• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.167-170
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• 2004

We present a novel graph labeling problem called S-edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be ${ a_n / a_n = 4 a_{n-l}+l,\;a_{n-1}=0}$. We show that every binomial tree is possible S-edge labeling by giving labeling schems to them. The labelings on the binomial trees are applied to their embedings into interconnection networks.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.345-350
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• 2022

In this work, we confirm a weak version of a conjecture proposed by Hong Wang. The ideal of the work comes from the tree packing conjecture made by Gyárfás and Lehel. Bollobás confirms the tree packing conjecture for many small tree, who showed that one can pack T₁, T₂, …, $T_{n/\sqrt{2}}$ into Kn and that a better bound would follow from a famous conjecture of Erdős. In a similar direction, Hobbs, Bourgeois and Kasiraj made the following conjecture: Any sequence of trees T₁, T₂, …, T_n, with T_i having order i, can be packed into K_n-1,[n/2]. Further Hobbs, Bourgeois and Kasiraj [3] proved that any two trees can be packed into a complete bipartite graph K_n-1,[n/2]. Motivated by the result, Hong Wang propose the conjecture: For each k-partite tree T(𝕏) of order n, there is a restrained packing of two copies of T(𝕏) into a complete k-partite graph B_n+m(𝕐), where $m={\lfloor}{\frac{k}{2}}{\rfloor}$. Hong Wong [4] confirmed this conjecture for k = 2. In this paper, we prove a weak version of this conjecture.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.259-263
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• 2007

Which spheres are shellable?[2]. We present one of them which is the k-tree with n-labeled vertices. We found that the number of ways to shell the k-dimensional trees on n-labeled vertices is $$\frac{n!}{(k+1)!}(nk-k^2-k+1)!k$$.

• Horticultural Science & Technology
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• v.33 no.4
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• pp.591-597
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• 2015

We determined the total C and N stocks in trees and soils after 1 year of fertilization in an experimental orchard with 16-year-old 'Niitaka' pear (Pyrus pyrifolia Nakai cv. Niitaka) trees planted at $5.0m{\times}3.0m$ spacing on a Tatura trellis system. Pear trees were fertilized at the rate of 200 kg N, 130 kg P and $180kg\;K\;ha^{-1}$. At the sampling time (August 2013), trees were uprooted, separated into six fractions [trunk, main branches, lateral branches (including shoots), leaves, fruit, and roots] and analyzed for their total C and N concentrations and dry masses. Soil samples were collected from 0 to 0.6 m in 0.1 m intervals at 0.5 m from the trunk, air-dried, passed through a 2-mm sieve, and analyzed for total C and N concentrations. Undisturbed soil core samples were also taken to determine the bulk density. Dry mass per tree was 5.6 kg for trunk, 12.0 kg f or m ain branches, 15.7 kg for lateral branches, 5.7 kg for leaves, 9.8 kg for fruits, and 10.5 kg for roots. Total amounts of C and N per tree were respectively 2.6 and 0.02 kg for trunk, 5.5 and 0.04 kg for main branches, 7.2 and 0.07 kg for lateral branches, 2.6 and 0.11 kg for leaves, 4.0 and 0.03 kg for fruit, and 4.8 and 0.05 kg for roots. Carbon and N stocks stored in the soil per hectare were 155.7 and 14.0 Mg, respectively, while those contained in pear trees were 17.8 and $0.2Mg{\cdot}ha^{-1}$ based on a tree density of 667 trees/ha. Overall, C and N stocks per hectare stored in the pear orchard were 173.6 and 14.2 Mg, respectively. Compared with results obtained in 2012, the amounts of C stocks have increased by $17.7Mg{\cdot}ha^{-1}$, while those of N stocks remained virtually unchanged ($0.66Mg{\cdot}ha^{-1}$).

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• Journal of the Korea Computer Industry Society
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• v.2 no.2
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• pp.203-210
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• 2001

To estimate relational models and test the theoretical hypotheses of binary tree search algorithms, we built binary search trees with random permutations of n (number of nodes) distinct numbers, which ranged from three to seven. Probabilities for building binary search trees corresponding to each possible height and balance factor were estimated. Regression models with variables of number of nodes, height, and average number of comparisons were estimated and the theorem of O(1g(n)) was accepted experimentally by a Lack of Test procedure. Analysis of Variance model was applied to compare the average number of comparisons with three groups by height and balance factor of the trees to test theoretical hypotheses of a binary search tree performance statistically.

