• Journal of Korean Society of Transportation
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• v.25 no.4
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• pp.99-108
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• 2007

This paper presents an elastic demand stochastic user equilibrium traffic assignment that could not be easily tackled. The elastic demand coupled with a travel performance function is known to converge to a supply-demand equilibrium, where a stochastic user equilibrium (SUE) is obtained. SUE is the state in which all equivalent path costs are equal, and thus no user can reduce his perceived travel cost. The elastic demand SUE traffic assignment can be formulated based on a dynamic system, which is a means of describing how one state develops into another state over the course of time. Traditionally it has been used for control engineering, but it is also useful for transportation problems in that it can describe time-variant traffic movements. Through the Lyapunov Function Theorem, the author proves that the model has a stable solution and confirms it with a numerical example.

• Communications of Mathematical Education
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• v.5
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.

• International Journal of Highway Engineering
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• v.19 no.6
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• pp.191-199
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• 2017

PURPOSES : The objective of this study is to develop a methodology to estimate the minimum required separation distance (MRSD) between a vehicle and a bicycle when overtaking. METHODS : Three steps have been conducted to develop a methodology to estimate MSRD. First, a literature review has been conducted on the measurement of MSRD, and how it may be applied in Korea. Second, two assumptions have been made to develop a methodology to estimate the MSRD. The first assumption is that the maximum separation distance between a vehicle and a bicycle can be observed when they are at the same location longitudinally. In addition, it is assumed that the separation distance is invalid when the contra-flow exists. Finally, three cameras were installed at a height of 10 m to record the vehicle-bicycle interaction. Moreover, the vehicle trajectories as well as the separation distance were coded and analyzed. Through the hypothesis test and the interval estimation, the sample mean was tested and the confidence interval was estimated. RESULTS : 141 records of separation distance data were collected, and the hypothesis test demonstrated that the MSRD in Korea is significantly higher than other countries. In addition, the confidence interval of the population mean of MSRD is from 1.51 m to 1.65 m with 95% level of confidence. CONCLUSIONS : It is expected that the proposed methodology to estimate MSRD would be beneficial in studying road safety of vehicles and bicycles. Also, the proposed MSRD is expected to be designated in the act of road and transportation.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.111-127
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• 2004

In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.3018-3038
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• 2020

In the stereoscopic or multiview display, the depth video illustrates visual distances between objects and camera. To promote the computational efficiency of depth video encoder, we exploit the intra prediction of depth videos under Versatile Video Coding (VVC) and observe a diverse distribution of intra prediction modes with different coding unit sizes. We propose a hybrid scheme to further boost fast depth video coding. In the first stage, we adaptively predict the HADamard (HAD) costs of intra prediction modes and initialize a candidate list according to the HAD costs. Then, the candidate list is further improved by considering the probability distribution of candidate modes with different CU sizes. Finally, early termination of CU splitting is performed at each CU depth level based on the Bayesian theorem. Our proposed method is incorporated into VVC intra prediction for fast coding of depth videos. Experiments with 7 standard sequences and 4 Quantization parameters (Qps) validate the efficiency of our method.

• The Journal of the Korea Contents Association
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• v.13 no.10
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• pp.37-45
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• 2013

In recent years, the demands of multimedia data in wireless sensor networks have been significantly increased for the high-quality environment monitoring applications that utilize sensor nodes. However, since the amount of multimedia data is very large, the network lifetime is significantly reduced due to excessive energy consumption on particular nodes. To overcome this problem, in this paper, we propose a high efficiency data compression scheme in wireless multimedia sensor networks. The proposed scheme reduces the packet size by a multiple compression technique that consists of primary compression that deletes the lower priority bits considering characteristics of multimedia data and secondary compression based on Chinese Remainder Theorem. To show the superiority of our scheme, we compare it with the existing compression scheme. Our experimental results show that our proposed scheme reduces the amount of transmitted data by about 55% and increases network lifetime by about 16% over the existing scheme on average.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.12
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• pp.841-847
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• 2019

Time series data of 6-component loads were computed for a horizontal axis wind turbine rotor in yawed operating conditions with both rotating and non-rotating coordinate systems fixed at a center of a rotor hub. In this study, a well-known 20 kW class of the NREL Phase VI rotor was used for a model wind turbine, and this paper focuses on the yaw moments and over-turning moments for the operating wind speed range between 6 to 25 m/s. Unsteady blade element momentum theorem was adopted to get the aerodynamic loads acting on the wind turbine rotor. Computed 6-component loads using the developed UBEM code were compared with those using the NREL FAST program. From the computed results, both yaw and over-turning moments would be basic inputs to determine not only the specification of yawing mechanism but also the design condition of foundation.

• School Mathematics
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• v.18 no.1
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• pp.85-103
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• 2016

This study was to find characteristics of argumentation derived from a discourse in a math-gifted 5 grade class, which was held for finding a Pick's formula using Geoboard function of TI-73 calculator. For the analysis, a video record of the class, transcript of its voice record, and activity paper were used as data and Toulmin's argument schemes were applied as analysis standard. As a result of the study, we found that the graphing calculator helped the students to create an experimental environment that graphing a grid-polygon and figuring out its area. Furthermore, it also provided a basic demonstration through 'data->claim' composition and reasoning activities which consisted of guarantee, warrant, backing, qualifier and refutal for justifying. The basic argumentation during the process of deriving the Pick's theorem by the numbers of boundary points and inner points was developed into a 'collective argumentation' while a teacher took a role of a conductor of the argumentation and an authorizer on the knowledge at the same time.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.15-29
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• 2011

This study was carrying out research on the geometry of Sulbas${\={u}}$tras as parts of looking for historical roots of oriental mathematics, The Sulbas${\={u}}$tras(rope's rules), a collection of Hindu religious documents, was written between Vedic period(BC 1500~600). The geometry of Sulbas${\={u}}$tras in ancient India was studied to construct or design for sacrificial rite and fire altars. The Sulbas${\={u}}$tras contains not only geometrical contents such as simple statement of plane figures, geometrical constructions for combination and transformation of areas, but also algebraic contents such as Pythagoras theorem and Pythagorean triples, irrational number, simultaneous indeterminate equation and so on. This paper examined the key features of the geometry of Sulbas${\={u}}$tras and the geometry of Sulbas${\={u}}$tras for the construction of the sacrificial rite and the fire altars. Also, in this study we compared geometry developments in ancient India with one of the other ancient civilizations.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.79-86
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• 2008

The sex ratio at birth of South Korea is exceeding the natural sex ratio at birth, which is estimated to be about 105. One of the reasons of high sex ratio at birth is due to sex-selective abortion which is caused by strong son preference. The main objective of this study is to identify whether the families which are trying to bear children only until they acquire one son contribute to high sex ratio at birth. As a result, we obtain the theorem that if the number of such families diverge, the sex ratio at birth converges to the natural sex ratio almost surely. Therefore, we conclude that the existence of the families which are trying to bear children only until they receive one son does not affect the sex ratio at birth.