• Journal for History of Mathematics
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• v.14 no.2
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• pp.45-54
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• 2001

Jules Henri Poincare was great not only as a mathematician brit also as a philosopher of science. He received many honors for his outstanding research. He was elected to the Academie des Sciences in 1887 and was elected President of tile Academy in 1906. In 1908 he was elected to the Academie Francaise and was elected director in the year of his death. The Poincare Conjecture was selected Millennium Prize Problems fly The Clay Mathematics Institute of Cambridge, Massachusetts(CMI). The Board of Directors of CMI have designated a $1 million prize fund for the solution to his problem. In this paper, Poincare's major works, his life, his philosophy and the Poincare Conjecture are given.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.107-116
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• 2006

This article reviews the exciting developments in Morse theory by S.Smale, Freedmann and others, including a proof of the generalized Poincare' Conjecture in the handle body theory. We study its relations with handle body theory _and geodesic theory.

• Journal of Korea Water Resources Association
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• v.35 no.6
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• pp.817-826
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• 2002

Many researchers have been tried to forecast the future as analyzing data characteristics and the forecasting methodology may be divided into two cases of deterministic and stochastic techniques. However, the understanding data characteristics may be very important for model construction and forecasting. In the sense of this view, recently, the deterministic method known as nonlinear dynamics has been studied in many fields. This study uses the geometrical methodology suggested by Poincare for analyzing nonlinear dynamic systems and we apply the methodology to understand the characteristics of known systems and hydrologic data, and determines the possibility of forecasting according to the data characteristics. Say, we try to understand the data characteristics as constructing Poincare map by using Poincare section and could conjecture that the data sets are linear or nonlinear and an appropriate model.