• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.119-139
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• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.69-74
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• 2015

This paper offers solutions to unresolved $43{\leq}R(5,5){\leq}49$ and $102{\leq}R(6,6){\leq}165$ problems of Ramsey's number. The Ramsey's number R(s,t) of a complete graph $k_n$ dictates that n-1 number of incidental edges of a arbitrary vertex ${\upsilon}$ is dichotomized into two colors: (n-1)/2=R and (n-1)/2=B. Therefore, if one introduces the concept of distance to the vertex ${\upsilon}$, one may construct a partite graph $K_n=K_L+{\upsilon}+K_R$, to satisfy (n-1)/2=R of {$K_L,{\upsilon}$} and (n-1)/2=B of {${\upsilon},K_R$}. Subsequently, given that $K_L$ forms the color R of $K_{s-1)$, $K_S$ is attainable. Likewise, given that $K_R$ forms the color B of $K_{t-1}$, $K_t$ is obtained. By following the above-mentioned steps, $R(s,t)=K_n$ was obtained, satisfying necessary and sufficient conditions where, for $K_L$ and $K_R$, the maximum distance should be even and incidental edges of all vertices should be equal are satisfied. This paper accordingly proves R(5,5)=43 and R(6,6)=91.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.2 s.233
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• pp.287-293
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• 2005

In the present study, to determine the flow rate of droplets supplied to heat transfer surface after (j-1)th rebound, $D_X[j{\ge}2]^{\ast}$, it was assumed that the rebound droplets are distributed according to the Gaussian distribution from 0 to L, in which the flight distance L is determined by maximum flight distance $L_{max}$. We also assumed that $L_{max}$ is dependent on the air flow velocity and mean size of droplets. The local heat flux of a dilute spray in high temperature region was predicted using the newly evaluated $D_X[j{\ge}2]^{\ast}$. In addition, the predicted results by the present model were compared with the existing experimental data.

• Journal of Environmental Science International
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• v.32 no.11
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• pp.801-809
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• 2023

The purpose of this study is to predict the reflection distance following to the pulsing pressure, total air supplying, filter bag size using numercial analysis techniques and use it as an efficient operation condition and economic data for off-line type pulse air jet bag filter. In this research, filtration area 6 m² condition, calculate filter resistance coefficient for simulation through the main experiments using coke dust. Ansys fluent V19.0 apply to CFD simulation, and analysis pulsing characteristics about pulsing pressure, filtration velocity and nozzle diameter. The maximum reflecting distance of off-line type pulse air jet bag filter is 1,000 mm regardless of total air supplying at over the 42 L/m² conditions, that indicates off-line type can extend filter bag length 1,000 mm than on-line type. In order to effective primary and secondary pulsing of off-line type pulse air jet bag filter, over the 5 bar of pulsing pressure and over the 42 L/m² of total air supplying are needed.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.22 no.4
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• pp.201-213
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• 1989

This study is just to be carried out to grasp the efficiency of jet stream excavating for the ground. Changing the dynamic pressure, nozzle diameter, distance off the ground, we measured the impulse, the excavated depth, the excavated width. According as each dynamic pressure increases from 100 to $500gf/cm^2$, the impulse of the jet stream increases from 43 to 114gf, from 52 to 227gf, from 114 to 506gf, from 137 to 768gf, in 4, 6, 8, 10mm nozzles respectively, but it makes no difference in the value of distance within 50cm off ground. The excavated depth increases at the invariable rate in accordance with nozzle diameter, dynamic pressure, nozzle distance. We obtain the equations relevant to the ground I, II as follows: $$L_I=[0.01(H/r-100) -0.43\cdot\iota+11.78]{\cdot}D/4$$ $$L_{II}=[0.03(H/r-100) -0.34\cdot\iota+6.39]{\cdot}D/4$$ where, $L_I,\;L_{II}$ are respectively the excavated depths of the ground I, II, cm; H is the dynamic pressure, $gf/cm^2\;:\;\iota$ is the distance off the ground, cm; D is Nozzle diameter, mm; r is the specific weight, $1gf/cm^2$.

