• Korean Journal of Mathematics
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• 제27권2호
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• pp.525-534
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• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• Advances in environmental research
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• 제3권4호
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• pp.367-377
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• 2014

In this study, we investigated a life cycle assessment (LCA) of six roof-waterproofing systems [asphalt (C1), synthetic polymer-based sheet (C2), improved asphalt (C3), liquid applied membrane (C4), Metal sheet with asphalt sheet (N1), and liquid applied membrane with asphalt sheet (N2)]for reinforced concrete building using an architectural model. To acquire accurate and realistic LCA results, minimum units of material compositions for life cycle inventory and real data for compositions of waterproofing materials were used. Considering only materials and energy demands for waterproofing systems per square meter, higher greenhouse gas (GHG) emissions could be generated in the order of C1 > N2 > C4 > N1 > C2 > C3 during construction phase. However, the order was changed to C1 > C4 > C3 > N2 > N1 > C2, when the actual architecture model was applied to the roof based on each specifications. When an entire life cycle including construction, maintenance, and deconstruction were considered, the amount of GHG emission was in the order of C4 > C1 > C3 > N2 > C2 > N1. Consequently, N1 was the most environmental-friendly waterproofing system producing the lowest GHG emission. GHG emissions from maintenance phase accounted for 71.4%~78.3% among whole life cycle.

• 한국해양공학회지
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• 제13권4호통권35호
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• pp.55-62
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• 1999

Cold rolled steel has much plastic strain in the material surface produced by manufacturing process. The strain causes the variation of surface residual stress, in which influences the fatigue behavior under repeated loading. As experimental results, it was confirmed that the behavior of residual stress ${\sigma}_r$, with cycle N consisted of three stages except stress amplitude near fatigue limit in SPCC steel. On the first stage compressive residual stress decreased rapidly, on the second stage gradually, and on the last stage slightly. The relation between ${\sigma}_r$, and log N appeared linear behavior except the early part of cycle ratio $N/N_f$. The average gradient of ${\sigma}_r$, with respect to log N seemed to take a constant value without initial cycle ratio. On the other hand, the $N_f$ line was regressed by the first-order polynomial equation on ${\sigma}_r-log\;N_f$ diagram. Therefore, this study showed that both the gradient of ${\sigma}_r$, with respect to log N and the $N_f$ line was useful in predicting the cycle ratio $N/N_f$.

• Journal of Communications and Networks
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• 제14권2호
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• pp.213-221
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• 2012

The architecture of an interconnection network is usually represented by a graph, and a graph G is bipancyclic if it contains a cycle for every even length from 4 to ${\mid}V(G){\mid}$. In this article, we analyze the conditional edge-fault-tolerant properties of an enhanced hypercube, which is an attractive variant of a hypercube that can be obtained by adding some complementary edges. For any n-dimensional enhanced hypercube with at most (2n-3) faulty edges in which each vertex is incident with at least two fault-free edges, we showed that there exists a fault-free cycle for every even length from 4 to $2^n$ when n($n{\geq}3$) and k have the same parity. We also show that a fault-free cycle for every odd length exists from n-k+2 to $2^n-1$ when n($n{\geq}2$) and k have the different parity.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.9-17
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• 2016

In this paper, it has been shown that the hairy cycle C_n ⊙ rK₁, n ≡ 3(mod4), the graph obtained by adding pendant edge to each pendant vertex of hairy cycle C_n ⊙ 1K₁, n ≡ 0(mod4), double graph of path P_n and double graph of comb P_n ⊙ 1K₁ are k-graceful.

• 융합신호처리학회논문지
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• 제12권4호
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• pp.355-361
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• 2011

기존 발열체의 전력제어는 On-Off 제어, 위상제어, PWM 제어를 사용해왔다. 최근 개발된 PTC 발열체를 기존의 방법으로 전력제어를 하였을 경우, 온도를 정밀하게 제어하지 못하고 인체에 유해한 전자파가 발생한다. 본 논문은 AC Cycles 가변을 이용한 PTC 열선의 전력 제어를 제안한다. 이것은 N개의 교류 cycle을 전력 제어의 단위로 간주하여, 각 cycle 마다 On-Off 여부를 결정하여 N cycles 내의 on-cycle 을 랜덤하게 배치하여 지속적으로 AC전력제어방법이다. 이 때 최소 전력량은 1/N이 되고 최대 전력량은 1이 되며 설정 값에 따라 on cycle의 수를 설정하여 N개의 단계로 일정하게 전력을 제어할 수 있다. PTC 열선과 온도센서를 사용한 발열 시스템에서 제안한 전력제어 방식이 전자파 발생과 온도제어 특성에서 우수함을 MATLAB simulation과 실험 및 측정을 통하여 확인하였다.

