• Journal for History of Mathematics
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• v.18 no.1
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• pp.33-48
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• 2005

The Rule of False Position is known as an arithmetical solution of algebraical equations. On the other hand, the Excess-Deficit Rule is an algorithm for calculating about excessive or deficient quantitative relations, which is found in the ancient eastern mathematical books, including the nine chapters on the mathematical arts. It is usually said that the origin of the Rule of False Position is the Excess-Deficit Rule in ancient Chinese mathematics. In relation to these facts, we pose two questions: - As many authors explain, the excess-deficit rule is a solution of simultaneous linear equations？ - Which relation is there between the two rules explicitly？ To answer these Questions, we consider the Rule of Single/Double False Position and research the Excess-Deficit Rule in some ancient mathematical books of Chosun Dynasty that was heavily affected by Chinese mathematics. And we pursue their historical traces in Egypt, Arab and Europe. As a result, we can make sure of the status of the Excess-Deficit Rule differing from the Rectangular Arrays(the solution of simultaneous linear equations) and identify the relation of the two rules: the application of the Excess-Deficit Rule including supposition in ancient Chinese mathematics corresponds to the Rule of Double False Position in western mathematics. In addition, we try to appreciate didactical value of the Rule of False Position which is apt to be considered as a historical by-product.

• East Asian mathematical journal
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• v.29 no.2
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• pp.241-254
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• 2013

In this paper, we investigate the contents of Rule of Excess and Deficit in the second volume of San Hak Jeong Ui (Arithmetic Definition) compiled by Nam Byong Kil and corrcted by Lee Sang Hyok in the Choson Dynasty period.(Emperor Ko Jong, 1867).

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.137-159
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• 2012

In this paper, we deal with recent researches on Ying N$\ddot{u}$ and Ying Buzu(盈不足) which were addressed in the book Jiu Zhang Suan Shu(九章算術, The Nine Chapters on the Mathematical Art). Ying N$\ddot{u}$(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(盈不足術, the method of excess and deficit) represents an algorithm which has been used for solving many mathematical problems. It is known as a rule of double false position in the West. We show the importance of Ying Buzu Shu via an analysis of some problems in 'Ying Buzu' chapter. In 1202, Fibonacci(c.1170-c.1250) used Ying Buzu Shu in his book. This shows some of Asian mathematics were introduced to the West even before the year 1200. We present the origin of Ying Buzu Shu, and its relationship with Cramer's Rule. We have discovered how Asia's Ying Buzu Shu spread to Europe via Arab countries. In addition, we analyze some characters of Ying N$\ddot{u}$(Ying Buzu) in the book Suan Xue Bao Jian(算學寶鑑).

• Journal of Ecology and Environment
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• v.30 no.3
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• pp.225-229
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• 2007

The mating systems of natural populations of Potentilla freyniana in Korea were determined using allozyme analysis. The result suggests that P. freyniana is outcrossing as well as employing vegetative reproduction by stolon (self-fertilization rate, s < 0.5). The values of the inbreeding coefficient of eight populations in Korea varied from 0.244 to 0.331, with an average value of 0.274. For eight natural populations, multi-locus estimates of outcrossing (tm) was 0.603 across 13 polymorphic loci, with individual population values ranging from 0.530 to 0.652. The relatively low outcrossing rates of some populations could be attributed to extensive vegetative reproduction by stolon and the isolation of flowering mature plants. Although P. freyniana usually propagated by asexually-produced ramets, I could not rule out the possibility that sexual reproduction occurred at a low rate because each ramet may produce terminal flowers. Although heterozygote excess was observed in some natural populations, most populations exhibited varying degrees of inbreeding and a heterozygote deficit.