• 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.

• 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 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 The Korean Astronomical Society
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• v.8 no.1
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• pp.29-34
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• 1975

Solar electrical conductivity has been calculated, making use of Yun and Wyller's formulation. The computed results arc presented in a tabulated form as functions of temperature and pressure for given magnetic field strengths. The results of the calculation show that the magnetic field does not play any important role in characterizing the electrical conductivity of the ionized gas when the gas pressure is relatively high (e.g., $P{\geq}10^4\;dynes/cm^2$). However, when the gas pressure is low (e.g., $P{\leq}10\;dynes/cm^2$), the magnetic field becomes very effective even if its field strength is quite small (e.g., $B{\leq}0.01$ gauss). It is also found that, except for lower temperature region (e.g., $T{\leq}10^{4^{\circ}}K$), there is a certain linear relationship in a log- log graph between the pressure and the critical magnetic field strength, which is defined as a field strength capable of reducing the non-magnetic component of the electrical conductivity by 20%.

• The KIPS Transactions:PartB
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• v.18B no.2
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• pp.57-66
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• 2011

To prevent cardiac diseases, quantifying cardiac function is important in routine clinical practice by analyzing blood volume and ejection fraction. These works have been manually performed and hence it requires computational costs and varies depending on the operator. In this paper, an automatic left ventricle segmentation algorithm is presented to segment left ventricle on cardiac magnetic resonance images. After coil sensitivity of MRI images is compensated, a K-mean clustering scheme is applied to segment blood area. A graph searching scheme is employed to correct the segmentation error from coil distortions and noises. Using cardiac MRI images from 38 subjects, the presented algorithm is performed to calculate blood volume and ejection fraction and compared with those of manual contouring by experts and GE MASS software. Based on the results, the presented algorithm achieves the average accuracy of 6.2mL${\pm}$5.6, 2.9mL${\pm}$3.0 and 2.1%${\pm}$1.5 in diastolic phase, systolic phase and ejection fraction, respectively. Moreover, the presented algorithm minimizes user intervention rates which was critical to automatize algorithms in previous researches.

• ETRI Journal
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• v.46 no.3
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• pp.485-500
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• 2024

A hardware architecture is presented to decode (N, K) polar codes based on a low-density parity-check code-like decoding method. By applying suitable pruning techniques to the dense graph of the polar code, the decoder architectures are optimized using fewer check nodes (CN) and variable nodes (VN). Pipelining is introduced in the CN and VN architectures, reducing the critical path delay. Latency is reduced further by a fully parallelized, single-stage architecture compared with the log N stages in the conventional belief propagation (BP) decoder. The designed decoder for short-to-intermediate code lengths was implemented using the Virtex-7 field-programmable gate array (FPGA). It achieved a throughput of 2.44 Gbps, which is four times and 1.4 times higher than those of the fast-simplified successive cancellation and combinational decoders, respectively. The proposed decoder for the (1024, 512) polar code yielded a negligible bit error rate of 10^-4 at 2.7 E_b/N_o (dB). It converged faster than the BP decoding scheme on a dense parity-check matrix. Moreover, the proposed decoder is also implemented using the Xilinx ultra-scale FPGA and verified with the fifth generation new radio physical downlink control channel specification. The superior error-correcting performance and better hardware efficiency makes our decoder a suitable alternative to the successive cancellation list decoders used in 5G wireless communication.