• 대한수학회보
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• 제45권1호
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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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• 제31권5_6호
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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.

• 대한수학회지
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• 제51권1호
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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.

• 천문학회지
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• 제8권1호
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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%.

• 정보처리학회논문지B
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• 제18B권2호
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• pp.57-66
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• 2011

심장 질환을 예방하기 위해서는 정기적인 검진을 통해 심장 기능을 분석하고 관찰하는 것이 중요하다. 정기적인 검진에서 심장 기능은 심장을 촬영한 후에 관측자가 이를 수작업을 통하여 처리하여 혈류량과 심박구출률 등을 분석함으로서 이루어지나, 시간도 오래 걸리며 관측자에 따른 변이성이 문제가 된다. 본 논문에서는 심장 단축 자기공명영상에서 좌심실 영역을 분할하는 자동화된 알고리즘을 제안한다. 코일 위치에 따른 왜곡을 보정하고, K-평균 클러스터링 기법을 이용하여 좌심실 내부를 분할한다. 영상의 왜곡 및 잡음에 의하여 발생하는 분할 오류는 그래프 탐색 기법을 적용하여 수정하였다. 제안하는 알고리즘의 성능을 평가하기 위하여 38명의 지원자 그룹에 대하여 혈류량과 심박구출률을 계산하였고, 전문가에 의한 수동윤곽검출 결과와 GE MASS 소프트웨어와 비교하였다. 결과에 따르면 제안한 알고리즘의 수동윤곽검출과 혈류량의 차이는 평균적으로 이완기에 6.2mL${\pm}$5.6 및 수축기에 2.9mL${\pm}$3.0, 심박구출률의 차이는 2.1%${\pm}$1.5로 높은 정확성을 보였다. 특히 제안한 알고리즘은 기존 알고리즘에서 발생하던 사용자 간섭률을 최소화하여 자동화 성능을 향상하였다.

• ETRI Journal
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• 제46권3호
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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.