• Title/Summary/Keyword: $V^s_{\delta}$-sets

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Maximum Degree Vertex-Based Algorithm for Maximum Clique Problem (최대 클릭 문제에 관한 최대차수 정점 기반 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.1
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    • pp.227-235
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    • 2015

  • In this paper, I propose a linear time algorithm devised to produce exact solution to NP-complete maximum clique problem. The proposed algorithm firstly, from a given graph G=(V,E), sets vertex $v_i$ of the maximum degree ${\Delta}(G)$ as clique's major vertex. It then selects vertex $v_j$ of ${\Delta}(G)$ among vertices $N_G(v_i)$ that are adjacent to $v_i$, only to determine $N_G(v_i){\cap}N_G(v_j)$ as candidate cliques w and $v_k$. Next it obtains $w=w{\cap}N_G(v_k)$ by sorting $d_G(v_k)$ in the descending order. Lastly, the algorithm executes the same procedure on $G{\backslash}w$ graph to compare newly attained cliques to previously attained cliques so as to choose the lower. With this simple method, multiple independent cliques would also be attainable. When applied to various regular and irregular graphs, the algorithm proposed in this paper has obtained exact solutions to all the given graphs linear time O(n).

  • https://doi.org/10.9708/jksci.2015.20.1.227 인용 PDF KSCI

ON FUZZY 𝛽-VOLTERRA SPACES

  • V. CHANDIRAN;S. SOUNDARA RAJAN;G. THANGARAJ
    • Journal of applied mathematics & informatics
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    • v.42 no.1
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    • pp.189-197
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    • 2024

  • The purpose of this paper is to introduce and study the new class of spaces called the fuzzy 𝛽-Volterra spaces with the help of fuzzy β-dense and fuzzy 𝛽-G𝛿 sets. Examples are given to illustrate the concept. Some interesting characterizations of the fuzzy 𝛽-Volterra spaces are established in this paper.

  • https://doi.org/10.14317/jami.2024.189 인용 PDF

Size-resolved Source Apportionment of Ambient Particles by Positive Matrix Factorization at Gosan, Jeju Island during ACE-Asia (PMF 분석을 이용한 ACE-Asia 측정기간 중 제주 고산지역 입자상 물질의 입경별 발생원 추정)

  • Moon K.J.;Han, J.S.;Kong, B.J.;Jung, I.R.;Cliff Steven S.;Cahill Thomas A.;Perry Kelvin D.
    • Journal of Korean Society for Atmospheric Environment
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    • v.22 no.5
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    • pp.590-603
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    • 2006

  • Size-and time-resolved aerosol samples were collected using an eight-stage Davis rotating unit for monitoring (DRUM) sampler from 23 March to 29 April 2001 at Gosan, Jeju Island, Korea, which is one of the super sites of Asia-Pacific Regional Aerosol Characterization Experiment(ACE-Asia). These samples were analyzed using synchrotron X-ray fluorescence for 3-hr average concentrations of 19 elements including Al, Si, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As, Se, Br, Rb, and Pb. The size-resolved data sets were then analyzed using the positive matrix factorization(PMF) technique to identify possible sources and estimate their contributions to particulate matter mass. PMF analysis uses the uncertainty of the measured data to provide an optimal weighting. Twelve sources were resolved in eight size ranges($0.09{\sim}12{\mu}m$) and included continental soil, local soil, sea salt, biomass/biofuel burning, coal combustion, oil combustion, municipal incineration, nonferrous metal source, ferrous metal source, gasoline vehicle, diesel vehicle, and volcanic emission. The PMF result of size-resolved source contributions showed that natural sources represented by local soil, sea salt, continental soil, and volcanic emission contributed about 79% to the predicted primary particulate matter(PM) mass in the coarse size range ($1.15{\sim}12{\mu}m$) while anthropogenic sources such as coal combustion and biomass/biofuel burning contributed about 58% in the fine size range($0.56{\sim}2.5{\mu}m$). The diesel vehicle source contributed mostly in ultra-fine size range($0.09{\sim}0.56{\mu}m$) and was responsible for about 56% of the primary PM mass.

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The Impact of Market Environments on Optimal Channel Strategy Involving an Internet Channel: A Game Theoretic Approach (시장 환경이 인터넷 경로를 포함한 다중 경로 관리에 미치는 영향에 관한 연구: 게임 이론적 접근방법)

  • Yoo, Weon-Sang
    • Journal of Distribution Research
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    • v.16 no.2
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    • pp.119-138
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    • 2011

  • Internet commerce has been growing at a rapid pace for the last decade. Many firms try to reach wider consumer markets by adding the Internet channel to the existing traditional channels. Despite the various benefits of the Internet channel, a significant number of firms failed in managing the new type of channel. Previous studies could not cleary explain these conflicting results associated with the Internet channel. One of the major reasons is most of the previous studies conducted analyses under a specific market condition and claimed that as the impact of Internet channel introduction. Therefore, their results are strongly influenced by the specific market settings. However, firms face various market conditions in the real worlddensity and disutility of using the Internet. The purpose of this study is to investigate the impact of various market environments on a firm's optimal channel strategy by employing a flexible game theory model. We capture various market conditions with consumer density and disutility of using the Internet.

