• Advances in nano research
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• 제9권2호
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• pp.91-104
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• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.39-48
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• 2006

Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.

• 한국인터넷방송통신학회논문지
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• 제19권3호
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• pp.193-199
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• 2019

본 논문은 지금까지 NP-완전인 난제로 알려진 최대 독립집합(MIS) 문제를 선형시간 복잡도로 해결한 알고리즘을 제안하였다. 제안된 알고리즘은 "MIS 집합의 모든 정점들은 상호간에 연결되지 않는다"는 기본 성질을 적용하여 n개의 정점으로 구성된 그래프에서 최소 차수 ${\delta}(G)$ 정점 ${\nu}$를 선택하고 부속 간선을 제거하였을 때 차수가 변하지 않는 정점들을 차수 오름차순으로 계속적으로 선택하는 단순한 방법을 적용하였다. 제안된 알고리즘을 22개 그래프에 적용한 결과, 시각적으로 그래프를 보면서도 MIS를 쉽게 찾을 수 있는 장점을 갖고 있으며, 알고리즘은 항상 MIS 집합의 원소 개수인 ${\alpha}(G)$회를 수행하여 알고리즘 복잡도는 O(n)으로 선형 알고리즘이다. 결국, 제안된 MIS 알고리즘은 MIS의 최적 해를 도출하는 일반적인 알고리즘으로 적용할 수 있을 것이다.

• 대한수학회지
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• 제54권4호
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• Journal of Communications and Networks
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• 제16권4호
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• pp.371-377
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• 2014

Localized topology control is attractive for obtaining reduced network graphs with desirable features such as sparser connectivity and reduced transmit powers. In this paper, we focus on studying how to prolong network lifetime in the context of localized topology control for wireless multi-hop networks. For this purpose, we propose an energy efficient localized topology control algorithm. In our algorithm, each node is required to maintain its one-hop neighborhood topology. In order to achieve long network lifetime, we introduce a new metric for characterizing the energy criticality status of each link in the network. Each node independently builds a local energy-efficient spanning tree for finding a reduced neighbor set while maximally avoiding using energy-critical links in its neighborhood for the local spanning tree construction. We present the detailed design description of our algorithm. The computational complexity of the proposed algorithm is deduced to be O(mlog n), where m and n represent the number of links and nodes in a node's one-hop neighborhood, respectively. Simulation results show that our algorithm significantly outperforms existing work in terms of network lifetime.

• Nuclear Engineering and Technology
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• 제29권1호
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• pp.35-44
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• 1997

Critical too-Phase flow rates of subcooled water through Short Pipes (L 140039n) with small diameters (D$\leq$7.15 min) have been experimentally investigated for wide ranges of subcooling (0~199$^{\circ}C$) and pressure (0.5~2.0 MPa). To examine the effects of various parameters (i.e., the location of flashing inception, the degree of subcooling, the stagnation temperature and pressure, and the pipe size) on the critical two-phase flow rates of subcooled water through short pipes with small diameters, a total of 135 runs were made for various combinations of test parameters using four different L/D test sections. Experimental results that show effect of various parameters on subcooled critical two phase flow rates are presented in the form of graphs such as the dimensionless mass flux ( $G^{*}$) versus the dimensionless subcooling ( $T_{sub}$$^{*}$) curve. An empirical correlation expressed in terms of a dimensionless subcooling is also obtained for subcooled two-phase flow rates through present test sections. Comparisons between the mass fluxes calculated by present correlation and a total of 755 selected experimental data points of 9 different investigators show that the agreement is fairly good except for very low subcooling data obtained from small L/D (less than 10) orifices.s.s.s.

• 설비공학논문집
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• 제3권2호
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• pp.142-151
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• 1991

In the present investigation, it has been proposed to utilize a direct contact heat exchanger as an evaporator to solve the difficulties such as scaling, corrosion and law thermal efficiencies, associated with the conventional evaporator. Liquified nitrozen was utilized as a working fluid to investigate basic natures of bubble dynamics in the evaporator, and spray nozzles were adopted to inject liquified nitrozen into the spray column with varying flow rates of dispersed phase fluids. Experimentations were carried out in the range of $6.54{\times}10^{-4}kg/s$ - 0.030 kg/s for dispersed phase flow rates with one, three and five nozzle holes. Observing the bubble dynamics for the evaporator the feasibility of utilizing a direct contact heat exchanger as a LNG evaporator has been evaluated. The results show that no eruption phenomena was observed in the present investigation with $LN_2$ and the interface between $N_2$ bubbles and water was fully turbulent. It is believed that the high injection velocity of $LN_2$ through the spray nozzles provide good mixing effects for both heat and mass transfers between water and $N_2$ bubbles. Ice was formed on the surface of the spray nozzle for higher $LN_2$ flow rates. However, even in this case, it is observed that the ice was detached as soon as it was formed. Under the present experimental conditions, the shapes of $LN_2$ bubbles were in the spherical-cap region according to the Clift, Grace and Weber Graphs. The height of foam region caused by the breakup of larger bubbles keeps increasing with high injection velocities until it reaches it's maximum height.

