• The Mathematical Education
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• v.48 no.4
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• pp.365-385
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• 2009

Recently, mathematical modeling has been attractive in that it could be one of many efforts to improve students' thinking and problem solving in mathematics education. Mathematical modeling is a non-linear process that involves elements of both a treated-as-real world and a mathematics world and also requires the application of mathematics to unstructured problem situations in real-life situation. This study provides analysis of literature review about modeling perspectives, case studies about mathematical modeling, and textbooks from the United States and Korea with perspective which mathematical modeling could be potential and meaningful to students even in elementary school. Further, teaching method with mathematical modeling was investigated to see the possibility of application to elementary mathematics classroom.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.6
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• pp.93-100
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• 2003

This paper describes the thermoelastic instability arising from friction heat generation in braking and proposes the finite element methods to predict the variation of temperature and thermal deformation. In a conventional disc brake analysis, heat generation is only related with wheel speed and friction material and the interface pressure between disc and pad is assumed constant. But under dynamic braking conditions, the frictional heat causes the thermoelastic distortion that leads to more concentrated contact pressure distribution and hence more and more non-uniform temperature. In this paper, to complete the solution of the thermomechanically coupled problem, the linear relation model between pressure and temperature is proposed and demonstrated in examples of a simple two dimensional contact problem. And the two dimensional model has been extended to an annular three dimensional disc model in order to consider more realistic geometry and to provide a more accurate critical speed for automotive brake systems.

• Industrial Engineering and Management Systems
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• v.13 no.1
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• pp.29-42
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• 2014

Extensive research has been conducted on supplier evaluation and selection as a strategic and crucial component of supply chain management in recent years. However, few articles in the previous literature have been dedicated to the use of fuzzy inference systems as an aid in decision-making. Therefore, this essay attempts to demonstrate the application of this method in evaluating suppliers, based on a comprehensive framework of qualitative and quantitative factors besides the effect of gradual coverage distance. The purpose of this study is to investigate the applicability of the numerous measures and metrics in a multi-objective optimization problem of the supply chain network design with the aim of managing the allocation of orders by coordinating the production lines to satisfy customers' demand. This work presents a dynamic non-linear programming model that examines the important aspects of the strategic planning of the manufacturing in supply chain. The effectiveness of the configured network is illustrated using a sample, following which an exact method is used to solve this multi-objective problem and confirm the validity of the model, and finally the results will be discussed and analyzed.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.319-323
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• 1994

In this paper, we discuss a design method of iterative learning control systems for parabolic linear distributed parameter systems(DPSs). First, we discuss some aspects of boundary control of the DPS, and then propose to employ the Karhunen-Loeve procedure to reduce the infinite dimensional problem to a low-order finite dimensional problem. An iterative learning control(ILC) for non-square transfer function matrix is introduced finally for the reduced order system.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.5
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• pp.423-431
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• 2000

In this paper, the effect of computing time-delay in the real-time digital fuzzy control systems is investigated and the design methodology of a real-time digital fuzzy controller(DFC) to overcome the problems caused by it is presented. We propose the fuzzy feedback controller whose output is delayed with unit sampling period. The analysis and the design problem considering computing time-delay is very easy because the proposed controller is syncronized with the sampling time. The stabilization problem of the digital fuzzy control system is solved by the linear matrix inequality(LMI) theory. Convex optimization techniques are utilized to find the stable feedback gains and a common positive definite matrix P for the designed fuzzy control system Furthermore, we develop a real-time fuzzy control system for backing up a computer-simulated truck-trailer with the consideration of the computing time-delay. By using the proposed method, we design a DFC which guarantees the stability of the real time digital fuzzy control system in the presence of computing time-delay.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.439-444
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• 2012

In this study, we address the formation control problem of coupled unicycle-type mobile robots, each of which can interact with its neighboring robots by communicating their position outputs. Each communication link between two mobile robots is assumed to be established according to the given time-varying interconnection topology that switches within a finite set of connected fixed undirected networks and has a non-vanishing dwell time. Under this setup, we propose a distributed formation control algorithm by using the dynamics extension and feedback linearization methods, and by employing a consensus algorithm for linear multi-agent systems which provides arbitrary fast convergence rate to the agreement of the multi-agent system. Finally, the proposed result is demonstrated through a computer simulation.

• Smart Structures and Systems
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• v.18 no.4
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• pp.707-731
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• 2016

A unified mathematical model of the equations of generalized magneto-thermoelasticty based on fractional derivative heat transfer for isotropic perfect conducting media is given. Some essential theorems on the linear coupled and generalized theories of thermoelasticity e.g., the Lord- Shulman (LS) theory, Green-Lindsay (GL) theory and the coupled theory (CTE) as well as dual-phase-lag (DPL) heat conduction law are established. Laplace transform techniques are used. The method of the matrix exponential which constitutes the basis of the state-space approach of modern theory is applied to the non-dimensional equations. The resulting formulation is applied to a variety of one-dimensional problems. The solutions to a thermal shock problem and to a problem of a layer media are obtained in the present of a transverse uniform magnetic field. According to the numerical results and its graphs, conclusion about the new model has been constructed. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.243-250
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.39-54
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• 1997

This paper presents four process models for machining processes : 1) an economical mathematical model of machining process, 2) a prediction model for surface roughness, 3) a decision model for fuzzy cutting conditions, and 4) a judgment model of machinability with automatic selection of cutting conditions. Each model was developed the economic machining, and these models were applied to theories widely studied in industrial engineering which are nonlinear programming, computer simulation, fuzzy theory, and neural networks. The results of this paper emphasize the human oriented domain of a nonlinear programming problem. From a viewpoint of the decision maker, fuzzy nonlinear programming modeling seems to be apparently more flexible, more acceptable, and more reliable for uncertain, ill-defined, and vague problem situations.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.883-902
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• 2012

In this work we deal with a nonlinear dynamical system, namely the wastewater treatment model. We proceed to a dynamical analysis of the model. Invariance, boundness, controllability and the sensitivity with respect the initial conditions are studied. On the other hand, using the nonsmooth analysis tools, we look for the viability of the model, that is, the necessary and sufficient conditions under which trajectories move in a suitable time-moving sets, to avoid the washing problem (died of bacteria).