• 한국IT서비스학회지
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• 제7권4호
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• pp.221-230
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• 2008

Green's relations are five equivalence relations that characterize the elements of a semigroup in terms of the principal ideals. The J relation is one of Green's relations. Although there are known algorithms that can compute Green relations, they are not useful for finding all J relations in the semigroup of all $n{\times}n$ Boolean matrices. Its computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices. The size of the semigroup of all $n{\times}n$ Boolean matrices grows exponentially as n increases. It is easy to see that it involves exponential time complexity. The computation of J relations over the $5{\times}5$ Boolean matrix is left an unsolved problem. The paper shows theorems that can reduce the computation time, discusses an algorithm for efficient J relation computation whose design reflects those theorems and gives its execution results.

• 한국IT서비스학회지
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• 제9권4호
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• 대한수학회보
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• 제49권5호
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• pp.1015-1025
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• 2012

Let $[n]=\{1,2,{\cdots},n\}$, and let $PO_n$ be the partial order-preserving transformation semigroup on [n]. Let $$CPO_n=\{{\alpha}{\in}PO_n:({\forall}x,y{\in}dom{\alpha}),\;|x{\alpha}-y{\alpha}|{\leq}|x-y|\}$$ Then $CPO_n$ is a subsemigroup of $PO_n$. In this paper, we characterize Green's relations and the regularity of elements for $CPO_n$.

• Industrial Engineering and Management Systems
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• 제13권1호
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• pp.15-28
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• 2014

Evaluation of the implementation and performance of a firm's green supply chain management (GSCM) is an ongoing process. Balanced scorecard is a multi-criteria evaluation concept that highlights implementation and performance measures. The literature on the framework is abundant literature but scarce on how to build a hierarchical framework under uncertainty with dependence relations. Hence, this study proposes a hybrid approach, which includes applied interpretive structural modeling to build a hierarchical structure and uses the analytic network process to analyze the dependence relations. Additionally, this study applies the fuzzy set theory to determine linguistic preferences. Twenty dependence criteria are evaluated for a GSCM implemented firm in Taiwan. The result shows that the financial aspect and life cycle assessment are the most important performance and weighted criteria.

• 대한수학회지
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• 제48권2호
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• pp.289-300
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• 2011

Let T(X) denote the semigroup (under composition) of transformations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = {${\alpha}\;{\in}\;T(X)\;:\;Y\;{\alpha}\;{\subseteq}\;Y$}. Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S($A^1$, A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.

• 대한수학회보
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• 제61권1호
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• Nutrition Research and Practice
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• 제10권1호
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• pp.108-114
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• 2016

BACKGROUND/OBJECTIVES: Sustainable practices in foodservice organizations including commercial and noncommercial ones are critical to ensure the protection of the environment for the future. With the rapid growth of the foodservice industry, wiser usage of input sources such as food, utilities, and single use packaging should be reconsidered for future generations. Therefore, this study aims to investigate the customer's perceptions on sustainable practices and to identify the relationship among sustainable practices, social contribution and purchase intention. SUBJECTS/METHODS: The study was conducted using content analyses by reviewing articles on sustainable food service practices published domestically and abroad. Thereafter, data were collected with a face-to-face survey using a questionnaire and analyzed with factor analyses and multiple regressions. RESULTS: Sustainable practices classified with factor analysis consisted of 6 dimensions of green food material procurement, sustainable food preparation, green packaging, preservation of energy, waste management, and public relations on green activity, with a total of 25 green activities in foodservice operations. Consumers were not very familiar with the green activities implemented in the foodservice unit, with the lowest awareness of "green food material procurement (2.46 out of 5 points)", and the highest awareness of "green packaging (3.74)" and "waste management (3.28). The factors influencing the perception of social contribution by foodservice organizations among 6 sustainable practice dimensions were found to be public relations on green activity (${\beta}=0.154$), waste management (${\beta}=0.204$) and sustainable food preparation (${\beta}=0.183$). Green packaging (${\beta}=0.107$) and the social contribution of the foodservice organization (${\beta}=0.761$) had strong relationships with the image of the organization. The purchase intentions of customers was affected only by the foodservice image (${\beta}=0.775$). CONCLUSIONS: The results of this study suggest that sustainable practices by foodservice organization present a good image to customers and increase the awareness of valuable contributions that benefit the customer as well as the community.

• 호남수학학술지
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• 제41권3호
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• pp.505-514
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• 2019

In this paper, some results are obtained from studying convolution on the spectrum of full transformation semigroup and some of its subsemigroups using Cayley's table. The shift of ${\alpha}$ determines its eigenvalues and one-dimensional linear convolution is complex in Symmetric group.

• 한국의류학회지
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• 제23권2호
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• pp.296-306
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• 1999

This study reflects the aim of analyzing the fashion design connection with ecology. Ecology has been linked to human life through its changing relations with environment. In order to recover eco-system ecology-nature oriented methodology and technology oriented approach will suffice. On the modern design field Green design Recycling and Green marketing resulted in increasing rates of environment-friendly production and an effort to deliver environment-friendly corporate image. Based on above research ecological image on fashion design during the year 1990 to 1995 represents the following conclusion. In the fashion design field natural image primitive image nature -harmonious image material-recyling image culture-recycling image are proposed. In the technology field clean image and high-tech image are proposed. In the marketing field happy image harmonious image serious image and realistic image are proposed.

• 한국콘텐츠학회논문지
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• 제7권1호
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• pp.124-130
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• 2007

네모 동축선은 동축선과 도파관을 연결하는 대표적인 천이구조이다. 또한 TEM 셀은 DUT의 EMC 측정을 위해 광범위하게 사용되는 소자이다. 네모 동축선과 TEM 셀의 동작을 정확히 예측하기 위해서는 네모 동축선과 TEM 셀의 분산관계 해석이 필수적이다. 본 논문에서는 TEM 모드에 대한 분석을 기반으로 고차 모드인 TE와 TM 모드에 대한 분산관계를 단순하면서도 정확한 방법을 이용해 유도한다. 모드정합법과 그린 함수를 이용하여 네모 동축선과 TEM 셀의 분산관계를 해석적으로 정확히 다룬다. 이를 위해 네모 동축선의 구조를 4개의 L블록으로 나누고 중첩의 원리를 사용하여 전체 전자장 표현식을 쉽게 구한다. 분산관계 수렴성을 파악하기 위해 수치해석을 행하고 FDTD 결과와 비교한다.