• Communications of Mathematical Education
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• v.23 no.2
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• pp.349-381
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• 2009

The purpose of this study is to propose issues in selecting gifted children in mathematics by in-depth analysis of the selection process and items. In order to accomplish the purpose, the rate of right and wrong answers were examined based on the reaction of the students by 1st, 2nd and 3rd selection test. Also, the types of the errors were identified for the 2nd and 3rd selection test. According to the study results, the rate of right answers was low in short response questions and essay questions rather than in multiple-choice questions. In addition, the academic achievements were lower in the fields other than number & operations and logic. The conclusion of this study is that following studies regarding selection of gifted children are required linked with the project tasks and programs.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.37-58
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• 2011

The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.

• The Transactions of the Korea Information Processing Society
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• v.6 no.4
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• pp.952-958
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• 1999

This paper presented the application of GAs as a means of finding optimal solutions over a parameter space in the controller design for a fuzzy control system. The performance can involve a weighted combination of various performance characteristics such as rise-time, settling-time, settling-time, overshoot. The results obtained here are compared with those for a traditional design obtained using the root-locus method. In contrast to traditional methods, the GA-based method does not require the usual mathematical processess or mathematical model of the system. In this paper, the Ga-based Fuzzy control system combining Fuzzy control theory with the GA, that is known to be very effective in the optimization problem, will be proposed The effectiveness of the proposed control system will be demonstrated by computer simulations using task tracking position system in stable and unstable linear systems. It is shown that the GA-based controller is better than the traditional controller used It stable and unstable linear systems.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.335-354
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• 2019

The purpose of this study is to explore alternative ways of teaching derivatives in a way that emphasizes intuition. For this purpose, the contents related to derivatives in Korean curriculum and textbooks were analyzed by comparing with contents in Singapore Curriculum and textbooks. Singapore, where the curriculum deals with derivatives relatively earlier than Korea, introduces the concept of derivatives and differentiation as the slope of tangent instead of the rate of instantaneous change in textbook. Also, Singapore use technology and inductive extrapolation to emphasize intuition rather than form and logic. Further, from the results of the exploration of other foreign cases, we confirm that the UK and Australia also emphasized intuition in teaching derivatives and differentiation. Based on the results, we discuss the meaning and implication of introducing derivatives and teaching differentiation in a way that emphasizes intuition. Finally, we propose the implications for the alternative way of teaching differentiation.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.417-420
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• 1990

The conventional quantitative techniques of system analysis are intrinsically unsuited for dealing with humanistic systems. Therefore, the rule based modeling of fuzzy linguistic type has been developed for the analysis of humanistic systems and complex systems and it is very significant for analysis and design of fuzzy logic controller. The activated sludge process is a commonly used method for treating sewage and waste waters. A mathematical tool to build a fuzzy model of the activated sludge process where fuzzy implications and linear reasoning are used is presented in here. A root-mean square error is used as the criterion of the fuzzy model's adequacy to the A.S.P. and the least square method is used for the identification of optimum consequence parameters. A method of modeling of the activated sludge process using its input-output data and simulation results for its application are shown.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.497-502
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• 2002

The problem of maneuvering target tracking has been studied in the field of the state estimation over decades. The Kalman filter has been widely used to estimate the state of the target, but in the presence of a maneuver, its performance may be seriously degraded. In this paper, to solve this problem and track a maneuvering target effectively, a DNA coding-based interacting multiple model (DNA coding-based W) method is proposed. The proposed method can overcome the mathematical limits of conventional methods by using the fuzzy logic based on DNA coding method. The tracking performance of the proposed method is compared with those of the adaptive IMM algorithm and the GA-based IMM method in computer simulations.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.58 no.3
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• pp.249-256
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• 2009

The widely used control theory based design of PI family controllers fails to perform satisfactorily under parameter variation, nonlinear or load disturbance. In high performance applications, it is useful to automatically extract the complex relation that represent the drive behaviour. The use of learning through example algorithms can be a powerful tool for automatic modelling variable speed drives. They can automatically extract a functional relationship representative of the drive behavior. These methods present some advantages over the classical ones since they do not rely on the precise knowledge of mathematical models and parameters. The paper proposes high performance speed and current control of synchronous reluctance motor(SynRM) drive using adaptive learning mechanism-fuzzy neural network (ALM-FNN) and fuzzy logic control (FLC) controller. The proposed controller is developed to ensure accurate speed and current control of SynRM drive under system disturbances and estimation of speed using artificial neural network(ANN) controller. Also, this paper proposes the analysis results to verify the effectiveness of the ALM-FNN, FLC and ANN controller.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.406-410
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• 2003

B. M. Schein([1]) considered systems of the form (${\Phi}$; ${\circ}$,-), where ${\Phi}$ is a set of functions closed under the composition "${\circ}$" of functions and the set theoretic subtraction "-". In this structure, (${\Phi}$; ${\circ}$) is a function semigroup and (${\Phi}$;-) is a subtraction algebra in the sense of [1]. He proved that every subtraction semigroup is isomorphic to a difference semigroup of invertible functions. Also this structure is closely related to the mathematical logic, Boolean algebra, Bck-algera, etc. In this paper, we define the near subtraction semigroup as a generalization of the subtraction semigroup, and define the notions of strong for it, and then we will search the general properties of this structure, the properties of ideals, and the application of it.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.143-153
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• 1997

At the on-line control method FLC(Fuzzy Logic Controller) is stronger to the disturbance than a classical controller and its overshoot of the initialized value is excellent. The fuzzy controller can do a proper control, though it doesn't know the mathematical model of the system or the parameter value. But to make the control rule of the fuzzy controller through an expert's experiance has a changes of the control system, the control rule is fixed, it can't adjust to the environment changes of the control system, the controller output value has a minute error and it can't convergence correctly to the desired value[1][2]. There are many ways to eliminate the minute error[3][4][5], but in this paper suggests EP-FNNIC(Fuzzy Neurla Network Intelligence Controller) intelligence controller which combines FLC with NN(Neural Network) and EP(Evolution Programming). The output characteristics of EP-FNNIC controller will be compared and analyzed with FLC. It will be showed that this EP-FN IC controller converge correctly to the desirable value without any error. The convergence speed, overshoot, rising time, error of steady state of controller of these two kinds also will be compared.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1147-1153
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• 1999

The attitude control of a double inverted pendulum with a periodical disturbance at link top is dealt in this paper. The proposed system is consisted of the double inverted pendulum and a disturbing link; a triple inverted pendulum with two motors. The lower link is hinged on the plate to free for rotation in the vertical plane. The upper link is connected to the lower link through a DC motor. The DC motor is used to control the posture of the pendulum by adjusting the position of the upper link. The periodical disturbance can be generated by the additional like attached at the end of link 2 through another DC motor, which is the modeling of a posture for a biped supporting with one leg. The motor for the joint simulates the knee joint(or hip joint) and the disturbance for the legs moving in air. The algorithm for controlling the proposed inverted pendulum which is regarded as a virtual double inverted pendulum with a periodic disturbance, is consisted of a state feedback control and a fuzzy logic controller connected in parallel. The fuzzy controller keeps the center of gravity of the biped within the specified range through the nonlinear feedback compensator. The state feedback control takes over the role to maintain a desired posture regardless the disturbance at the link top. Simulations with a mathematical model and experiments are conducted to show the validity of the proposed controller.