• Korean Journal of Environmental Agriculture
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• v.35 no.4
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• pp.256-262
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• 2016

BACKGROUND: 'Shiranuhi' mandarin is one of the popular citrus cultivars in Jeju Island, Korea. However, the emergence of scion roots since the past few years has altered its flowering, fruiting, and quality. Girdling of branches is one of the methods of increasing flowering in citrus trees. METHODS AND RESULTS: This experiment was conducted to determine the effect of girdling on the flowering and yields of scion rooted 'Shiranuhi' mandarin hybrid. We selected normal trees without scion roots as controls. The trees with scion roots were divided into two groups: trees without girdling and with girdling on main branches. Each group contained five replications and the experiment was conducted in Gosan and Harye of Jeju Island. The scion rooted trees revealed severely decreased flowering and low flowering/leaf ratios; however, the leaf/fruit ratio significantly increased. But, girdling on main branches significantly increased flowering and the flowering/leaf ratio. In the scion rooted trees, yields dropped due to poor flowering; however, girdling of branches efficiently improved the yields of the trees. Fruit quality, fruit size, and fruit weight of scion rooted trees were low in comparison with the control, whereas girdling of the branches improved flowering and the fruit weight to some extent. No significant difference in soluble solid contents was observed. CONCLUSION: Girdling is an effective method to induce flowering of the scion rooted 'Shiranuhi' mandarin trees. In addition, yields of scion rooted trees were improved.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.181-192
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• 2003

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

• Korean Journal of Environmental Agriculture
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• v.38 no.3
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• pp.154-158
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• 2019

BACKGROUND: 'Shiranuhi' mandarin is a major cultivar among all late ripening type of citrus, and is widely cultivated in Korea. However, many farmers have reported scion root problems in their orchard resulting in reduced flowering and fruiting. It is necessary that the physiology of scion-rooted 'Shiranuhi' mandarin trees is further understood. METHODS AND RESULTS: This experiment was conducted to understand the growth response and physiology of scion-rooted 'Shiranuhi' mandarin hybrids. In our study, 'Shiranuhi' mandarin trees were divided into two groups: trees without scion roots (control) and trees with scion roots. The experiment was conducted in Seogwipo of Jeju, with ten replicates for each group. Growth of trees with scion roots was more vigorous and the trees were taller than the controls. Tree height and trunk diameter of scion-rooted trees were significantly higher than those of control trees. Exposed length of rootstocks of scion-rooted trees was significantly lower (by about 2 cm) than that of control trees (8.6 cm). In terms of root nutrition, carbon contents of scion-rooted trees was significantly lower than that of control trees, but nitrogen and potassium concentrations in scion roots were significantly higher than those in control roots. CONCLUSION: Based on the results, we infer that growth of scion-rooted trees was very vigorous and the content of nitrogen in these roots was higher than that in the control tree roots. Thus, the carbon/nitrogen ratio of scion roots was significantly lower than that of the control roots.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.899-910
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• 2019

In this paper, we enumerate the cardinalities for the set of all vertices of outdegree ${\geq}k$ at level ${\geq}{\ell}$ among all rooted ordered d-trees with n edges. Our results unite and generalize several previous works in the literature.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.427-432
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• 1998

When an undirected tree T and a vertex ${\gamma}$ in the tree are given the problem to transform T into a rooted tree with ${\gamma}$ as its root is considered. Using Euler tour and prefix sum an optimal algorithm has been developed [2,3]. We will present another parallel algorithm which is optimal also on EREW PRAM. Our approach resuces the given tree step by step by pruning and pointer jumping. That is the tree structure is retained during algorithm processing such that than other tree computations can be carried out in parallel.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.11
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• pp.2052-2067
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• 2011

Complementary trees are two spanning trees rooted at the sink node satisfying that any source node's two paths to the sink node on the two trees are node-disjoint. Complementary trees routing strategy is a special node-disjoint multi-path routing approach. Several complementary trees routing algorithms have been proposed, in which path discovery methods based on depth first search (DFS) or Dijkstra's algorithm are used to find a path for augmentation in each round of path augmentation step. In this paper, a novel path discovery method based on multi-tree-growing (MTG) is presented for the first time to our knowledge. Based on this path discovery method, a complementary trees routing algorithm is developed with objectives of low average path length on both spanning trees and low complexity. Measures are employed in our complementary trees routing algorithm to add a path with nodes near to the sink node in each round of path augmentation step. The simulation results demonstrate that our complementary trees routing algorithm can achieve low average path length on both spanning trees with low running time, suitable for wireless sensor networks in industrial scenarios.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.883-896
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• 2022

A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.16.1-16
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• 2003

A subset S of vertices of a graph G is independent if no two vertices of S are adjacent by an edge in G. Also we say that S is maximal independent if it is contained In no larger independent set in G. A planted plane tree is a tree that is embedded in the plane and rooted at an end-vertex. A (k＋1) -valent tree is a planted plane tree in which each vertex has degree one or (k＋1). We classify maximal independent sets of (k＋1) -valent trees into two groups, namely, type A and type B maximal independent sets and consider specific independent sets of these trees. We study relations among these three types of independent sets. Using the relations, we count the number of all maximal independent sets of (k＋1) -valent trees with n vertices of degree (k＋1).

• ETRI Journal
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• v.22 no.1
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• pp.30-37
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• 2000

Existing tree construction mechanisms are classified into source-based trees and center-based trees. The source-based trees produce a source-rooted tree with a low delay. However, for the applications with multiple senders, the management overheads for routing tables and resource reservations are too high. The center-based trees are easy to implement and manage, but a priori configuration of candidate center nodes is required, and the optimization mature such as tree cost and delay is not considered. In this paper, we propose a new multicast tree building algorithm. The proposal algorithm basically builds a non-center based shared tree. In particular, any center node is not pre-configured. In the purposed algorithm, a multicast node among current tree nodes is suitably assigned to each incoming user: Such a node is selected in a fashion that tree cost and the maximum end-to-end delay on the tree are jointly minimized. The existing and proposed algorithms are compared by experiments. In the simulation results, it is shown that the proposed algorithm approximately provides the cost saving of 30% and the delay saving of 10%, compared to the existing approaches. In conclusion, we see that the cost and delay aspects for multicast trees can be improved at the cost of additional computations.