• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1753-1763
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• 2013

In this paper, we show that tree products of certain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.601-631
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• 2010

In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalar-valued $W^*$-probability on a given graph von Neumann algebra. We show that a diagonal graph $W^*$-probability space (as a scalar-valued $W^*$-probability space) and a graph W¤-probability space (as an amalgamated $W^*$-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility, we observe the scalar-valued freeness on a graph von Neumann algebra.

• The Mathematical Education
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• v.51 no.3
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• pp.197-210
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• 2012

In this study, we will develop and implement the teaching program of 'Function', on the subject of "Poster-Making utilizing the Graph Art" in the Math Camp for middle-school students. And we will examine the didactical significance through student's activities and products. The teaching program of 'Function' utilizing the Graph Art can be promoted self-directly the understanding of 'Function' concept and the ability for handling 'Function'. In the process of drawing up the graph art, in particular, this program help students to promote the ability for problem-solving and mathematical thinking, and to communicate mathematically and attain the his own level. Ultimately, this program have a positive influence upon cognitive and affective and areas with regard to mathematics.

• Journal of Internet Computing and Services
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• v.25 no.1
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• pp.69-78
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• 2024

Recently, consumers have shown an increasing tendency to seek information related to environmental, social, and governance (ESG) aspects in order to choose products with higher social value and environmental friendliness. In this paper, we proposes a product recommendation system applying ESG indicators tailored to the recent consumer trend of value-based consumption, utilizing a model called MultiSAGE that combines GraphSAGE and GAT. To achieve this, ESG rating data for 1,033 companies in 2022 collected from the Korea ESG Standard Institute and actual product data from N companies were transformed into a Heterogeneous Graph format through a data processing pipeline. The MultiSAGE model was then applied in machine learning to implement a recommendation system that, given a specific product, suggests eco-friendly alternatives. The implementation results indicate that consumers can easily compare and purchase products with ESG indicators applied, and it is anticipated that this system will be utilized in recommending products with social value and environmental friendliness.

• Industrial Engineering and Management Systems
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• v.2 no.1
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• pp.35-44
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• 2003

Recovery of end-of-life (EOL) products is an environmentally and economically sound way to achieve many of the goals of sustainable development. Many product recovery systems are dependent upon destructive disassembly such as shredding, which undesirably causes a large volume of shredder dust and makes parts reuse impossible. Although non-destructive disassembly has been considered as an alternative for solving the problems, the classification of disassembled items has not been sufficiently investigated. In this paper, we propose a model that mathematically optimizes the disassembly and classification of EOL products. Based on the AND/OR graph that illustrates all possible disassembly sequences of a given product, we identify the physical properties that are considered as constraints in the model. As a result of the solution procedure, the recovery problem can be transformed into a mixed integer linear programming (MILP) model. We show an example that illustrates the concept of our model.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1045-1056
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• 2020

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, $^{\bar{\mathbb{AG}}}$(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n, m ∈ ℕ such that IⁿJ^m = (0) with Iⁿ, J^m ≠ (0). First, we differentiate when 𝔸𝔾(R) and $^{\bar{\mathbb{AG}}}$(R) coincide. Then, we have characterized the diameter and the girth of $^{\bar{\mathbb{AG}}}$(R) when R is a finite direct products of rings. Moreover, we show that $^{\bar{\mathbb{AG}}}$(R) contains a cycle, if $^{\bar{\mathbb{AG}}}$(R) ≠ 𝔸𝔾(R).

• Korean Journal of Community Nutrition
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• v.8 no.2
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• pp.220-230
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• 2003

The purpose of this study was to investigate consumer preferred formats of nutrition labels: the type of nutritional information provided on the labels. A survey was conducted on 222 housewives between the age of 20 and 65 in Daejeon city in 1998, using an interview questionnaire showing illustrated nutritional label formats. Among twelve nutrients and caloric values listed on the nutrition labels, the housewives ranked their interest in the items in the following order of calorie (58.56%), calcium (56.76%), cholesterol (54.05%), protein (39.19%) and vitamin C (36.04%). The majority of the subjects (69.37%) checked labels when they bought milk or dairy products, whereas only 8.11% looked at labels when they bought Ramyon or noodles. Most of the subjects (90.99%) preferred products with labels with nutritional information as compared with products without labels. this was especially so true of the younger individuals and of pc-ople who checked food labels more frequently. The subjects preferred labeling which described the nutrient content per Package (55.41%), sewing size (32.88%) and food weight of 1009 (11.71%) as a standard nit. Generally, they prefer-red a simplified list to a detailed list of the number of nutrients, a figure graph to bar graph in nutrition claim, vertical bar graph to horizontal bar graph showing the nutritional content of foods and a web-type graphic format to a radiation-format when describing the item's percentage of the Korean RDA's nutrient content. The subjects who checked labels frequently especially preferred detailed list, while housewives with job or with unhealthy family members preferred a simplified list and graphic, rather than a numerical display. From this result, it is suggested that providing consumers with more nutrients information in a more easily understood graphic format would encourage the consumers to check nutritional labels. Therefore this should be considered when developing the regulations far nutrition labeling or when educating the Public about nutrition. (Korean J Community Nutrition 8(2) : 220∼230, 2003)

• Journal of Information Technology Services
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• v.22 no.1
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• pp.43-56
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• 2023

With the development of the e-commerce market, various types of products continue to be released. However, customers face an information overload problem in purchasing decision-making. Therefore, personalized recommendations have become an essential service in providing personalized products to customers. Recently, many studies on GCN-based recommender systems have been actively conducted. Such a methodology can address the limitation in disabling to effectively reflect the interaction between customer and product in the embedding process. However, previous studies mainly use implicit feedback data to conduct experiments. Although implicit feedback data improves the data scarcity problem, it cannot represent customers' preferences for specific products. Therefore, this study proposed a novel model combining explicit and implicit feedback to address such a limitation. This study treats the average ratings of customers and products as the features of customers and products and converts them into a high-dimensional feature vector. Then, this study combines ID embedding vectors and feature vectors in the embedding layer to learn the customer-product interaction effectively. To evaluate recommendation performance, this study used the MovieLens dataset to conduct various experiments. Experimental results showed the proposed model outperforms the state-of-the-art. Therefore, the proposed model in this study can provide an enhanced recommendation service for customers to address the information overload problem.