• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.303-311
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• 2011

Every topology is generated by a quasi-uniform distance system. The quasi-uniform distance system is a uniform distance system. The topology is uniformizable if and only if it is generated by the uniform distance system with the symmetric distance function.

• The Mathematical Education
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• v.56 no.4
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• pp.387-405
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• 2017

The purpose of this study is to investigate the change of students 'perception and expression about the motion of object following distance function $={x \atop 3}$ and distance function $y=\frac{x^3}{3}+3$ according to the necessity of research on students' perception and expression about integral constant. In this paper, we present the recognition and the expression of the difference of the constant in the relationship between the distance function and the speed function of the students, while examining the process of constructing the speed function and the inverse process of the distance function. This provides implications for the relationship between the derivative and the indefinite integral corresponding to the inverse process. In particular, in a teaching experiment, a constructive activity was performed to analyze the motion of two distance functions, where the student had a difference of the constant term. At this time, the students used the expression 'starting point' for the constants in the distance function, and the motion was interpreted by using the meaning. This can be seen as a unique 'students' mathematics' in the process of analyzing the motion of objects. These scenes, in introducing the notion of the relation between differential and indefinite integral, it is beyond the comprehension of the integral constant as a computational procedure, so that the learner can understand the meaning of the integral constant in relation to the motion of the object. It is expected that it will be a meaningful basic research on the relationship between differential and integral.

• Environmental and Resource Economics Review
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• v.16 no.1
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• pp.171-197
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• 2007

In this paper we provide a methodology that permits test of feasibility of Porter hypothesis under limited data environment by utilizing two types of output distance function: Shephard distance function and directional distance function. The production technology supported by Porter hypothesis is embodied in the directional distance function. The average annual marginal abatement cost for $SO_2$ obtained by estimating the directional distance function is higher than the one obtained with the Shephard distance function by about 50 percent in the Korean electric power industry over the period 1970~1998. This result implies that feasibility of Porter hypothesis depends upon whether investment in production capital and process can bring more than a 50 percent increase in the average productivity.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.783-790
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• 2014

Most distance functions, including taxicab distance, are defined on Cartesian plane, and recent studies on distance functions have been mainly focused on Cartesian plane. However, most streets in cities include not only straight lines but also curves. Therefore, there is a significant need for a distance function to be defined on a curvilinear coordinate system. In this paper, we define a new function named polar taxicab distance, using polar coordinates. We prove that this function satisfies the conditions of distance function. We also investigate the geometric properties and classifications of circles in the plane with polar taxicab distance.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.668-672
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• 2005

In this paper, a distance measuring system using a PSD sensor in proposed, which in suitable for low-cost localization sensor of a mobile robot. Because the distance-voltage output of PSD sensor has a non-linear property, the linearizing function is proposed through the experimental characteristics of the sensor. And the characteristics are tested and the distance-voltage data are measured in various colors and materials of object. The parameters of the proposed function are extracted by using the measured data. Finally, the performance and the accuracy of the developed system are verified according to the comparison of the distance by the proposed function with the real distance.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.337-347
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• 2012

The taxicab distance and Chinese-checker distance in the plane are practical distance notions with a wide range of applications compared to the Euclidean distance. The ${\alpha}$-distance was introduced as a generalization of these two distance functions. In this paper, we study alpha circle, trigonometry, and the area of a triangle in the plane with ${\alpha}$-distance.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.9
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• pp.411-416
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• 2001

Distance relay is the most widely used in transmission line protection because it is applicable not only as main protection but also as back-up protection. However, the protection range of the distance relay is always fixed in the unchangeable operating range while the power system varies, and therefore the distance relay is the device that is the highly influenced by the power system changes. In this regard, this paper describes an approach to minimize the mal-operation of the distance relay due to the power system changes through changing protection range of the distance relay into optimal condition in response to the load variation and power system condition. Also mal-function of the distance repay in case of high resistance ground faults could be minimized through modeling the protection range into quadratic function.

• School Mathematics
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• v.18 no.4
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• pp.881-901
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• 2016

This study is about investigating students' recognition and expression on relationship of 'time, distance, speed' via teaching experiment. In this process, students showed not only a change in perception of the relationship of 'time, distance, speed' but also recognizing the average speed as a viewpoint of the slope of the line connecting the end points of the interval in the distance function as well as another way of perceiving average speed of a height of a rectangle. In this process, the study shows the scene of expanding the relation of 'distance = time ${\times}$ speed' to 'distance = time ${\times}$ average speed', and also the student who makes the continuous reasoning shows the possibility of constructing a new function that can explain the change of the primitive function by allocating the average rate of change to the interval. Although this study was conducted with a limited number of students, this study suggests some implications through the observation of relationship of 'time, distance, speed' the students'. We hope that these results will be the starting point for various studies for constructing the integral learning model in the future.

• Journal of the Korean Regional Science Association
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• v.31 no.2
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• pp.47-61
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• 2015

The purpose of this study to empirical analysis of the effects of distance-decay for the relocated firms in the Seoul Metropolitan Area(SMA). In addition, this study was constructed distance-decay function for the relocated firms by industrial types using a general distance-decay function. The data of relocated firms in the SMA extracted from the spatial database which was constructed in an previous research. The industrial type divided into 3 parts which are construction, manufacturing, and service. The result of empirical analysis by each industrial type of the effect of distance-decay, the explanatory power($R^2$) of the each function were all high. In the construction, the adjusted $R^2$ of the distance-decay function was 0.728, the manufacturing was 0.802 and the service was 0.812. It means the effect of distance decay for the relocated firms in construction industrial type more big than the effects of distance decay for the manufacturing and service industrial types.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.21-22
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• 2008

Fuzzy entropy is designed for non-convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non-convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.