    shows the channel structures analyzed in this study. Before the Internet channel is introduced, a monopoly manufacturer sells its products through an independent physical store. From this structure, the manufacturer could introduce its own Internet channel (MI). The independent physical store could also introduce its own Internet channel and coordinate it with the existing physical store (RI). An independent Internet retailer such as Amazon could enter this market (II). In this case, two types of independent retailers compete with each other. In this model, consumers are uniformly distributed on the two dimensional space. Consumer heterogeneity is captured by a consumer's geographical location (ci) and his disutility of using the Internet channel (${\delta}_{N_i}$).
    shows various market conditions captured by the two consumer heterogeneities.
    (a) illustrates a market with symmetric consumer distributions. The model captures explicitly the asymmetric distributions of consumer disutility in a market as well. In a market like that is represented in
    (c), the average consumer disutility of using an Internet store is relatively smaller than that of using a physical store. For example, this case represents the market in which 1) the product is suitable for Internet transactions (e.g., books) or 2) the level of E-Commerce readiness is high such as in Denmark or Finland. On the other hand, the average consumer disutility when using an Internet store is relatively greater than that of using a physical store in a market like (b). Countries like Ukraine and Bulgaria, or the market for "experience goods" such as shoes, could be examples of this market condition. summarizes the various scenarios of consumer distributions analyzed in this study. The range for disutility of using the Internet (${\delta}_{N_i}$) is held constant, while the range of consumer distribution (${\chi}_i$) varies from -25 to 25, from -50 to 50, from -100 to 100, from -150 to 150, and from -200 to 200.
    summarizes the analysis results. As the average travel cost in a market decreases while the average disutility of Internet use remains the same, average retail price, total quantity sold, physical store profit, monopoly manufacturer profit, and thus, total channel profit increase. On the other hand, the quantity sold through the Internet and the profit of the Internet store decrease with a decreasing average travel cost relative to the average disutility of Internet use. We find that a channel that has an advantage over the other kind of channel serves a larger portion of the market. In a market with a high average travel cost, in which the Internet store has a relative advantage over the physical store, for example, the Internet store becomes a mass-retailer serving a larger portion of the market. This result implies that the Internet becomes a more significant distribution channel in those markets characterized by greater geographical dispersion of buyers, or as consumers become more proficient in Internet usage. The results indicate that the degree of price discrimination also varies depending on the distribution of consumer disutility in a market. The manufacturer in a market in which the average travel cost is higher than the average disutility of using the Internet has a stronger incentive for price discrimination than the manufacturer in a market where the average travel cost is relatively lower. We also find that the manufacturer has a stronger incentive to maintain a high price level when the average travel cost in a market is relatively low. Additionally, the retail competition effect due to Internet channel introduction strengthens as average travel cost in a market decreases. This result indicates that a manufacturer's channel power relative to that of the independent physical retailer becomes stronger with a decreasing average travel cost. This implication is counter-intuitive, because it is widely believed that the negative impact of Internet channel introduction on a competing physical retailer is more significant in a market like Russia, where consumers are more geographically dispersed, than in a market like Hong Kong, that has a condensed geographic distribution of consumers.
    illustrates how this happens. When mangers consider the overall impact of the Internet channel, however, they should consider not only channel power, but also sales volume. When both are considered, the introduction of the Internet channel is revealed as more harmful to a physical retailer in Russia than one in Hong Kong, because the sales volume decrease for a physical store due to Internet channel competition is much greater in Russia than in Hong Kong. The results show that manufacturer is always better off with any type of Internet store introduction. The independent physical store benefits from opening its own Internet store when the average travel cost is higher relative to the disutility of using the Internet. Under an opposite market condition, however, the independent physical retailer could be worse off when it opens its own Internet outlet and coordinates both outlets (RI). This is because the low average travel cost significantly reduces the channel power of the independent physical retailer, further aggravating the already weak channel power caused by myopic inter-channel price coordination. The results implies that channel members and policy makers should explicitly consider the factors determining the relative distributions of both kinds of consumer disutility, when they make a channel decision involving an Internet channel. These factors include the suitability of a product for Internet shopping, the level of E-Commerce readiness of a market, and the degree of geographic dispersion of consumers in a market. Despite the academic contributions and managerial implications, this study is limited in the following ways. First, a series of numerical analyses were conducted to derive equilibrium solutions due to the complex forms of demand functions. In the process, we set up V=100, ${\lambda}$=1, and ${\beta}$=0.01. Future research may change this parameter value set to check the generalizability of this study. Second, the five different scenarios for market conditions were analyzed. Future research could try different sets of parameter ranges. Finally, the model setting allows only one monopoly manufacturer in the market. Accommodating competing multiple manufacturers (brands) would generate more realistic results.

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