• Applied Biological Chemistry
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• v.36 no.6
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• pp.469-475
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• 1993

In order to elucidate the metabolism of the systemic insecticide, phosphamidon(2-chloro-2-diethylcarbamoyl-1-methylvinyl dimethyl phosphate), treated to pine trees against pine leaf gall midges (Thecodiplosis japonensis Uchida et Inouye), $[vinyl,\;carbonyl-^{14}C]$phosphamidon was implanted into the trunks of 10-year-old Korean red pine (Pinus densiflora Sieb. et Zucc.) and Japanese black pine (Pinus thunbergii Parl.), respectively. This chemical was degraded very quickly in pine trees after implanting, as confirmed by TLC/autoradiography of the extracts of pine needles. Phosphamidon metabolites in phosphate buffer extracts of pine needles include the major metabolite, ${\alpha}-chloroacetoacetic$ acid diethyl-amide, ${\alpha}-chloroacetoacetic$ acid ethylamide, 3-hydroxy-N,N-d iethylbutanamide, acetoacetamide, and trimethyl phosphate. The metabolism within pine trees is expected to be similar to this. Based on these findings, it is believed that the major pathway leading to the metabolites would be related to the P-O-vinyl hydrolysis of the chemical structure.

• Journal of Biosystems Engineering
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• v.19 no.4
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• pp.311-317
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• 1994

Warts and barks of apple trees were vector of White rot. Two devices removing warts and barks for the use of pest control on apple trees were developed and evaluated in this study, and their results are as follows ; 1. A total of 148 warts were examined to determine the average size. About 35 percent of the examined warts were 6~8mm long, 4~8mm wide and 4~6mm thick in size. About 30 percent of the examined warts were 4~6mm long, 2~4mm wide and 6~8mm thick in size. 2. Seventy-one percent of the examined barks removed were 4~8mm in thickness. 3. A blade with 30 degree of cutting angle required 3 to 22 percent less cutting energy than those with 15 and 45 degrees of cutting angles. 4. The cutting torque decreased from 31 N-cm to 12 N-cm with an increase of cutting speed from 26cm/s to 104cm/s for a feeding speed of 0.31 mm/s with the blade angle of 30 degrees. 5. The cutting torque increased from 6N-cm to 32N-cm with an increase of branch diameter from 6mm to 14mm for a feeding speed of 0.31 mm/s with the blade angle of 30 degrees. 6. Two devices mounted on a mower for removing warts and barks were evaluated and proved effective.

• Horticultural Science & Technology
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• v.28 no.5
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• pp.728-734
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• 2010

We studied the accumulation and partitioning of dry weight (DW) and nitrogen (N) in different parts of field-grown 'Fuyu' persimmon to elucidate that the foliar applications of supplemental N in June or September compared favorably with the traditional soil application in securing leaf area and fruit production. We also estimated the proportion of N permanently removed from the tree at the end of a growing season. Urea was applied either to leaves in June and/or September or to the soil in June and September for three consecutive years, and the trees were excavated in November for analyses. Total DW ranged from 4.2-4.8, 8.7-9.2, and 17.1-21.5 kg in a 4-, 5-, and 6-year-old tree, respectively, without statistical difference among the four treatments. Of the total DW, 3.3-10.2% was in shoots, 5.7-10.5% in leaves, 8.3-31.4% in aerial woods, 13.0-27.0% in root, and 28.0-59.3% in fruits. As the trees became more productive, DW proportion of fruits significantly affected that of the root: in 6-year-old trees, root DW accounted for only 10.6-15.8% of the tree total when fruit DW accounted for 50-60%. N contents ranged from 24.6-28.3, 48.3-53.5, and 98.3-122.6 g in a 4-, 5-, and 6-year-old trees, respectively, without statistical difference among the treatments. Of the total N, 6.2-11.5% was in shoots, 16.7-24.3% in leaves, 17.6-23.5% in aerial woods, 17.2-37.5% in roots, and 16.9-34.4% in fruits. As in DW, the increase in the proportion of N in fruits decreased in the root most significantly. Application methods for supplemental N did not affect the proportion of DW and N removed from the tree through abscising leaves and harvested fruits. Percentage of DW removal was 41 in 4- and 5-year-old trees, but it was 61 in more productive 6-year-old trees; that of N was 39, 43, and 49%, respectively. No significant changes in the contents of DW and N in field-grown trees, as well as their percentages removed from the tree at the end of the season, demonstrated that foliar application of supplemental N was as good as soil applications with much less N.

• Korean Journal of Organic Agriculture
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• v.19 no.spc
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• pp.165-168
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• 2011

An organic apple (Malus ${\times}$ domestics Borkh.) orchard was established to study the interaction effects of ground cover management systems (GMS) and nutrient sources (NS) on soil and tree nutrient status and tree growth. Trees received one of four GMS: 1) green compost (GC), 2) wood chips (WC), 3) shredded paper (SP), and 4) mow-and-blow (MB). Across all GMS, one of three NS was applied: A) a commercial organic fertilizer (CF), B) poultry litter (PL), and C) control (NF). Overall, GMS had greater effects on the variables than did NS. GC mulch supplied greater nutrients, followed by WC, SP, and MB mulches. SP trees had lower foliar [N] in the first two years than the GC and WC trees. GC-and WC-treated trees had larger trunk cross sectional area than the SP and MB trees.