• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.263-271
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• 2010

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.341-347
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• 2012

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 improve our theorem for formulae for Nielsen type essential orbit numbers.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• 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.

• 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.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.75-86
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• 2002

A Nielsen number $\bar{N}(f:X-A)$ is a homotopy invariant lower bound for the number of fixed points on X-A where X is a compact connected polyhedron and A is a connected subpolyhedron of X. This number is extended to Nielsen type numbers $\bar{NP_{n}}(f:X-A)$ of least period n and $\bar{N{\phi}_{n}}(f:X-A)$ of the nth iterate on X-A where the subpolyhedron A of a compact connected polyhedron X is no longer path connected.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.361-369
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• 2013

We introduce a Nielsen type number of a fibre preserving map, and show that it is a lower bound for the number of $n$-orbits in the homotopy class. Under suitable conditions we show that it is equal to the Nielsen type relative essential $n$-orbit number. We also give necessary and sufficient conditions for it and the essential $n$-orbit number to coincide.

• Industrial Engineering and Management Systems
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• v.15 no.1
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• pp.110-121
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• 2016

With the growing interest in skincare and maintenance, there are increasing numbers of studies on the classification of skin type and the factors influencing each type. This study presents a novel methodology by using data mining, for the determination of the relationships between skin type, lifestyle, and patterns of cosmetic utilization. Eight skin-specific factors, which are moisture, sebum in U-zone (both cheeks), sebum in T-zone (forehead, nose, and chin), pore, melanin, wrinkle, acne, hemoglobin, were measured in 1,246 subjects living in South Korea, in conjunction with a questionnaire survey analyzing their lifestyles and pattern of cosmetic utilization. Using various multivariate statistical methods and data mining techniques, we classified the skin types based on the skin-specific values, determined the relationship between skin type and lifestyle, and accordingly sorted the subjects into clusters. Logistic regression analysis revealed gender-related differences in the skin; therefore, separate analyses were performed for males and females. Using the Gaussian Mixture Modeling (GMM) technique, we classified the subjects based on skin type (two male and four female). Using the ANOVA and decision tree techniques, we attempted to characterize the relationship between each skin type and the lifestyles of the subjects. Menstruation, eating habits, stress, and smoking were identified as the major factors affecting the skin.

• Journal of Plant Biotechnology
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• v.42 no.3
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• pp.235-238
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• 2015

Adventitious buds were obtained from isolated cotyledons cultured on MS medium with various concentrations of 6-benzylamino purine (BA) and thidiazuron (TDZ). The highest numbers of adventitious buds were obtained on MS medium supplemented with 0.2 mg/L BA. Experimental culturing with half the petiole portion and half with the terminal segments were grown on MS medium contained with 0.2 mg/L BA. Frequency of the adventitious bud induction was variable accordingly to the type of cultured explants. Explants with the half petiole showed the highest adventitious bud induction rate (80%) compared to explants of half with terminal segment (20%). An elongated shoot from the buds and growth of advent roots were both possible on the 1/2 MS medium without a plant growth regulator. These results offer an effective way in which clonal propagation can be accomplished.