• 한국컴퓨터정보학회논문지
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• 제18권9호
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• pp.121-129
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• 2013

본 논문은 아직까지 정확한 해를 다항시간으로 구하는 알고리즘이 존재하지 않아 NP-완전 문제로 알려진 지배집합 (DS) 문제의 정확한 해를 선형시간으로 구하는 알고리즘을 제안하였다. 제안된 알고리즘은 그래프의 간선이 존재하지 않을 때까지 최소차수 ${\delta}(G)$를 가진 정점 u의 인접정점들 중 최대차수 ${\Delta}(G)$를 가진 정점 v를 최소 독립지배집합(MIDS)의 원소로 포함시키고 v의 부속 간선을 삭제하는 방법을 반복적으로 수행하여 구하였다. MIDS로부터 최소 지배집합 (MDS)으로 변환시키고, MDS로부터 최소연결 DS (MCDS)로 변환시키는 방법으로 DS 관련 모든 문제의 정확한 해를 구할 수 있었다. 제안된 알고리즘을 10개의 다양한 그래프에 적용한 결과 정확한 해를 선형 시간복잡도 O(n)으로 구하는데 성공하였다. 결국, 제안된 지배집합 알고리즘은 지배집합 문제가 P-문제임을 증명하였다.

• 한국통신학회논문지
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• 제17권1호
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• pp.1-10
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• 1992

새로운 정보 통신 서어비스의 출현 및 가입자측에서 이에 대한 욕구가 서로 부합되어 가입자 영역에는 기존의 단말기외에 새로운 형태의 데이터 단말의 수요가 증가되고 있는 추세이다. 이에 따라 전송로의 경제성을 고려하여 SMUX에 대한 연구가 진행되고 있다. 따라서 본 논문에서는 SMUX에 Go-back N ARQ 재전송 방식을 적용하여 queueing 모델을 설정한 후 이에 따른 수학적 해석 방법을 제시하였고, 평균 waiting 시간 및 overflow 확률의 일반식을 산출하였다. SMUX의 설계시에 영향을 미치는 파라미터로서는 입력비율, 출력 비율 및 접속되는 단말기들의 batch 크기로 표현되는 트래픽 밀도나 버퍼가 수용할 수 있는 최대 버퍼 크기에 따른 overflow 확률 및 평균 버퍼 크기, 평균 waiting 시간을 비교,분석하였다. 또한 수학적 해석에 따른 각 파라미터들이 SMUX에 미치는 영향은 평균 메세지 크기는 40characters로 고정하였을 경우 전송 선로상의 에러율이 10­$^3$이하에서 운용되어야 하고, 트래픽 밀도가 낮은 (0.5이하)상태에서 운용이 효울적이라 사료된다. 향후 본 논문에서 제시한 자료를 기초로 하여 SMUX를 설계시에 참고 자료가 되리라 사료된다.

• 대한환경공학회지
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• 제34권8호
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• pp.557-565
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• 2012

본 연구는 초기 강우시 축사주변 지역을 대상으로 강우 유출수와 함께 배출되는 비점오염물질의 특성에 대하여 분석하였다. 강우량에 따른 유출특성 중 수리 수문-농도곡선 분석결과 유량이 증가함에 따라 농도가 점점 증가하는 경향을 보였으며, 첨두 유량이 발생한 후에는 급격히 감소하였다. 축사주변지역에서의 유량평균가중농도(EMCs)는 TSS EMC 146.80~424.95 mg/L, COD EMC 11.64~55.66 mg/L, BOD EMC 6.66~49.88 mg/L, T-N EMC 7.650~43.825 mg/L, T-P EMC 0.711~3.855 mg/L였다. 또한 TSS와 BOD, COD, T-N 그리고 T-P의 오염물질별 상관계수를 분석해보면 0.53~0.95를 나타내었으며, 정량화된 EMCs와 강우 유출량($m^3$) 등 다른 요소들간의 회귀분석을 통한 상관관계를 분석한 결과는 3차 다항식으로 설명되었으며, 물질별 결정계수는 TSS 0.767~0.835, T-N은 0.773~0.901로 비교적 높게 분석되었다, 이는 두 항목간 상관관계가 높다는 것을 의미하며, 강우유출량이 많을수록 EMC가 증가한다는 것을 의미한다. 이는 추후 강우유출량을 모니터링하면 유출량에 따른 유량가중평균농도를 예측할 수 있을 것으로 판단된다.