• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.163-176
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• 2019

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.33 no.4
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• pp.145-152
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• 2023

The average Nusselt numbers in the source and crystal region for the variation of thermal Grashof number (Gr_t) in the range of 2.31 × 10⁴ ≤ Gr_t ≤ 4.68 × 10⁴ are obtained through numerical simulations. It is shown the average Nusselt number in the crystal region is more than twice as large as the average Nusselt number in the source region. The average Nusselt number in the source region shows an increasing tendency with increasing the thermal Grashof number, Gr_t, while the average Nusselt number in the crystal region shows a decreasing tendency with increasing thermal Grashof number, Gr_t. For the variation of the solutal Grashof number (Gr_s) in the ran ge of 3.28 × 10⁵ ≤ Gr_s ≤ 4.43 × 10⁵, the average Sherwood number in the source region and crystal region tends to decrease as the solutal Grashof number, Gr_s increases. The average Sherwood number in the crystal region is about four times greater than the average Sherwood number in the source region.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.1-12
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• 2021

A dominating set S of a graph G is said to be nonsplit dominating set if the subgraph ⟨V - S⟩ is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number and is denoted by ��ns(G). For a minimum nonsplit dominating set S of G, a set T ⊆ S is called a forcing subset for S if S is the unique ��ns-set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing nonsplit domination number of S, denoted by f��ns(S), is the cardinality of a minimum forcing subset of S. The forcing nonsplit domination number of G, denoted by f��ns(G) is defined by f��ns(G) = min{f��ns(S)}, where the minimum is taken over all ��ns-sets S in G. The forcing nonsplit domination number of certain standard graphs are determined. It is shown that, for every pair of positive integers a and b with 0 ≤ a ≤ b and b ≥ 1, there exists a connected graph G such that f��ns(G) = a and ��ns(G) = b. It is shown that, for every integer a ≥ 0, there exists a connected graph G with f��(G) = f��ns(G) = a, where f��(G) is the forcing domination number of the graph. Also, it is shown that, for every pair a, b of integers with a ≥ 0 and b ≥ 0 there exists a connected graph G such that f��(G) = a and f��ns(G) = b.

• Computers and Concrete
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• v.29 no.1
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• pp.31-45
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• 2022

Experimental and numerical simulation were used to investigate the effects of angle and number of T shape non-persistent crack on the shear behaviour of crack's bridge area under uniaxial compressive test. concrete samples with dimension of 150 mm×150 mm×40 mm were prepared. Within the specimen, T shape non-persistent notches were provided. 16 different configuration systems were prepared for T shape non-persistent crack based on two and three cracks. In these configurations, the length of cracks were taken as 4 cm and 2 cm based on the cracks configuration systems. The angle of larger crack related to horizontal axis was 0°, 30°, 60° and 90°. Similar to cracks configuration systems in the experimental tests, 28 models with different T shape non-persistent crack angle were prepared in numerical model. The length of cracks were taken as 4 cm and 2 cm based on the cracks configuration systems. The angle of larger crack related to horizontal axis was 0°, 15°, 30°, 45°, 60°, 75° and 90°. Tensile strength of concrete was 1 MPa. The axial load was applied to the model. Displacement loading rate was controlled to 0.005 mm/s. Results indicated that the failure process was significantly controled by the T shape non-persistent crack angle and crack number. The compressive strengths of the specimens were related to the fracture pattern and failure mechanism of the discontinuities. Furthermore, it was shown that the compressive behaviour of discontinuities is related to the number of the induced tensile cracks which are increased by increasing the crack number and crack angle. The strength of samples decreased by increasing the crack number. In addition, the failure pattern and failure strength are similar in both methods i.e. the experimental testing and the numerical simulation methods (PFC2D).

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.665-668
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• 2012

For a given graph G we consider a set S(G) of all symmetric matrices A = [$a_{ij}$] whose nonzero entries are placed according to the location of the edges of the graph, i.e., for $i{\neq}j$, $a_{ij}{\neq}0$ if and only if vertex $i$ is adjacent to vertex $j$. The minimum rank mr(G) of the graph G is defined to be the smallest rank of a matrix in S(G). In general the computation of mr(G) is complicated, and so is that of the maximum multiplicity MaxMult(G) of an eigenvalue of a matrix in S(G) which is equal to $n$ - mr(G) where n is the number of vertices in G. However, for trees T, there is a recursive formula to compute MaxMult(T). In this note we show that this recursive formula for MaxMult(T) also computes the path cover number $p$(T) of the tree T. This gives an alternative proof of the interesting result, MaxMult(T) = $p$(T).

