• The Mathematical Education
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• v.62 no.3
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• pp.435-455
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• 2023

This study primarily focused on the development of an Explainable Artificial Intelligence (XAI) model to discern and analyze papers with significant impact in the field of mathematics education. To achieve this, meta-information from 29 domestic and international mathematics education journals was utilized to construct a comprehensive academic research network in mathematics education. This academic network was built by integrating five sub-networks: 'paper and its citation network', 'paper and author network', 'paper and journal network', 'co-authorship network', and 'author and affiliation network'. The Random Forest machine learning model was employed to evaluate the impact of individual papers within the mathematics education research network. The SHAP, an XAI model, was used to analyze the reasons behind the AI's assessment of impactful papers. Key features identified for determining impactful papers in the field of mathematics education through the XAI included 'paper network PageRank', 'changes in citations per paper', 'total citations', 'changes in the author's h-index', and 'citations per paper of the journal'. It became evident that papers, authors, and journals play significant roles when evaluating individual papers. When analyzing and comparing domestic and international mathematics education research, variations in these discernment patterns were observed. Notably, the significance of 'co-authorship network PageRank' was emphasized in domestic mathematics education research. The XAI model proposed in this study serves as a tool for determining the impact of papers using AI, providing researchers with strategic direction when writing papers. For instance, expanding the paper network, presenting at academic conferences, and activating the author network through co-authorship were identified as major elements enhancing the impact of a paper. Based on these findings, researchers can have a clear understanding of how their work is perceived and evaluated in academia and identify the key factors influencing these evaluations. This study offers a novel approach to evaluating the impact of mathematics education papers using an explainable AI model, traditionally a process that consumed significant time and resources. This approach not only presents a new paradigm that can be applied to evaluations in various academic fields beyond mathematics education but also is expected to substantially enhance the efficiency and effectiveness of research activities.

• Journal of the Korean Institute of Landscape Architecture
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• v.51 no.2
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• pp.1-11
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• 2023

This study intended to develop a technique for quantitatively and 3-dimensionally predicting the potential failure zone and impulse that may occur when trees are fall down. The main outcomes of this study are as follows. First, this study established the potential failure zone and impulse calculation formula in order to quantitatively calculate the risks generated when trees are fallen down. When estimating the potential failure zone, the calculation was performed by magnifying the height of trees by 1.5 times, reflecting the likelihood of trees falling down and slipping. With regard to the slope of a tree, the range of 360° centered on the root collar was set in the case of trees that grow upright and the range of 180° from the inclined direction was set in the case of trees that grow inclined. The angular momentum was calculated by reflecting the rotational motion from the root collar when the trees fell down, and the impulse was calculated by converting it into the linear momentum. Second, the program to calculate a potential failure zone and impulse was developed using Rhino3D and Grasshopper. This study created the 3-dimensional models of the shapes for topography, buildings, and trees using the Rhino3D, thereby connecting them to Grasshopper to construct the spatial information. The algorithm was programmed using the calculation formula in the stage of risk calculation. This calculation considered the information on the trees' growth such as the height, inclination, and weight of trees and the surrounding environment including adjacent trees, damage targets, and analysis ranges. In the stage of risk inquiry, the calculation results were visualized into a three-dimensional model by summarizing them. For instance, the risk degrees were classified into various colors to efficiently determine the dangerous trees and dangerous areas.

• Economic and Environmental Geology
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• v.56 no.3
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• pp.311-330
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• 2023

