• Research in Mathematical Education
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• v.27 no.1
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.39-45
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• 2001

Maximum and minimum of rendom variables are frequently encountered in the stochastic modelling for various OR problems. We summarize and extend characteristics of maximum and minimum, emphasizing the case in which random variables are independent and all of them except one are distributed exponential. As an application, we derive a transform-free expression for the M/G/1 queue length distribution.

• The Mathematical Education
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• v.49 no.2
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• pp.247-257
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• 2010

In this article an explanation of monotonicity of functions and the definition of local extrema in Korean highschool textbooks based on national curriculum(revised in 2007) are analyzed critically. On the basis of this analysis, we indicate some problems and propose its improvements.

• Journal of Korean Society for Quality Management
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• v.7 no.2
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• pp.7-10
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• 1979

In this paper the Rao-Blackwell and Lehmann-$Scheff{\acute{e}}$ Theorem are used to drive the minimum variance unbiased estimators of system reliability for a number of distributions when a system consists of n Components whose random life times are assumed to be independent and identically distributed. For the case of a negative exponential life time, we obtain the maximum likelihood estimator of the system reliability and compair it with minimum variance unbiased estimator of the system reliability.

• KIEE International Transactions on Power Engineering
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• v.2A no.3
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• pp.121-128
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• 2002

This study proposes a new method for transmission system expansion planning using fuzzy integer programming. It presents stepwise cost characteristics analysis which is a practical condition of an actual system. A branch and bound method which includes the network flow method and the maximum flow - minimum cut set theorem has been used in order to carry out the stepwise cost characteristics analysis. Uncertainties of the permissibility of the construction cost and the lenient reserve rate and load forecasting of expansion planning have been included and also processed using the fuzzy set theory in this study. In order to carry out the latter analysis, the solving procedure is illustrated in detail by the branch and bound method which includes the network flow method and maximum flow-minimum cut set theorem. Finally, case studies on the 21- bus test system show that the algorithm proposed is efficiently applicable to the practical expansion planning of transmission systems in the future.

• Proceedings of the KIEE Conference
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• 2001.11b
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• pp.350-353
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• 2001

This study proposes a new method for the transmission system expansion planning using the fuzzy integer programming. It presents stepwise cost characteristics analysis which is a practical condition of an actual systems. A branch and bound method which includes the network flow method and the maximum flow-minimum cut set theorem has been used in order to proceed the stepwise cost characteristics analysis. Uncertainties of the permission of the construction cost and not strict reserve rate and load forecasting of expansion planning have been included and also processed using fuzzy set theory in this study. In order to proceed the latter analysis, the solving procedure is illustrated in detail by branch and bound method which includes the network flow method and maximum flow-minimum cut set theorem. Finally, case studies on 21-bus test system show that the algorithm proposed is efficiently applicable to the practical expansion planning of transmission systems in future.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.105-114
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• 1993

In this article, a planar geodesic (2-dimensional minimum length curve between two points) on which the maximum curvature is constrained and with prescribed initial and terminal directions is studied. A generic problem is formulated by the minimum-time optimal control problem in free terminal time. It is shown that the optimal path ($G^2$) may contain a singular arc or not and that the general types of $G^2$ can he classified into the 3 classes of control sequences. Finally, the explicit form of $G^2$ is derived geometrically as well as algebraically form the main theorem of this article.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.1
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• pp.9-16
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• 1984

This paper describes the minimum cost expansion planning which is based on the economical aspect under the various conditions on the power system expansion planning. It presents not only linear cost characteristics analysis but also stepwise cost characteristics analysis which satisfies practical condition in the power system. The latter analysis must be handled by integer programming (IP), because the relation between the cost and the capacity has stepwise characteristics. In order to proceed the latter analysis, the solving procedure is illustrated in detais by using branch and bound method which includes the network flow theory and maximum flow-minimum cut theorem.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.329-334
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• 1996

The notion of approximate derivative was introduced by Denjoy in 1916 [3]. Khintchine [5] proved that Rolle's theorem holds for approximate derivatives and Tolstoff [8] proved that every approximate derivative is of Baire class 1 and has Darboux property. Goffman and Neugebauer [4] proved the above results of Tolstoff [8] in a different and simplified method. Also they [4] proved indirectly (via Darboux property) that approximate derivatives possess mean value property.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5A
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• pp.477-486
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• 2009

This paper deals with the strongest static arches with the solid regular polygon cross-section. Both span length and volume of arch are always held constant regardless the shape functions of cross-sectional depth of regular polygon. The normal stresses acting on such arches are calculated when both static vertical and horizontal point loads are subjected. By using the calculating results of stresses, the optimal shapes of strongest static arches are obtained, under which the maximum normal stress become to be minimum. For determining the redundant of such indeterminate arches, the least work theorem is adopted. As the numerical results, the configurations, i.e. section ratios, of the strongest static arches are reported in tables and figures. The results of this study can be utilized in the field of the minimum weight design of the arch structures.