• 한국세라믹학회지
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• 제48권5호
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• pp.342-347
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• 2011

Nanocrystalline TiN films were deposited on Si(100) substrate using asymmetric pulsed DC reactive magnetron sputtering. We investigated the growing behavior and the structural properties of TiN films with change of duty cycle and pulsed frequency. Grain size of TiN films were decreased from 87.2 nm to 9.8 nm with decrease of duty cycle. The $2{\theta}$ values for (111) and (200) crystallographic planes of the TiN films were also decreased with decrease of duty cycle. This shift in $2{\theta}$ could be attributed to compressive stress in the TiN coatings. Thus, the change of plasma parameter has a strong influence not only on the microstructure but also on the residual stresses of TiN films.

• 한국재료학회지
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• 제8권5호
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• pp.377-382
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• 1998

Ti[N ($C_{2}$$H_{5}$ $CH_{3}$)$_{2}$]$_{4}$ [tetrakis(ethylmethylammino)titanium.TEMAT]와 $NH_{3}$를 반응가스로 하여 각각 펄스(pulse) 형태로 시분할 주입되는 새로운 박막 증착방법(이하 Cycle-CVD라 함)을 이용하여 TiN박막이 $SiO_2$.기판위에 증착되었다.Cycle-CVD에서 반을로 내로 주입되는 반응가스와 Ar가스는 TEAM 펄스, Ar 펄스,$NH_{3}$펄스, Ar 펄스의 순서로 시분할주입되었고, 이렇게 차례대로 주입되는 4개의 펄스를 하나의 cycle로 규정하고, Cycle-CVD는 이러한 cycle이 연속하여 반복적으로 주입되도록 설계되었다. 기판온도가 $170^{\circ}C$-$210^{\circ}C$에서는 atomic layer deposition(ALD)특성을 보였고, $200^{\circ}C$에서 충분한 반응가스의 펄스시간 후에 cycle당 증착된 박막의 두께가 0.6nm/cycle로 포화되는 양상을 보여주었는데, 이는 cycle당 증착된 TiN 박막의 두께가 1.6 monolayer(ML)/cycle에 해당된다. 이와 같이 반등가스의 흡착을 이용ㅇ하여 TiN이 제한된 표면반응만에 의하여 ALD 기구에 의해 증착이 이루어지므로 TiN 박막의 두께는 단지 cycle 횟수만으로 정확하게 제어할 수 있었고, 우수한 step coverage 특성을 얻었다. 또한 반응가스간의 기상반응을 방지함으로써 입자의 발생을 억제할 수 있었고, 상대적으로 낮은 온도임에도 불구하고 4at% 이하의 낮은 탄소함량을 갖는 양호한 특성을 보여주었다.

• International Journal of Precision Engineering and Manufacturing
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• 제3권2호
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• pp.78-86
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• 2002

In general, X-ray diffraction method detects the changes of crystal lattice under material surface using the angle of diffraction 2$\theta$. This technique which deals with in the presented paper can be applied to a behavior on the slipped band or the micro crack cause to material degradation. The relation between half-value breadth and cycle numbers shows three stages, which consist of rapid decrease in the initial cycle, slight decrease in the middle cycle, and then rapid decrease in the final cycle. The ratio of half-value breadth has a constant value on B/B$\_$0/ - N diagram under the loading condition except early part of fatigue life. The ratio of half-value breadth B/B$\_$0/ - log N$\_$f/ with respect to number of cycle to failure N$\_$f/ has linear behavior on B/B$\_$0/ - log N$\_$f/ diagram. Therefore, the evaluation of fatigue life by the average gradient has much less mean error than the estimation of fatigue life by log B/B$\_$0/ - log N/N$\_$f/ relation.

• 한국표면공학회지
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• 제35권6호
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• pp.408-414
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• 2002

TiN and TiAlN coating layer were deposited on WC-Co steel substrates by an arc ion plating(AIP) technique. The crystallinity and morphology for the deposited coating layers were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The impact behaviors of the deposited TiN and TiAlN coating layer were investigated with a ball-on-plate impact tester. Beyond $10^2$ impact cycle, TiAlN coating layer showed superior impact wear resistance compared to TiN coating layer. On the other hand, both TiN and TiAlN coating layers started to be partially failed between $10^2$ and $10^3$ impact cycle. Above $10^3$ impact cycle, TiN and TiAlN coating layers showed similar impact behavior because of the substrate effect.