Development of Carbon Capture and Storage (CCS) technique is becoming increasingly important as a method to mitigate the strengthening effects of global warming, generated from the unprecedented increase in released anthropogenic CO₂. In the recent years, the characteristics of basaltic rocks (i.e., large volume, high reactivity and surplus of cation components) have been recognized to be potentially favorable in facilitation of CCS; based on this, research on utilization of basaltic formations for underground CO₂ storage is currently ongoing in various fields. This study investigated the feasibility of underground storage of CO₂ in basalt, based on the examination of the CO₂ storage mechanisms in subsurface, assessment of basalt characteristics, and review of the global research on basaltic CO₂ storage. The global research examined were classified into experimental/modeling/field demonstration, based on the methods utilized. Experimental conditions used in research demonstrated temperatures ranging from 20 to 250 ℃, pressure ranging from 0.1 to 30 MPa, and the rock-fluid reaction time ranging from several hours to four years. Modeling research on basalt involved construction of models similar to the potential storage sites, with examination of changes in fluid dynamics and geochemical factors before and after CO₂-fluid injection. The investigation demonstrated that basalt has large potential for CO₂ storage, along with capacity for rapid mineralization reactions; these factors lessens the environmental constraints (i.e., temperature, pressure, and geological structures) generally required for CO₂ storage. The success of major field demonstration projects, the CarbFix project and the Wallula project, indicate that basalt is promising geological formation to facilitate CCS. However, usage of basalt as storage formation requires additional conditions which must be carefully considered - mineralization mechanism can vary significantly depending on factors such as the basalt composition and injection zone properties: for instance, precipitation of carbonate and silicate minerals can reduce the injectivity into the formation. In addition, there is a risk of polluting the subsurface environment due to the combination of pressure increase and induced rock-CO₂-fluid reactions upon injection. As dissolution of CO₂ into fluids is required prior to injection, monitoring techniques different from conventional methods are needed. Hence, in order to facilitate efficient and stable underground storage of CO₂ in basalt, it is necessary to select a suitable storage formation, accumulate various database of the field, and conduct systematic research utilizing experiments/modeling/field studies to develop comprehensive understanding of the potential storage site.

• Asia Marketing Journal
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• v.15 no.3
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• pp.117-139
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• 2013

Research on purchase intention had showed remarkable progress in contributing to the theory of consumer behavior. Despite the popularity of academic discussions on various issues influencing purchase intention, the mediating role of brand recall and brand attitude on purchase intention, in particular advergames, has not yet been well explored, especially in developing economies such as Malaysia. Furthermore, the influence of self-brand congruity, entertainment and brand placement acceptance as antecedents to brand recall and brand attitude are expected to add value to the brand recall, brand attitude and purchase intention relationships. This paper aims to investigate the impact of the mediating role of brand recall and brand attitude on purchase intention in advergames among Malaysian gamers. The antecedents towards brand recall and brand attitude are also examined to measure their influence on purchase intention. A total of 350 Malaysian gamers were interviewed through online survey in this study. The results showed that brand recall and brand attitude mediate the relationship between self-brand congruity, entertainment and brand placement acceptance with purchase intention. Also, entertainment and brand placement acceptance were found to have a significant relationship with brand recall. As expected, brand recall and brand attitude showed a positive relationship with consumer purchase intention in advergames. It was found that self-brand congruity has a significant influence on brand attitude and purchase intention. When users see the brand which matches with them, they tend to act positively toward the brand exposed in the game. This is consistent with Escalas and Bettman (2005) who suggested that the greater the congruity, the more positive the consumer's attitude toward the brand in question. This leads to game usage and purchase (Davis and Lang, 2013). In the advergaming context, the entertainment value in advergames is very important to determine the level of enjoyment and pleasure experienced by gamers during game-playing. Therefore, the more entertaining the ads, the more it will be remembered and the greater the positive behavior of the consumer towards the advergames - this ultimately stimulates their intention to purchase the brand. This study shows the effect of brand placement on brand recall and brand attitude and also purchase intention. Brand placements might not work in games due to the interactivity involved in game-playing as people could be distracted from noticing the brand placements (Yang et al., 2006). However, the significant influence of brand placements found in this study may provide major promise for advertisers. Game players may or may not explicitly remember the brands they see in the games, but these placements may influence their brand recall and brand attitude and could therefore influence later decisions (Yang et al., 2006). In this study, it was found that self-brand congruity was not significantly related with brand recall. The reason for this could be attributed to the fact that this study examined gamers who are highly involved in the interactive medium of games which force them to focus on game play rather than advertisements; the level of recognition to remember the brand exposed in the game is low and contributes to the "mismatch" between the gamers and the said brand. The present study contributes to the existing literature of the antecedents of brand recall and brand attitude in advergames. This study contributes to the role of brand recall and brand attitude as mediators in purchase behavior theory. Academically, the relationship between brand recall and brand attitude is well known in advergaming research, but their impact as important mediators on purchase intention add new understanding in the interactive communication literature. Their mediating role may provide new insights on how they facilitate the effects of self-brand congruity, entertainment and brand placement on purchase intention. Besides that, the studies on the influence of self-brand congruity on brand recall and brand attitude and also consumer intention to purchase had not well-investigated in advergames. This study contributes to fill those gaps in advergames literature. For practitioners, this study could suggest the use of illustrative or demonstrative placements of new products to help customers remember new brands, and the use of associative placements for existing products to increase consumers' purchase intention (Ho et al., 2011). To advertisers, this study may provide useful information to improve their current advertising strategies in games, for instance, by considering game players' congruity, entertainment value and brand placement factors.

