• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.61-69
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• 2001

The purpose of this paper is to introduce the Nielsen root number for the complement N(f:X-A,c) which shares such properties with the Nielsen root number N(f;c) as lower bound and homotopy invariance.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Journal of Ginseng Research
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• v.7 no.2
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• pp.133-147
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• 1983

This study was carried out to obtain the basic information for the development of new ginseng varieties. The two variants (violet-stem variant and yellow-berry variant) of Korean ginseng (Panax ginseng C.A. Meyer) and American ginseng (Panax quinquefolium L.) of one to four-year were used for this study. All of the characteristics, such as leaf length, leaf width, petiol length, number of leaves per plant, number of leaflets per plants, stem diameter, stem length, number of stems per plant, root length, primary root length, root diameter, root weight were determined and correlations among them were estimated. The results obtained were summarized as follows. 1. Leaf length, petiol length, number of leaves per plant, and number of leaflets per plant of Panax ginseng, violet-stem variant and yellow-berry variant, were larger than those of Panax quinquefolium at all of the plant ages, while leaf width was wider in Panax quinquefolium. 2. The length of stem of Panax quinquefolium was shorter than that of Panax ginseng, and the frequency of multi-stem plants at 4-year-old ginseng was larger in violet-stem variant than in Panax quinquefolium and yellow-berry variant. 3. In the characteristics of ginseng root, the primary root length of Panax ginseng, violet-stem variant and yellow-berry variant, were less than that of Panax quinquefolium, while root weight, root diameter, and umber of secondary root related to yield were larger in Panax ginseng. 4. The root weight per plant related to the yield had positive and highly significant correlations with stem diameter, leaf length, leaf length, leaf width, number of compound leaves and leaflets in Panax ginseng and Panax quinguefolium. 5. The root weight related to the wield of ginseng had been influenced to stem diameter, leaf length, and leaf width directly, and number of compound leaves and leaflets indirectly. 6. The number, total area and activity of stomate per mm2 of Panax quinquefolium were more, larger and stronger than those of Panax ginseng.

• IEMEK Journal of Embedded Systems and Applications
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• v.13 no.1
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• pp.45-51
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• 2018

In this paper, a tentative Kth order Newton-Raphson's floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Newton-Raphson root algorithm. Using the proposed algorithm, $F^{-1/N}$ and $F^{-(N-1)/N}$ can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration and iterates only until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.245-252
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• 1996

The relative Nielsen number N(f;X,A) was introduced in 1986. It gives us a better, and ideally sharp, lower bound for the minimum number MF[f;X,A] of fixed points in the homotopy class of the map $f;(X,A) \to (X,A)$. Similarly, we also can think about the Nielsen map $f:(X,A) \to (X,A)$. Similarly, we also can be think about the Nielsen root theory. In this paper, we introduce a relative root Nielsen number N(f;X,A,c) of $f:(X,A) \to (Y,B)$ and show some basic properties.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• Journal of Ginseng Research
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• v.8 no.2
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• pp.82-90
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• 1984

The Present study was undertaken to obtain the basic information on the development of multistem varieties of ginseng. The root weight per plant of multi-stem ginseng was hi燥or than that of single stem ginseng, and it was found that the greater variance due to the growing area was clear in the frequency of multistem plant. The broad heritability estimate for the number of steams was lower with the increase of the age of ginseng. The number of stems per plant was positively correlated with the number of branch roots, number of dormancy buds, and root weight. However, the root diameter was negatively correlated with the number of stems is per plant. Based on path analysis, the number of branch roots and dormancy buds showed the maximum indirect positive effects on the number of stems.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.357-370
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• 2000

In [6], Cheng-Ye You gave a condition equivalent to the Nielsen number product formula for fiber maps. And Jerzy Jezierski also gave a similar condition for coincidences of fiber maps. The main purpose of this paper is to find the condition for which holds the product formula for Nielsen root numbers N(f;a) = N(f;a) N(fb;a).

• Journal of Ginseng Research
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• v.31 no.3
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• pp.142-146
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• 2007

This experiment was conducted to find identification of ginseng root's age using the number of stem vestiges in rhizome. The number of stem vestiges in rhizome is a useful key to confirm the age of ginseng root as follow : 4-year-old root has two, 5-year-old root has three, 6-year-old root has four. The distribution of stem vestiges in rhizome each year root are as follow : 2 stem vestiges in 4-year-old root is 89.5%, 3 stem vestiges in 5-year-old root is 79.7%, 4 stem vestiges in 6-year-old root is 46.3%. However, the limiting factors of identification of ginseng root's age using the number of stem vestiges in rhizome is appearance of multi-stem per plant and appearance of destroyed stem vestige in rhizome. The ratio of appearance of multi-stem per plant and destroyed stem vestige in rhizome are increased according to root age.

• Journal of Plant Biology
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• v.28 no.2
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• pp.127-140
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• 1985

A comparative anatomy between the secondary xylem in the root and stem of Korean Betulaceae, including 5 genera and 6 species, was carried out in this study. Anatomical characteristics of the secondary xylem in the root and stem are as follows: Diameter of vessel and fiber is wider in the root than the stem, while the number of vessel and fiber per unit area is fewer in the root than the stem. The length of vessel element is longer in the stem than the root, whereas length of the fiber is longer in the root than the stem. Number of bar in the perforation plate is more in the stem than the root, and the angle of perforation plate is broader in the root than the stem. Number of ray per unit area is more in the root than the stem.