• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

• Korean System Dynamics Review
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• v.17 no.2
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• pp.5-32
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• 2016

Purpose of this paper is to review series of Limits to Growth studies from its original Rome Club Report published in 1972 to the most recent one in 2012 by Jorgen Randers and finds its implications on concept and strategy of sustainable development. For this purpose first, this paper reviewed series of Limits to Growth studies in details with focus on scenarios used in simulation of world model. Second, response to the original Limit to Growth was reviewed and to see validity of its scenario based simulations, simulated results of interest variables and actual historical data up to the year 2010 was compared. Third, structure and key arguments in both studies, Limit to Growth studies and Our Common Future was explained and compared. Finally, implications of the Limit to Growth studies on concept and strategy for sustainable development was discussed. Based on the comparison, this paper argued that even if the term sustainable development was not used in the Limit to Growth at all, concept and strategies for sustainable development implied in the Limit to Growth are more clear and specific than those of Our Common Future. Since Limit to Growth studies were simulation based ones that produce detailed behaviors on interest variables, it clarifies more clearly the abstract concept of sustainable development and thus, provides specific guidelines for the direction of sustainable policy which has been suffering long from vagueness of concept of sustainable development.

• Steel and Composite Structures
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• v.5 no.2_3
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• pp.159-168
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• 2005

Four design codes/regulations for steel structures in Japan are briefly reviewed. Some of them employ the limit state design concept while the others are still based on the allowable stress design concept. The process for revision is now in action. The directions in the development of structural design codes are also reported herein. It is noted that a current trend in this development is to employ the performance-based design concept that has been successfully implemented in some seismic design codes.

• The Mathematical Education
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• v.42 no.3
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• pp.303-325
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• 2003

This study sought to provide an explanation of university students' concept understanding on the infinity and infinite process and utilized a psychological constructivist perspective to examine the differences in transitions that students make from static concept of limit to actualized infinity stage in context of problems. Open-ended questions were used to gather data that were used to develop an explanation concerning student understanding. 47 university students answered individually and were asked to solve 16 tasks developed by Petty(1996). Microgenetic method with two cases from the expert-novice perspective were used to develop and substantiate an explanation regarding students' transitions from static concept of limit to actualized infinity stage. The protocols were analyzed to document student conceptions. Cifarelli(1988)'s levels of reflective abstraction and Robert(1982) and Sierpinska(1985)'s three-stage concept development model of infinity and infinite process provided a framework for this explanation. Students who completed a transition to actualized infinity operated higher levels of reflective abstraction than students who was unable to complete such a transition. Developing this ability was found to be critical in achieving about understanding the concept of infinity and infinite process.

• The Mathematical Education
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• v.57 no.2
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• Journal of Korean Society for Quality Management
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• v.49 no.4
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• pp.467-482
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• 2021

Purpose: The main theme of this study is to determine the optimal control limit of conditional variance investigation by mathematical approach. According to the determination approach of control limit presented in this study, it is possible with only one parameter to calculate the control limit necessary for budgeting control system or standard costing system, in which the limit could not be set in advance, that's why it has the advantage of high practical application. Methods: This study followed the analytical methodology in terms of the decision model of information economics, Bayesian probability theory and Taguchi's quality loss function concept. Results: The function suggested by this study is as follows; ${\delta}{\leq}\frac{3}{2}(k+1)+\frac{2}{\frac{3}{2}(k+1)+\sqrt{\{\frac{3}{2}(k+1)\}^2}+4$ Conclusion: The results of this study will be able to contribute not only in practice of variance investigation requiring in the standard costing and budgeting system, but also in all fields dealing with variance investigation differences, for example, intangible services quality control that are difficult to specify tolerances (control limit) unlike tangible product, and internal information system audits where materiality standards cannot be specified unlike external accounting audits.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.04a
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• pp.375-382
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• 2000

This paper briefly summarizes the basic concepts and main characteristics of seismic design of New Zealand Standards(NZS) with regard to reinforced concrete(RC) structures. NZS used the concept of the capacity design and the limit state design to satisfy the requirements of serviceability and safety. Plastic mechanisms and details with respect to the limit state of safety are briefly presented in this paper. The understanding of this advanced seismic design concept will enable us to implement the basic theory of capacity design and contribute to the development of Korean seismic code in new generation,

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.3 s.234
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• pp.390-401
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• 2005

In this study, extinction limit extension of unsteady $(CH_{4}+N_{2})$/air diffusion flames was investigated experimentally. A spatially locked flame in an opposing jet burner was perturbed by linear velocity variation, and time-dependent flame luminosity, transient maximum flame temperature and OH radical were measured over time with the high speed camera, Rayleigh scattering method and OH laser-induced fluorescence, respectively. Unsteady flames survive at strain rates that are much higher than the extinction limit of steady flames, and unsteady extinction limits extend as the slope of the strain rate increases or the initial strain rate decreases. We verified the validity of the equivalent strain rate concept by comparing the course of unsteady extinction process and steady extinction process, and it was found that the equivalent strain rate concept represents well the unsteady effect of a convective-diffusive zone. To investigate the reason of the unsteady extinction limit extension, we subtracted the time lag of the convective-diffusive zone by using the equivalent strain concept. Then the modified unsteady extinction limits become smaller than the original unsteady extinction limits, however, the modified unsteady extinction limits are still larger than the steady extinction limits. These results suggest that there exist the unsteady behavior of a diffusive-reactive zone near the extinction limit due to the chemical non-equilibrium states associated with unsteady flames.

• Special Issue of the Society of Naval Architects of Korea
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• 2015.09a
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• pp.69-73
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• 2015

An evaluation of the accidental limit state (ALS) for design of a semi-submersible drilling rig is one of the essential design requirements as well as ultimate limit state (ULS) and fatigue limit state (FLS). This paper describes the ALS evaluation on the explosion accident at shale shaker room of semi-submersible drilling rig. There are three steps for the ALS evaluation such as structural analysis at concept design, risk based safety design and structural analysis at detailed design. For the ALS evaluation at concept design, conceptual explosion overpressure from the Rule guided by the classification society was used in the structural analysis that was carried out using LS-DYNA. To set up the design accidental load (DAL), explosion analysis was carried out using FLACS taking safety barriers into consideration. Then, the structural analysis was carried out applying DAL for the ALS evaluation at detailed design. Through the ALS evaluation on the explosion at shale shaker room, the importance of the risk based safety design was described.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.931-940
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• 2006

Defect assessment of a weld zone is important in fitness-for-service evaluation of plant components. Typically a J and $C^*$ estimation method for a defective homogeneous component is extended to a mismatched component, by incorporating the effect due to the strength mismatch between the weld metal and the base material. The key element is a mismatch limit load. For instance, the R6/R5 procedure employs an equivalent material concept, defined by a mismatch limit load. A premise is that if a proper mismatch limit load solution is available, the same concept can be used for any defect location (either a weld centre defect or a heat affected zone (HAZ) defect) and for any material combination (either two-material or multi-material combinations; either similar or dissimilar joints). However, validation is still limited, and thus a more systematic investigation is needed to generalise the suggestion to any geometry, any defect location and any material combination. This paper describes the effect of structural geometry on the $C^*$ integral for defective similar welds, based on systematic elastic-creep 2-D and 3-D finite element (FE) analyses, to attempt to elucidate the questions given above. It is found that the existing 'equivalent material' concept is valid only for limited cases, although it provides conservative estimates of $C^*$ for most of cases. A modification to the existing equivalent material concept is suggested to improve accuracy.