• Korean Journal of Culture and Social Issue
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• v.12 no.1
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• pp.129-160
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• 2006

The purposes of this study were to find 1) the realities of social anxiety and perception of various kinds of social problems that exists in Korean society as well as the perception on the events that causes the social anxiety, 2) to see the difference of perceived level of social anxiety through variables of social demography and difference of perception on Korean society. The sample was distributed according to population size distinguishing the nation to 6 regions. The data of 1,375 adult respondents were analysed. The results are as follows. First of all, respondents mentioned that the most immediate problem to be solved in Korean society was financial anxiety, and the most desirable state of society was when the society is financially stabled. Single question was measured about social anxiety of Korean society and scored 6.84 from full marks of 10, showing difference in variables for instance sex, age, and subjective S.E.S. where women, aged under 20, and perceived low class group showed the highest rate of social anxiety. However, there weren't any difference found in social anxiety of the variables like presence of religion, educational background, residence, and monthly average household income. Also, there were differences in level of social anxiety according to the difference of perception of Korean society. Higher the perceived unpredictability, uncontrollability, and unmovability to the upper class, unfairness, and uncertainty, unreliability of the Korean society, higher the social anxiety. And the lower the perceived chance of success of reformation, higher the social anxiety. It was also found that the perceived social anxiety is influenced by social accidents and phenomenon as unemployment, economic depression, and the gap between rich and poor as well as the increase of crime through effluence of personal information. Finally the limitations and implications of this study were discussed.

• Bangmulgwan gwa yeongu (The National Museum of Korea Journal)
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• v.1
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• pp.306-329
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• 2024

Established in 1909, the Imperial Museum was the forerunner of Korean museums, and its collection formed the foundation of today's National Museum of Korea. However, when the Imperial Museum was first established in Changgyeonggung Palace, a zoo and botanical garden were created in addition to the museum. From 1911 onward, these three facilities were collectively referred to as Changgyeongwon Park. The zoo and botanical garden remained at Changgyeongwon when the museum was relocated in 1938, as did some of the items from the collection of the Yi Royal Household Museum. Among them were palanquins used by the royal family and folk items such as armor, as well as taxidermized birds. These stuffed birds were displayed in the corridor of Myeongjeongjeon Hall in Changgyeongwon, and were also displayed in the specimen hall at the back of Myeongjeongjeon Hall. The stuffed birds in particular should prompt a reconsideration of the nature of the Imperial Museum (Yi Royal Household Museum). The museum had been known as a prominent art museum, mainly collecting masterpieces of ceramics (such as Goryeo celadon), Buddhist sculptures, and paintings. However, this character seems to have been just one aspect of the museum. Along with the zoo, which housed live animals, and the botanical garden, which included greenhouses for tropical plants, the museum also featured specimens like taxidermy, suggesting that its initial aim, from a museological perspective, was to be a more comprehensive museum. Notably, Shimogoriyama Seiichi, who managed the general affairs of the museum, collected and cataloged Korean avian specimens from 1908 to 1917. This suggests that the zoo and botanical garden were not merely for entertainment purposes, but also served a museological purpose. However, the Imperial Museum (Yi Royal Household Museum) lacked the essential research and educational functions necessary for a museum, beyond its collecting and exhibition roles. For instance, although specimens of stuffed Korean birds were collected, they were not thoroughly researched. This indicates that while the museum's collection was acquired from a museological perspective, it did not advance into more specialized research. This study aims to examine how the characteristics of the Yi Royal Household Museum have evolved by analyzing the inventory of the museum's collections and the list of Korean bird specimens it held.

