• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.137-143
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• 1992

The purpose of this paper is to provide the affirmative solution of the following conjecture due to Davis and Geramita. Conjecture; Let A=R[T] be a polynomial ring in one variable, where R is a regular local ring of dimension d. Then maximal ideals in A are complete intersection. Geramita has proved that the conjecture is true when R is a regular local ring of dimension 2. Whatwadekar has rpoved that conjecture is true when R is a formal power series ring over a field and also when R is a localization of an affine algebra over an infinite perfect field. Nashier also proved that conjecture is true when R is a local ring of D[ $X_{1}$,.., $X_{d-1}$] at the maximal ideal (.pi., $X_{1}$,.., $X_{d-1}$) where (D,(.pi.)) is a discrete valuation ring with infinite residue field. The methods to establish our results are following from Nashier's method. We divide this paper into three sections. In section 1 we state Theorems without proofs which are used in section 2 and 3. In section 2 we prove some lemmas and propositions which are used in proving our results. In section 3 we prove our main theorem.eorem.rem.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.102.4-102
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• 2002

A deadzone compensator is designed for a positioning system using fuzzy logic. The classification property of fuzzy logic systems make them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates, formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is implemented on a positioning system to show its efficacy. 1. Deadzone Compansation 2. XY positioning table 3. Fuzzy Logic 4. Actuator nonlinearity

• School Mathematics
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• v.4 no.1
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• pp.1-13
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• 2002

The purpose of this study is to investigate the reasons and backgrounds of drawing auxiliary lines in the proof of geometry. In most of proofs in geometry, drawing auxiliary lines provide important clues, thus they play a key role in deductive proof. However, many student tend to have difficulties of drawing auxiliary lines because there seems to be no general rule to produce auxiliary lines. To alleviate such difficulties, informal activities need to be encouraged prior to draw auxiliary lines in rigorous deductive proof. Informal activities are considered to be contrasting to deductive proof, but at the same time they are connected to deductive proof because each in formal activity can be mathematically represented. For example, the informal activities such as fliping and superimposing can be mathematically translated into bisecting line and congruence. To elaborate this idea, some examples from the middle school mathematics were chosen to corroborate the relation between informal activities and deductive proof. This attempt could be a stepping stone to the discussion of how to teach auxiliary lines and deductive reasoning.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.2
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• pp.17-28
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• 2004

A deadzone compensator is designed for a XY positioning table using fuzzy logic. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is implemented on a XY positioning table to show its efficacy.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• Research in Mathematical Education
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• v.13 no.3
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• pp.217-233
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• 2009

The purpose of this study is to describe how dynamic geometry systems can be useful in proof activity; teaching sequences based on the use of dynamic geometry systems and to analyze the possible roles of dynamic geometry systems in both teaching and learning of proof. And also dynamic geometry environments can generate powerful interplay between empirical explorations and formal proofs. The point of this study was to show that how using dynamic geometry software can provide an opportunity to link between empirical and deductive reasoning, and how such software can be utilized to gain insight into a deductive argument.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.250-278
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• 2004

The product rate variation problem, to be called the PRVP, is to sequence different type units that minimizes the maximum value of a deviation function between ideal and actual rates. The PRVP is an important scheduling problem that arises on mixed-model assembly lines. A surge of research has examined very interesting methods for the PRVP. We believe, however, that several issues are still open with respect to this problem. In this study, we consider convex bipartite graphs, perfect matchings, permanents and balanced sequences. The ultimate objective of this study is to show that we can provide a more efficient and in-depth procedure with a graph theoretic approach in order to solve the PRVP. To achieve this goal, we propose formal alternative proofs for some of the results stated in the previous studies, and establish several new results.

• Research in Mathematical Education
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• v.23 no.1
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• pp.1-12
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• 2020

In this case study, a professor was observed to investigate use of instructional examples when teaching the Intermediate Value Theorem in a calculus course. Video-recorded lessons were analyzed with constant comparison to video-stimulated recall interviews and field notes. The professor employed multiple instructional examples, which was initiated by students and modified by the professor. The professor asked students to build non-existing examples as an informal proof of the Intermediate Value Theorem and assessment of students' previous knowledge. Use of incorrect examples on instructional purpose can be an appropriate way for formative assessment as well as a bridge between informal and formal proofs in college mathematics.

• Proceedings of the KIEE Conference
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• 2008.10b
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• pp.187-192
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• 2008

A saturation and deadzone compensator is designed for robot systems using fuzzy logic (FL) and neural network (NN). The classification property of FL system and the function approximation ability of the NN make them the natural candidate for the rejection of errors induced by the saturation and deadzone. The tuning algorithms are given for the fuzzy logic parameters and the NN weights, so that the saturation and deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The NN saturation and FL deadzone compensator is simulated on a robot system to show its efficacy.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.375-382
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• 2004

This paper presents control designs using neural networks (NN) for a XY positioning table. The proposed neuro-controller is composed of an outer PD tracking loop for stabilization of the fast flexible-mode dynamics and an NN inner loop used to compensate for the system nonlinearities. A tuning algorithm is given for the NN weights, so that the NN compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded weight estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The proposed neuro-controller is implemented and tested on an IBM PC-based XY positioning table, and is applicable to many precision XY tables. The algorithm, simulation, and experimental results are described. The experimental results are shown to be superior to those of conventional control.