• Journal for History of Mathematics
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• v.33 no.6
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• pp.327-343
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• 2020

This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.1
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• pp.31-40
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• 2012

Distributed arrival time control (DATC) is a distributed feedback control algorithm for real-time scheduling problems in dynamic operational environment. Even though DATC has provided excellent performance for dynamic scheduling problems, it can be improved by considering the following considerations. First, the original DATC heavily depends on the quality of initial solution. In this paper, well-known dispatching rules are incorporated DATC algorithm to enhance its performance. Second, DATC improves its solution with adjusting virtual arrival times of jobs to be scheduled in proportion to the gap between completion time and due date iteratively. Since this approach assigns the same weight to all gaps generated with iterations, it fails to utilize significantly more the latest information (gap) than the previous ones. To overcome this issue we consider exponential smoothing which enable to assign different weight to different gaps. Using these two consideration This paper proposes A-DATC (Advanced-DATC). We demonstrate the effectiveness of the proposed scheduling algorithm through computational results.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.4
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• pp.467-475
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• 2016

Ultrasonic propagation imaging (UPI) has shown great potential for detection of impairments in complex structures and can be used in wide range of non-destructive evaluation and structural health monitoring applications. The software implementation of such algorithms showed a tendency in time-consumption with increment in scan area because the processor shares its resources with a number of programs running at the same time. This issue was addressed by using field programmable gate arrays (FPGA) that is a dedicated processing solution and used for high speed signal processing algorithms. For this purpose, we need an independent and flexible block of logic which can be used with continuously evolvable hardware based on FPGA. In this paper, we developed an FPGA-based ultrasonic propagation imaging system, where FPGA functions for both data acquisition system and real-time ultrasonic signal processing. The developed UPI system using FPGA board provides better cost-effectiveness and resolution than digitizers, and much faster signal processing time than CPU which was tested using basic ultrasonic propagation algorithms such as ultrasonic wave propagation imaging and multi-directional adjacent wave subtraction. Finally, a comparison of results for processing time between a CPU-based UPI system and the novel FPGA-based system were presented to justify the objective of this research.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1173-1196
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• 2014

Real-time dynamic substructuring tests have been conducted on a cable-deck system. The cable is representative of a full scale cable for a cable-stayed bridge and it interacts with a deck, numerically modelled as a single-degree-of-freedom system. The purpose of exciting the inclined cable at the bottom is to identify its nonlinear dynamics and to mark the stability boundary of the semi-trivial solution. The latter physically corresponds to the point at which the cable starts to have an out-of-plane response when both input and previous response were in-plane. The numerical and the physical parts of the system interact through a transfer system, which is an actuator, and the input signal generated by the numerical model is assumed to interact instantaneously with the system. However, only an ideal system manifests a perfect correspondence between the desired signal and the applied signal. In fact, the transfer system introduces into the desired input signal a delay, which considerably affects the feedback force that, in turn, is processed to generate a new input. The effectiveness of the control algorithm is measured by using the synchronization technique, while the online adaptive forward prediction algorithm is used to compensate for the delay error, which is present in the performed tests. The response of the cable interacting with the deck has been experimentally observed, both in the presence of delay and when delay is compensated for, and it has been compared with the analytical model. The effects of the interface delay in real-time dynamic substructuring tests conducted on the cable-deck system are extensively discussed.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.18 no.4
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• pp.343-350
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• 2000

This study deals with the Definition of the Earth-volume quantity and direction of throwing down stones (Q.R.R) into the Breakwater using Real-time DGPS & Echo-Sounding method. Generally, the buoy in the center line of Breakwater has been set up so as to throw down stones in the correct area. After throwing stones down there, surveyors have been surveying the depth and direction of stones with rod and sounding lead. The method, however, is not effective because of long time and a lot of human power, in addition it is incorrect. This paper has studied on the solution of those problems using Real-time DGPS & Echo-Sounding data to calculate the earth-volume quantity, direction and depth of throwing down stones. This paper says the effective and economical methods using Real-time DGPS & Echo-Sounding data there.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.690-693
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• 2004

This paper proposes a multi-resolution electrostatic potential field (MREPF) based solution to the mobile robot path planning and collision avoidance problem in 2D dynamic environment. The MREPF is an environment method in calculation time and updating field map. The large scale resolution map is added to EPF and this resolution map interacts with the small scale resolution map to find an optimal solution in real time. This approach can be interpreted with Atlantis model. The simulation studies show the efficiency of the proposed algorithm.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.5
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• pp.217-224
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• 2002

This paper presents an algorithm to obtain an approximate optimal solution for the service restoration and load balancing of large scale radial distribution system in a real-time operation environment. Since the problem is formulated as a combinatorial optimization problem, it is difficult to solve a large-scale combinatorial optimization problem accurately within the reasonable computation time. Therefore, in order to find an approximate optimal solution quickly, the authors proposed an algorithm which combines optimization technique called cyclic best-first search with heuristic based feeder loadings balance index for computational efficiency and robust performance. To demonstrate the validity of the proposed algorithm, numerical calculations are carried out the KEPCO's 108 bus distribution system.

• Korean Management Science Review
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• v.20 no.2
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• pp.33-43
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• 2003

In this paper we applied dynamic programming to determining work schedule type. In dynamic programming formulation, each day during a planning horizon represents a stage for which a decision is made. The alternatives are given by work schedule types that combine regular time, overtime, additional shift, and so on. In this case, their associated return function is labor cost. The state is defined as the amount of work time allocated to stage 1, stage 2,…, and current stage. A case study for a real manufacturing company was performed to apply dynamic programming to scheduling daily work hours during a week. The case study showed that total cost of our solution derived from dynamic programming decreased by about 6％ as compared with the solution obtained from the previous method.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.299-310
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• 1998

Actually mixed assembly line is mixed with open and close type workstation. This workstation is called hybridworkstation. The propose of this paper is to determine the sequencing of model that minimize line length for actual(hybridworkstation) mixed model assembly line. we developed three mathematical formulation of the problem to minimize the overall length of a line with hybrid station. Mathematical formulation classified model by operato schedule. Mixed model assembly line is combination program and NP-hard program. Thus computation time is often a critical factor in choosing a method of determining the sequence. This study suggests a tabu search technique which can provide a near optimal solution in real time and use the hill climbing heuristic method for selecting initial solution. Modified tabu search method is compared with MIP(Mixed Integer Program). Numerical results are reported to demonstrate the efficiency of the method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.339-352
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• 2001

The inverse kinematics problem of Stewart platform is straightforward, but no closed form solution of the forward kinematic problem has been presented. Since we need the real-time forward kinematic solution in MIMO control and the motion monitoring of the platform, it is important to acquire the 6 DOF displacements of the platform from measured lengths of six cylinders in small sampling period. Newton-Raphson method a simple algorithm and good convergence, but it takes too long calculation time. So we reduce 6 nonlinear kinematic equations to 3 polynomials using Nairs method and 3 polynomials to 2 polynomials. Then Newton-Raphson method is used to solve 3 polynomials and 2 polynomials respectively. We investigate operation counts and performance of three methods which come from the equation reduction and Newton-Raphson method, and choose the best method.