• The Korean Journal of Ecology
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• v.21 no.5_1
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• pp.457.2-486
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• 1998

Ecological success of introduced species is frequently attributed to the reproductive characters of those species. We examined the relationship between both flowering season and plant size and reproductive characters in two introduced species of Taraxacum, e.g., T. officinale and T.laevigatum. Seventy six plants of T. officinale and 23 plants of T. laevigatum were randomly tagged from a population at the sungshin Women's University in April of 1997. The size and number of vegetative characters such as rosette diameter, leaf number, and the largest leaf length and width were measured for each plant at the onset of flowering. The infructescence was collected continually from each plant before seed dispersal from April to August of 1997. The number of infructescence per plant, and seed number and total seed weight per infructescence were measured. Mean individual seed weight per infructescence was also obtained. T. officinale possessed larger sized, but smaller number of, leaves than T. laevigatum, thereby resulting in no significant difference in total leaf area. There was a trend that vegetatively larger plants in both of these species produced reproductive characters larger in size or greater in number, except for seed number and total seed weight per infructescence in T. laevigatum. All reproductive characters examined in T. officinale decreased toward the end of flowering season. In T. laevigatum, infructescence number per plant also declined during a flowering season: however, mean seed number per infructescence increaed toward the end of flowering season with no significant seasonal change in the total seed weight per infructescence. T. officinale produced on average about twice as many seeds per plant as T. laevigatum during a growing season. These two Taraxacum species produced quite small seeds in size compared to the endemic species, exhibiting a far better dispersal ability of introduced species. These data demonstrate that most reproductive characters decline in size and number in both species during a long flowering period, but the two species appear to employ different strategies to achieve reproductive success in disturbed habitats.

• Journal of The Korean Society of Grassland and Forage Science
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• v.16 no.2
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• pp.93-104
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• 1996

A field experiment was conducted in Chungju and Jungwon to evaluate growth characteristics, dry matter yield, protein yield and palatability of intercropping comparing with monocropping forage crops by the use of sorghum $\times$ sudangrass hybrid(S.S.H.), five forage soybeans and two forage cowpeas of superior to selected experiment of varieties. All eight treatment plots were replicated three times and cutting date were cut July 6 and September 9. 1. The mean leaf number of S.S.H. in intercropping T2 treatment showed high compared to T1 treatment in all treatment except for Hwangkeum treatment, but T3 treatment was lower than the other treatments. In the leaf number of soybean, Jangbaek treatment was the highest as 47 leaves per plant, cowpea treatments showed high above 50 leaves. The stem diameter of S.S.H. in Jangyeob treatment of T2 treatment was 9.6mm. In legume, cowpea of T3 treatment was high as ranged from 7.9mm to 8.2mm. In stem hardiness of S.S.H., TI treatment was the lower than the other treatments, while Jangbaek treatment of T2 treatment was the highest as $2.0kg/cm^2$. In legume crops, Jangbaek and Baekun treatment were the highest as $1.6kg/cm^2$, but T3 treatment was very low as $0.3~0.6kg/cm^2$. 2. In the mean leaf ratio of S.S.H., T1 treatment was higher than T2 and T3 treatment as 34.9%. In the legume crops, Togyu treatment was the highest as 40.9%. In the mean tiller number of S.S.H., T2 treatment showed high compared to TI treatment, but T3 treatment of was rather decrease than The tiller number of S.S.H. in Jangyeob treatment of T2 treatment was the highest as 4.6 per plant. The dead stubble of S.S.H. was high in order to T3>T1>T2 treatment>, T3 treatment was highly about 2 times compared to T2 treatment. 3. S.S.H. as T3 treatment was resistant to lodging, but T3 and T1 treatment showed highly lodging. In the legums, T3 treatment was resistant to lodging, but T2 treatment showed highly lodging. In the S.S.H. of T2 treatment, the leaf of summer depression was not occurrence, but T3 treatment was higher than the other treatments. 4. The palatability of domestic animals was high in order of T2>Tl>T3, especially Togyu treatment of T2 treatment was the highest at the holstein and deer, and Jangyeob treatment of T2 treatment was the highest in the Korean native cattle. But T3 treatment was lower than other treatments in the holstein and Korean native cattle. 5. Fresh yield of monocropping(T1) was the highest as 94, 650kg/ha, while dry matter yield in Jangyeob treatment of T2 treatment was the highest as 15, 575/ha But fresh yield and dry matter yield of T3 treatment were the lowest(P<0.05). 6. Protein yield in T2 treatment was high, especially Jangyeob treatment of T2 treatment was the highest as 1, 605.5 kg/ha T3 treatment was low in spite of high protein content, because dry matter yield was lower than the other treatments. In conclusion, among T1, T2 and T3 treatment, Jangyeob, Togyu and Baekun treatments of T2 treatment showed optimum varieties for intercropping with S.S.H., because they showed high Dry matter yield, protein yield and palatability.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.4
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• pp.11-20
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• 1994

The error rate equation of DS-CDMA/DQPSK skgnal adopting ARQ scheme has been derived in indoor radio channel which is characterized by AWGN, multi-user interference (MUI) and Rician fading, Using the derived equation the error performance has been evaluated and shown in figures as a function of direct to diffuse signal power ratio(KS1rT), the number of active users (K), PN code sequence length (N), the number of parity bit of linear code (b), forward channel BER, and ES1bT/NS1OT. From the results it is known that in severe fading environments (KS1rT=6) the performance of DS-CDMA/DQPSK system is not reliable so it is needed to adopt techniques for improvement. When an ARQ scheme is adopted, as a method for improving error performance, the performance improves compared with that of non-ARQ scheme and the degree of improvement is proportional to the number of parity bits of linear code. As increasing the number of parity bits, system performance is improved vut system throughput efficiency must be considered. In severe fading channel Hybrid ARQ scheme is more effective than ARQ scheme. As a result, ARQ scheme is appropriate for the high-reliability data communication systems over the radio channel in which the real time processing is not required.