for the production of copolyester consisting of 3-hydroxybutyrate and 3-hydroxyvalerate. Anaerobic light culture condition was better for PHA production and cell growth than anaerobic dark or aerobic dark culture condition. The organism was capable of synthesizing ALA when glycine and succinic acid were added to the culture medium. ALA was produced to ca.400 mg/ι when levulinic acid, soccinic acid, and glycine were repeatedly added with a reductant (sodim thioglycolate). However, the presence of glycine, levulinic acid and sodium glycolate inhibited the cell growth and the conversion of carbon substrates to PHA. From these results it is apparent that the production yields of PHA and ALA could not be increased simultaneously because the optimal conditions for the production of PHA and ALA are opposed to each other.
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교수공학 친화적, 실용적, 교수학적 변환의 실제적 연구 (10-나 삼각함수 단원을 중심으로)
이영하,신정은 대한수학교육학회 2009 학교수학 Vol.11 No.1
This paper is about didactical trans- position, which is to transpose academic knowledge into practical knowledge intended to teach. The research questions are addressed as follows. 1. Are the 13 mathematics textbooks of the 10-Na level indisputable regarding with the didactical transposition, in terms that the order of arrangement and the way of explaining the knowledge of trigonometric functions being analyzed and that its logical construction and students’ understandings are considered? 2. Can some transpositions for easier use of didactical manipulative, for more practical and for more principle based be proposed? To answer these questions, this research examined previous studies of mathematics education, specifically the organization of the textbook and the trigonometric functions, and also compared orders of arranging and ways of explaining trigonometric functions from the perspective of didactical transposition of 13 versions of the 10-Na level reorganized under the 7th curriculum. The paper investigated what lacks in the present textbook and sought a teaching guideline of trigonometric functions(especially about sector and graph, period, characters of trigonometric function, and sine rule). 본 연구는 교육적 의도를 가지고 학문적인 지식을, 가르칠 지식으로 변형하는 일, 즉 지식의 교수학적 변환(didactical transposition)에 관한 것으로서, 제 7차 교육과정에 따라 개편된 13종의 10-나 수학 교과서에서 삼각함수 단원의 내용 배열순서 및 설명 방식을 분석하고 그 결과, 교수법적 어려움과 서술의 논리성 및 학생의 이해를 함께 고려할 때, 나타나는 교수학적 변환의 어려움은 무엇이며 이를 위한 대안적 교수학적 변환의 방법이나 실제적인 어려움 해소 방안은 무엇인가를 생각해 보았다. 이를 위해 13종의 수학교과서 10-나 단계 삼각함수 단원의 설명방식의 차이를 위주로 비교 분석하고, 그 결과를 최근의 교수법 이론과 암묵적으로 비교하여 새 교수법의 적용 가능성을 높이는데 개연적이나마 도움이 되리라고 예상되는 대안적 내용서술 지도방안(부채꼴, 삼각함수의 그래프, 성질, 주기, 사인법칙에 대한 내용을 위주로)을 제안하였다.
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