• The Mathematical Education
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• v.63 no.2
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• pp.123-138
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• 2024

This study described the utilization of ChatGPT in teaching and students' learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at 'S' University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students' discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

• Journal of Intelligence and Information Systems
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• v.23 no.1
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• pp.69-93
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• 2017

The development of ICT has leaded the diversification and changes of supplies and demands in markets. It also caused the creations of a variety of values which are differentiated from those in the existing market. Therefore, a new-type market is created, which can include multi-value chains which are from ICT-based created markets as well as the existing markets. We defined the platform as the new-type market. In the platform, the multi-value chains can be coexisted with multi-values. In true market, when a new-type value chain entered into an existing market, it is general that it can be conflicted with the existing value chain in the market. The conflicted problem among multi-value chains in a market is caused by the sharing of limited market resources like suppliers, consumers, services or products among the value chains. In other words, if there are multi-value chains in the platform, then it is possible to have conflictions, overlapping, creations or losses of values among the value chains. To solve the problem, we introduce coexistence factors to reduce the conflictions to reach market equilibrium in the platform. In the other hand, it is possible to lead the creations of differentiated values from the existing market and to augment the total market values in the platform. In the early era of ICT development, ICT was introduced for improvement of efficiency and effectiveness of the value chains in the existing market. However, according to the changed role of ICT from the supporter to the promotor of the market, ICT became to lead the variations of the value chains and creations of various values in the markets. For instance, Uber Taxi created a new value chain with ICT-based new-type service or products with new resources like new suppliers and consumers. When Uber and Traditional Taxi services are playing at the same time in Taxi service platform, it is possible to create values or make conflictions among values between the new and old value chains. In this research, like Uber and traditional taxi services, if there are conflictions among the multi-value chains, then it is necessary to minimize the conflictions in the platform for the coexistence of multi-value chains which can create the value-added values in the platform. So, it is important to predict and discuss the possible conflicted problems between new and old value chains. The confliction should be solved to reach market equilibrium with multi-value chains in the platform. That is, we discuss the possibility of the coexistence of multi-value chains in the platform which are comprised of a variety of suppliers and customers. To do this, especially we are focusing on the healthcare markets. Nowadays healthcare markets are popularized in global market as well as domestic. Therefore, there are a lot of and a variety of healthcare services like Traditional-, Tele-, or Intelligent- healthcare services and so on. It shows that there are multi-suppliers, -consumers and -services as components of each different value chain in the same platform. The platform can be shared by different values that are created or overlapped by confliction and loss of values in the value chains. In this research, as was said, we focused on the healthcare services to show if a platform can be shared by different value chains like traditional-, tele-healthcare and intelligent-healthcare services and products. Additionally, we try to show if it is possible to increase the value of each value chain as well as the total value of the platform. As the result, it is possible to increase of each value of each value chain as well as the total value in the platform. Finally, we propose a coexistence model to overcome such problems and showed the possibility of coexistence between the value chains through experimentation.

• Journal of Korean Academy of Nursing
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• v.11 no.2
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• pp.55-68
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• 1981