• Journal of Ecology and Environment
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• v.38 no.4
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• pp.397-403
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• 2015

Rice (Oryza sativa L.) is an important feeding crop in Asia, and utilization of genetically modified (GM) rice is highly demanding. For co-existence of GM rice and non-GM rice, the proper confinement measures should be provided. Thus, we surveyed gene flow from herbicide resistant GM rice to the conventional rice cultivars in the field tests. Gene flow frequency decreased with increasing distance between the pollen donor and recipients and did not exceed more than 1% even at the nearest distance. In single recipient model plot, a maximum gene flow frequency was observed at the shortest distance and hybrid was detected up to 12 m from the pollen donor. The direction of gene was coincided with the dominant wind direction. Gene flow assessment to multiple recipient plots was conducted under the high raining season by chance, and abrupt decline of gene flow frequency and maximum distance were resulted. According to the survey results, current regulation for isolation distance is reasonable for environmental safety or for general crop production. However, we suggest an alternative measure for GM rice cultivation that should be supplemented to overcome the out of estimation and in the environment asking higher security levels.

• The Transactions of the Korea Information Processing Society
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• v.6 no.8
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• pp.2124-2132
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• 1999

Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

• Journal of information and communication convergence engineering
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• v.9 no.1
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• pp.105-109
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• 2011

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.

• Journal of Korean Neurosurgical Society
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• v.37 no.5
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• pp.336-339
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• 2005

Objective: The goal of this study is to establish the anatomical criteria of the normal and stenotic lumbosacral extraforaminal tunnel, and also to determine the effect of the pathologic intervertebral disc on the size of extraforaminal tunnel in the lumbosacral spine. Methods: MRI and CT scans were reviewed and classified into two groups: (1) 40 patients with normal discs at L5- S1 (Group 1) and (2) 43 patients that had undergone successful decompression surgery for extraforaminal entrapment at the lumbosacral region(Group 2). In these two groups, the following parameters were compared are compared: the distance between the disc margin and the ala (lumbosacral tunnel) on the axial MRI, and the posterior disc height at L5-S1 on the mid-sagittal MRI. Results: In the group 1, the mean distance of the lumbosacral tunnel on the axial MRI was $10.1{\pm}2.2mm$. The mean posterior disc height at L5-S1 was $7.4{\pm}1.7mm$ on the mid-sagittal MRI. In the group 2, the mean distance between the disc margin and the ala (costal process) was $1.6{\pm}1.3mm$ on the axial MRI. The average posterior disc height was $4.4{\pm}1.5mm$ on the mid-sagittal MRI. The posterior disc height and the size of the lumbosacral tunnel between the two groups were statistically different on the paired t-test (p<0.0001). However, the posterior disc height was not positively correlated with the size of the extraforaminal tunnel for group 2 (p=0.909). Conclusion: The extraforaminal stenosis was correlated to pathologic disc. However, the posterior disc height was not correlated to the size of the of the extraforaminal tunnel.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.69-80
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• 2014

The free distance of (n, k, l) convolutional codes has some connection with the memory length, which depends on not only l but also on k. To efficiently obtain a large memory length, we have constructed a new class of (2k, k, l) convolutional codes by (2k, k) block codes and (2, 1, l) convolutional codes, and its encoder and generation function are also given in this paper. With the help of some matrix modules, we designed a single structure Viterbi decoder with a parallel capability, obtained a unified and efficient decoding model for (2k, k, l) convolutional codes, and then give a description of the decoding process in detail. By observing the survivor path memory in a matrix viewer, and testing the role of the max module, we implemented a simulation with (2k, k, l) convolutional codes. The results show that many of them are better than conventional (2, 1, l) convolutional codes.