• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.53-57
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• 2008

Let G be a graph, and let a, b, k be integers with $0{\leq}a{\leq}b,k\geq0$. Then graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, the relationship between binding number bind(G) and (a, b, k)-critical graph is discussed, and a binding number condition for a graph to be (a, b, k)-critical is given.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.31-46
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• 2021

Let a and b be positive integers, and let V (G), ��(G), and ��2(G) be the vertex set of a graph G, the minimum degree of G, and the minimum degree sum of two non-adjacent vertices in V (G), respectively. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b, where dH(v) is the degree of v in H. Matsuda conjectured that if G is an n-vertex 2-edge-connected graph such that $n{\geq}2a+b+{\frac{a^2-3a}{b}}-2$, ��(G) ≥ a, and ${\sigma}_2(G){\geq}{\frac{2an}{a+b}}$, then G has an even [a, b]-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even [a, b]-factor. For even an, we conjecture a lower bound for the largest eigenvalue in an n-vertex graph to have an [a, b]-factor.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.435-441
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• 2016

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

• Journal of Acupuncture Research
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• v.25 no.2
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• pp.139-149
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• 2008

Objectives : The 7-zone-diagnostic system is a diagnostic device to predetermine bodily locations by measuring the energy of body. This study was to investigate the relation between the different patterns of Zone 2, 6 of Factor AA in VEGA DFM 722(VEGA, Germany), 7-zone-diagnostic system and clinical parameters. The purpose of this study was relation Korean traditional medicine and western medicine with the data from 7-zone-diagnostic system and the clinical parameters. Methods : This study was carried out with the data from some clinical parameters. We made two groups according to the Factor AA patterns of VEGA DFM 722. The Factor AA pattern of Group A is that the red bar graph of zone 2 was higher than the normal range and the red bar graph of zone 6 was lower than the normal range. The Factor AA pattern of Group B was that the red bar graph of zone 2 was lower than the normal range and the red bar graph of zone 6 was higher than the normal range. After the data from clinical parameters to correspond with conditions of each group were selected, the data from clinical parameters between each gropus analyzed statistically. Results and Conclusions : The values of Direct Bilirubin, GOT, BUN and BUN/Creatinine ratio of Group A were higher than them of Group B. The values of Sodium and Tyroxine of Group A were lower than them of Group B. These results mean that Group A has low energy but has increading tendency. To conclude, it is thought that the red bar graph of zone 2 is higher, the group is the more increasing and the red bar graph of zone 6 is lower, the group has the lower energy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.2
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• pp.703-722
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• 2016

Passive wireless devices have increasing civilian and military applications, especially in the scenario with wearable devices and Internet of Things. In this paper, we study indoor localization of a target equipped with radio-frequency identification (RFID) device in ultra-wideband (UWB) wireless networks. With known room layout, deterministic multipath components, including the line-of-sight (LOS) signal and the reflected signals via multipath propagation, are employed to locate the target with one transmitter and a single inaccurate receiver. A factor graph corresponding to the joint posterior position distribution of target and receiver is constructed. However, due to the mixed distribution in the factor node of likelihood function, the expressions of messages are intractable by directly applying belief propagation on factor graph. To this end, we approximate the messages by Gaussian distribution via minimizing the Kullback-Leibler divergence (KLD) between them. Accordingly, a parametric message passing algorithm for indoor passive localization is derived, in which only the means and variances of Gaussian distributions have to be updated. Performance of the proposed algorithm and the impact of critical parameters are evaluated by Monte Carlo simulations, which demonstrate the superior performance in localization accuracy and the robustness to the statistics of multipath channels.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.757-774
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• 2022

Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), d_H(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ₂(G) = min_uv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ₂(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ₂(G) is sharp.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.27-40
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• 2002

For two integers m, n with m $\leq$ n, an [m,n]-factor F in a graph G is a spanning subgraph of G with m $\leq$ d$\_$F/(v) $\leq$ n for all v ∈ V(F). In 1996, H. Enomoto et al. proved that every 3-connected Planar graph G with d$\_$G/(v) $\geq$ 4 for all v ∈ V(G) contains a [2,3]-factor. In this paper. we extend their result to all 3-connected locally finite infinite planar graphs containing no unbounded faces.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.669-676
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• 2013

Let $a$ and $b$ be two even integers with $2{\leq}a<b$, and let k be a nonnegative integer. Let G be a graph of order $n$ with $n{\geq}\frac{(a+b-1)(a+b-2)+bk-2}{b}$. A graph G is called an ($a,b,k$)-critical graph if after deleting any $k$ vertices of G the remaining graph of G has an [$a,b$]-factor. In this paper, it is proved that G is an ($a,b,k$)-critical graph if $${\mid}N_G(X){\mid}&gt;\frac{(a-1)n+{\mid}X{\mid}+bk-2}{a+b-1}$$ for every non-empty independent subset X of V (G), and $${\delta}(G)>\frac{(a-1)n+a+b+bk-3}{a+b-1}$$. Furthermore, it is shown that the result in this paper is best possible in some sense.

• Journal of Acupuncture Research
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• v.25 no.6
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• pp.67-76
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• 2008

Objectives : The 7-zone-diagnostic system is a diagnostic device to predetermine bodily locations by measuring the energy of body. This study was to investigate the relation between the different patterns of Zone 1, 2, 3 of Factor AA in CP-6000A(VEGA, Germany), 7-zone-diagnostic system and clinical parameters. The purpose of this study was relation Korean traditional medicine and western medicine with the data from 7-zone-diagnostic system and the clinical parameters. Methods : This study was carried out with the data from some clinical parameters. We made three groups according to the Factor AA patterns of CP-6000A. The Factor AA pattern of Group A is that the red bar graph of zone 1, 2, 3 were higher than the normal range and the others were the normal range. The Factor AA pattern of Group B was that the red bar graph of zone 1, 2, 3 was the normal range and the others were the normal range. The Factor AA pattern of Group C was that the red bar graph of zone 1, 2, 3 was lower than the normal range and the others were the normal range. After the data from clinical parameters to correspond with conditions of each group were selected, the data from clinical parameters among each groups analyzed statistically. Results : The values of GOT, GPT, r-GPT, Triglyceride, BUN, Uric acid of group A was higher than group C. Gastroscope of group A and B was higher than group C. Conclusions : It is thought that the red bar graph of zone 1, 2, 3 is higher, the group has the higher energy and the energy has a character of fire(熱). Those patterns have a high risk of hyperlipermia and liver, stomach disease.