The prime object of the study is to evaluate how much all the students of the Nursing Schools throughout the nation are in comprehension toward the application of nursing process to clinical experience as means of systematic solution of nursing problems. An effort has been made to find out the actual state whether they are in practice of clinical experience in accordance with application of nursing process, over the period of four weeks managing from December 1st to 28th, 1980 and centering on 36 nursing schools, and meanwhile and evaluation, employing the assessment tool used by Bertuccietal, has been made on the nursing process notes recorded by 200 senions out of 21 nursing schools where application of nursing process to clinical experience being in practice. The assessment tool is composed of 5 different criteria in view of patient nursing and authors made an attempt to find out the result of clinical experience on application students in accordance with 5 different scoring criteria and further evaluating all the findings thereof. The findings were disposed of accordance with practice duration and criteria of the specific sudents subject to this finding as to verify the scoring difference in significance and of which the results are as follows: 1) as of now, in 21 (58.2%) out of 36 nursing Schools nursing process in being appliced in clinical experience. 2) Schools that started the application of nursing process to clinical experience amount to - for more than 4 yrs -6 (28.6％) - for 2 to 3 yrs-11s(52.4％) - for 1 yr -4 (19.0％) 3) As for the response upon application of nursing process. To clinical etperience, the largest voice (61.9%) heard was that it is rather difficult beyond the lecturing thereof, to practically apply it outs patients and the second voice (19.1%) turned out to be that it is hard to put in practice owing to uninformed nurses of the process serving in the clinical field. 4) The response. Of the processors assigned to instruction as to the most difficult problem in criteria of nursing process, the largest voice (38.2%) centered on the problem assessment while the second voice (17.7%) on the indirect nursing activity and the objective data respectively and considered to be the easiest was the indirect nursing activity (11.7%). 5) In order for a satisfactory. application of nursing process to clinical experience hence-forth, it has been pointed out that sufficient number of nurses should be supplemented in clinical field (44.1%) and at the same time supplementory education (35.3%) centered around professors be necessary. 6) Of the criteria that record result of nursing process, a significant difference in comprehension of subjective and objective data has been revealed according to the degree of the practice duration of application to clinical experience. For instance, while although poor it may seen, only 74.9% in subjective data and 71.1% in objective data represent the student group in practice for more than 4 years and only 56.3% in subjective data and 66.8% in objective data represent the student group in practice for 2 to 3 years but they still surpass in comprehension over the student group in practice for 1 year attaning only 19.6% in subjective data and 16.8% in objective data (P < 0.005). 7) As for problem assessment, the student group who started application of nursing process for 4 years stand for 37,7% the group for 2 to 3 years started for 25.3% and the group for 1 year started for 5.4%, revealing no significant difference according to duration (P < 0.5) and as poor as to indicate only 22.8% on an overage is in comprehension. 8) On direct and indirect nursing activity, the student group of for more than 4 years in appling nursing process (representing 49.5% in direct nursing activity, 21.4% in indirect nursing activity). Know more about it than the student group of for 2 to 3 years (representing 36.3% in direct nursing activity, 20.8% in indirect nursing activity) but revealed no significant difference. (P ＜ 0.5) 9) The student group applying nursing process for more than 4 years subjective data (74.9%) comprehend were more than objective data (71.1%) but shown no significant difference (P < 0.5). 10) However, the student group applying nursing process for 2 to 3 years comprehend objective data (66.8%) well ever subjective data (55.5%) indicating that 40.9% in average is in comprehension, thereby revealing a significant difference (P < 0.005). 11) On the other hand, the student group applying nursing process to clinical experience for 1 year had revealed themselves as poorly as to comprehend only 11.7% are an average of it, revealing no significant difference (P < 0.5). In consequence of the fore going, I the conductor of the present study, hereby suggest the following points: 1) Application of nursing process to clinical experience be practiced in all the Nursing Schools all over the nation at the earliest possible date in order that scientific nursing be prevailed (as of now only 58.0%), 2) In teaching nursing process, it is desirable to teach specific method of applying to practical clinical situations. 3) In order to meet the end of satisfactory application of nursing process to clinical experience, sufgecient nursing man power be sysplemented in clinical field and at the save time supplementary education by professors is necessary. 4) Sinces the students whose application duration of nursing process to clinical experience is longer comprehend more about it, it is reguired that the schools not yet in practice of the application be promptlyurged to follow. 5) Of the criteria recording nursing process, since it is comparatively hard to comprehend“assessment”and“Direct and indirect nursing activity”, a concentrated instruction is desirable. 6) The students whose duration of application of nursing process to clinical experience falls short of 1 years be put in a concentrated guidance program on individual criterion.

