• Journal of Information Technology Services
• /
• v.7 no.4
• /
• pp.221-230
• /
• 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.

• Journal of Information Technology Services
• /
• v.9 no.4
• /
• pp.219-229
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1015-1025
• /
• 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
• /
• v.13 no.1
• /
• pp.15-28
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.289-300
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.117-133
• /
• 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
• /
• v.10 no.1
• /
• pp.108-114
• /
• 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.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.505-514
• /
• 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.

• Journal of the Korean Society of Clothing and Textiles
• /
• v.23 no.2
• /
• pp.296-306
• /
• 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.

• The Journal of the Korea Contents Association
• /
• v.7 no.1
• /
• pp.124-130
• /
• 2007

A rectangular coaxial line is mainly utilized as a transition structure from a coaxial line to a rectangular waveguide. A TEM cell is also widely used to measure the EMC characteristics of a DUT. In order to understand the operations of a rectangular coaxial line and a TEM cell, it is essential to analyze the dispersion relations of a rectangular coaxial line and a TEM cell. In this paper, we present simple yet accurate dispersion relations of the TE and TM higher modes based on the TEM mode. Manipulating a mode-matching technique and a Green's function approach allows us to obtain the analytic dispersion equations of a rectangular coaxial line and a TEM cell. In our approach, a rectangular coaxial line is divided into four L-blocks and its electromagnetic fields representations are easily obtained with a superposition. To verify the convergence of our dispersion relations, we perform numerical computations and compare our results with those of FDTD.