• East Asian mathematical journal
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• v.21 no.2
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.721-730
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• 2004

Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate that if a sequence of p-tuples of measures converges to another p-tuple of measures, then the corresponding sequence of operational calculi in the time dependent setting converges to the operational calculus determined by the limiting p-tuple of measures.

• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.149-157
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• 2012

By means of fractional calculus techniques, we find explicit solutions of confluent hypergeometric equations. We use the N-fractional calculus operator $N^{\mu}$ method to derive the solutions of these equations.

• Research in Mathematical Education
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• v.13 no.2
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• pp.75-90
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• 2009

There are concepts in calculus which are difficult to teach and learn. One of these concepts is integration. However, problem posing has not yet received the attention it deserves from the mathematics education community. There is no systematic study that deals with teaching of calculus concepts by problem posing oriented teaching strategy. In this respect this study investigated the effect of problem posing on students' (prospective teachers') academic success when problem posing oriented approach is used to teach the integral concept in Calculus-II (Mathematics-II) course to first grade prospective teachers who are enrolled to the Primary Science Teaching Program of Education Faculty. The study used intervention-posttest experimental design. Quantitative research techniques were employed to gather, analyze and interpret the data. The sample comprised 79 elementary prospective science teachers. The results indicate that problem posing approach effects academic success in a positive way and at significant level.

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.71-85
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• 2003

In this paper we study the usefulness of Maple in school calculus education. The use of computer and calculator is debated in many aspect in mathematics education. By the computer visualization of mathematical image and proper use of computer we can teach inductively and intuitively the mathematical concept and give rise to the students' interest. Maple is very popular in college but is not in middle school because of language. Maple application which is made by Maplet is very useful multimedia teaching-learning tools. We introduce the use of Maplet and some application of the calculus course which we made.

• Journal of Periodontal and Implant Science
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• v.28 no.2
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• pp.371-376
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• 1998

This study presents an evaluation of the effectiveness of nonsurgical subgingival scaling and root planing related to initial pocket depth, type of teeth, and individual root surfaces. A total of 110 teeth designated for periodontal surgery in 67 patients with marginal periodontitis were selected and received thorough scaling and root planing with standard rigid Gracey curettes. After a healing period of 4 to 8 weeks, residual calculus was assessed at the time of periodontal surgery following the reflection of mucoperiosteal flap. The results demonstrated a high correlation between the percentage of residual calculus and initial pocket depth. It was further noted that tooth type and involved root surface also influenced the rate of calculus remnant. The results of this study suggest that complete removal of subgingival calculus utilizing conventional instrumentation via closed approach is rare.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.633-647
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• 2005

The rapid change in school mathematics curricula occurred over last some periods requires lots of change or improvement in the education method for the university mathematics, especially in calculus. As an effort in this direction we restrict our concern to the freshmen of year 2002 of the Korea university of technology and education to investigate a correlation between their mathematics score on the national entrance examination and achievement score measured by their final grades in a calculus course. As a result of this research we propose a step-wise level educational model for the calculus education. In the model an appropriate teaching contents and method proceeding through the three steps are suggested and implementation issues are discussed. We believe that carrying out mathematics curricular are suggested in the model will be of service to calculus education particularly for student under the 7th national curriculum reform.

• Journal of Pharmacopuncture
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• v.12 no.3
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• pp.41-47
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• 2009

Objectives : This experimental study was performed to investigate the efficacy of Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. Methods : After administering Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) which cause Keratitis, MIC(Minimum Inhibition Concentration) and the size of inhibition zone were measured. Anti-bacterial potency was also measured using the size of inhibition zone. Results : There was no response to MIC on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) after Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution was medicated. Conclusions : The present study suggests that Fel Ursi, Bovis Calculus & Moschus pharmacopuncture solution dosen't have anti-bacterial effects on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans) which cause Keratitis. These study result recommends that more research on other herbal medicines of eye drop for Keratitis are required.