• Asia pacific journal of information systems
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• v.17 no.4
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• pp.31-59
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• 2007

We frequently use search engines to find relevant information in the Web but still end up with too much information. In order to solve this problem of information overload, ranking algorithms have been applied to various domains. As more information will be available in the future, effectively and efficiently ranking search results will become more critical. In this paper, we propose a ranking algorithm for the Semantic Web resources, specifically RDF resources. Traditionally, the importance of a particular Web page is estimated based on the number of key words found in the page, which is subject to manipulation. In contrast, link analysis methods such as Google's PageRank capitalize on the information which is inherent in the link structure of the Web graph. PageRank considers a certain page highly important if it is referred to by many other pages. The degree of the importance also increases if the importance of the referring pages is high. Kleinberg's algorithm is another link-structure based ranking algorithm for Web pages. Unlike PageRank, Kleinberg's algorithm utilizes two kinds of scores: the authority score and the hub score. If a page has a high authority score, it is an authority on a given topic and many pages refer to it. A page with a high hub score links to many authoritative pages. As mentioned above, the link-structure based ranking method has been playing an essential role in World Wide Web(WWW), and nowadays, many people recognize the effectiveness and efficiency of it. On the other hand, as Resource Description Framework(RDF) data model forms the foundation of the Semantic Web, any information in the Semantic Web can be expressed with RDF graph, making the ranking algorithm for RDF knowledge bases greatly important. The RDF graph consists of nodes and directional links similar to the Web graph. As a result, the link-structure based ranking method seems to be highly applicable to ranking the Semantic Web resources. However, the information space of the Semantic Web is more complex than that of WWW. For instance, WWW can be considered as one huge class, i.e., a collection of Web pages, which has only a recursive property, i.e., a 'refers to' property corresponding to the hyperlinks. However, the Semantic Web encompasses various kinds of classes and properties, and consequently, ranking methods used in WWW should be modified to reflect the complexity of the information space in the Semantic Web. Previous research addressed the ranking problem of query results retrieved from RDF knowledge bases. Mukherjea and Bamba modified Kleinberg's algorithm in order to apply their algorithm to rank the Semantic Web resources. They defined the objectivity score and the subjectivity score of a resource, which correspond to the authority score and the hub score of Kleinberg's, respectively. They concentrated on the diversity of properties and introduced property weights to control the influence of a resource on another resource depending on the characteristic of the property linking the two resources. A node with a high objectivity score becomes the object of many RDF triples, and a node with a high subjectivity score becomes the subject of many RDF triples. They developed several kinds of Semantic Web systems in order to validate their technique and showed some experimental results verifying the applicability of their method to the Semantic Web. Despite their efforts, however, there remained some limitations which they reported in their paper. First, their algorithm is useful only when a Semantic Web system represents most of the knowledge pertaining to a certain domain. In other words, the ratio of links to nodes should be high, or overall resources should be described in detail, to a certain degree for their algorithm to properly work. Second, a Tightly-Knit Community(TKC) effect, the phenomenon that pages which are less important but yet densely connected have higher scores than the ones that are more important but sparsely connected, remains as problematic. Third, a resource may have a high score, not because it is actually important, but simply because it is very common and as a consequence it has many links pointing to it. In this paper, we examine such ranking problems from a novel perspective and propose a new algorithm which can solve the problems under the previous studies. Our proposed method is based on a class-oriented approach. In contrast to the predicate-oriented approach entertained by the previous research, a user, under our approach, determines the weights of a property by comparing its relative significance to the other properties when evaluating the importance of resources in a specific class. This approach stems from the idea that most queries are supposed to find resources belonging to the same class in the Semantic Web, which consists of many heterogeneous classes in RDF Schema. This approach closely reflects the way that people, in the real world, evaluate something, and will turn out to be superior to the predicate-oriented approach for the Semantic Web. Our proposed algorithm can resolve the TKC(Tightly Knit Community) effect, and further can shed lights on other limitations posed by the previous research. In addition, we propose two ways to incorporate data-type properties which have not been employed even in the case when they have some significance on the resource importance. We designed an experiment to show the effectiveness of our proposed algorithm and the validity of ranking results, which was not tried ever in previous research. We also conducted a comprehensive mathematical analysis, which was overlooked in previous research. The mathematical analysis enabled us to simplify the calculation procedure. Finally, we summarize our experimental results and discuss further research issues.