• Korean Journal of Mathematics
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• v.27 no.2
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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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• v.3 no.4
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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.

• Journal of Ocean Engineering and Technology
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• v.13 no.4 s.35
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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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• v.14 no.2
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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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• v.34 no.1_2
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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.

• Journal of the Institute of Convergence Signal Processing
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• v.12 no.4
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• pp.355-361
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• 2011

The power control of the existing heating element has been using the On-Off control, phase control, and PWM control. In case of controlling power PTC heating element developed recently with the existing method, the temperature is unable to be precisely controlled or the harmful electromagnetic wave to human body is generated. In this paper, We suggest the power control of PTC heating cable using variable AC Cycles. This regards the AC cycle of N as the unit of the power control. It determines On-Off for each cycle. It is the AC power control method in which it arranges the on-cycle in N cycles in the random and it supplies the current continuously. At this time. the minimal electric power amount becomes 1/N. The maximum current amount becomes 1 and sets up the number of on cycles according to the set value and can control the electric power with the step of N consistently. In the PTC heating system, we show that proposed power control method is superior in the EMI and temperature control property using MATLAB simulation, experiments and measurements.

• Journal of the Korean Ceramic Society
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• v.48 no.5
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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.

• Korean Journal of Materials Research
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• v.8 no.5
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• pp.377-382
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• 1998

Atomic layer deposition(ALD) of amorphous TiN films on $SiO_2$ between 17$0^{\circ}C$ and 21O$^{\circ}C$ has been investigated by alternate supply of reactant sources, Ti[N($C_2,H_5,CH_3)_2]_4$ [tetrakis(ethylmethylamminoltitanium: TEMAT] and $NH_3$. Reactant sources were injected into the reactor in the order of TEMAT vapor pulse, Ar gas pulse, $NH_3$. gas pulse and Ar gas pulse. Film thickness per cycle was saturated at around 1.6 monolayer(MU per cycle with sufficient pulse times of reactant sources at 20$0^{\circ}C$. The results suggest that film thickness per cycle could be beyond 1 MLicycie in ALD, which were explained by rechemisorption mechanisms of reactant sources. The ideal linear relationship be¬tween number of cycles and film thickness is confirmed. As a results of surface limited reactions of ALD, step cover¬age was excellent. Particles caused by the gas phase reactions between TEMAT and NH3 were almost free because TEMAT was seperated from $NH_3$ by the Ar pulse. In spite of relatively low substrate temperature, carbon impurity was incorporated below 4 at%.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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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.

• Journal of the Korean institute of surface engineering
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• v.35 no.6
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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.