• Journal for History of Mathematics
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• v.19 no.1
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• pp.55-64
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• 2006

The thesis is about the development of mathematics starting from the old Greece and the old Babylonia. The modem mathematics has been developed, based on the set theory in the axiomatic method since the 19th century. The primary impetus of this thesis will be to summary the development of topology.

• International Journal of Quality Innovation
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• v.5 no.1
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• pp.52-67
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• 2004

Successful implementation of statistical process control techniques requires for operational definitions and precise measurements. Nevertheless, very often analysts can dispose of process data available only by linguistic terms, that would be a waste to neglect just because of their intrinsic vagueness. Thus a hybrid approach, which integrates fuzzy set theory and common statistical tools, sounds useful in order to improve effectiveness of statistical process control in such a case. In this work, a fuzzy approach is adopted to manage linguistic information, and the use of a Chi-squared control chart is proposed to monitor process performance.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.193-209
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• 2006

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.741-745
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• 1991

This paper describes a feature extraction in digitized chest X-ray image and CT head Image. There are Extraction, Thresholding, Region G rowing, Split-Merge and Relaxation in feature extraction technique. In this study, Region Growing System was realized and Fuzzy Set Theory was applied in order to extract the vague region which the conventional method has difficulties in extracting. The performance of proposed algorithm was proved by being applied to chest X-ray image and CT head image.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.352-357
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• 1987

The Auto Tuning Controller is designed using Fuzzy set theory. And to verify its validity it is Applied to the Auto Tuner of hydraulic Control System. Fuzzy Tuning Procedures are written by linguistic model and translated into C language formation by preprocessor. Then it is executed with state feedback controller in real time, Fuzzy Logic Controller adjusts state feedback gain by proper tuning logic in each step to satisfy the desired maximum overshoot and settling time.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.29-43
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• 2012

In this paper, we survey the history of search for axiomatic set theory and show that ${\exists}U(0{\in}U{\wedge}{\forall}x(x{\in}U{\leftrightarrow}{\exists}z(z{\in}U{\wedge}{\forall}y(y{\in}x{\rightarrow}y{\subseteq}z))){\rightarrow}$ ZR.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.721-734
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• 2014

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending our work on Reidemeister orbit sets, we obtain algebraic results such as addition formulae for irreducible Reidemeister orbit sets. Similar formulae for Nielsen type irreducible essential orbit numbers are also proved for fibre preserving maps.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.49-52
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• 1998

Neural Network has good performance in pattern classification, control and many other fields by learning ability. However, there is effective rule or systematic approach to determine optimal structure. In this paper, we propose a new method to find optimal structure of feed-forward multi-layer neural network as a kind of pruning method. That eliminating redundant elements of neural network. To find redundant elements we analysis error and weight changing with Rough Set Theory, in condition of executing back-propagation leaning algorithm.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.745-757
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• 2004

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G $\longrightarrow$ G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.

• Bulletin of the Korean Chemical Society
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• v.12 no.2
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• pp.211-213
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• 1991

The ground state of the oxygen molecule is calculated by various methods of coupled cluster approaches and many body perturbation theory using a double zeta plus polarization basis set and the UHF reference state. All the methods employed are capable of describing the oxygen molecule near the equilibrium bond length and the separated atom, but do not correctly depict the breaking of the multiple bond. For this basis set, including more correlations does not necessarily improve the agreement with experiment for molecular properties such as bond lengths and dissociation energies.