• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• The Journal of the Korea Contents Association
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• v.9 no.1
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• pp.147-158
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• 2009

Recently, the data model in stream data environment has massive, continuous, and infinity properties. However the stream data processing like query process or data analysis is conducted using a limited capacity of disk or memory. In these environment, the traditional frequent pattern discovery on transaction database can be performed because it is difficult to manage the information continuously whether a continuous stream data is the frequent item or not. In this paper, we propose the method which we are able to predict the frequent items using the regression model on continuous stream data environment. We can use as a prediction model on indefinite items by constructing the regression model on stream data. We will show that the proposed method is able to be efficiently used on stream data environment through a variety of experiments.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.8
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• pp.731-740
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• 1991

This paper presents a knowledge based system to solve reactive power/voltage control problem in a power system. The methods to reduce inference time are proposed in inferring the solution of problem in the knowledge base which consists of heuristic rules and inowledge of experts. A set of indices drawn from the heuristic knowledge on the power system is utilized to make up for the defect of existing knowledge based systems which determine both the location and the amount of reactive power compensation devices. The concept of set of indices developed in this paper makes it possible to infer the amount of reactive power source only since the bus order list representing priority for the location of reactive power compensator to be switched on can be determined in advance. From the fact that there exists a relationship between the system voltage pattern and the reactive power pattern in operation, the pattern recognition technique is introduced to reduce the inference time in solving the severe voltage problem. To demonstrate the usefulness of the proposed knowledge based system, the IEEE 30 bus system is chosen as a sample system. The results of case study are also presented.

• The KIPS Transactions:PartD
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• v.8D no.5
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• pp.513-522
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• 2001

Active database execute an action of active rule defined in advance which is triggered automatically, whenever an event with the matching event specifications occurs, its condition is evaluated. Because these rules may in turn trigger other rules, the set of rules may be triggered each other indefinitely, Therefore, we propose a termination analysis method to guarantee termination. This proposed method considers composite event as well as rule execution time. Above all, the method not only uses deactivation graph combined to trigger graph for exact analysis, but also improves the complexity of analysis. Also the proposed method enhances accuracy of analysis result.

• The KIPS Transactions:PartD
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• v.14D no.7
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• pp.733-742
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• 2007

A data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. Due to this reason, memory usage for data stream analysis should be confined finitely although new data elements are continuously generated in a data stream. To satisfy this requirement, data stream processing sacrifices the correctness of its analysis result by allowing some errors. The old distribution statistics are diminished by a predefined decay rate as time goes by, so that the effect of the obsolete information on the current result of clustering can be eliminated without maintaining any data element physically. This paper proposes a grid based clustering algorithm for a data stream. Given a set of initial grid cells, the dense range of a grid cell is recursively partitioned into a smaller cell based on the distribution statistics of data elements by a top down manner until the smallest cell, called a unit cell, is identified. Since only the distribution statistics of data elements are maintained by dynamically partitioned grid cells, the clusters of a data stream can be effectively found without maintaining the data elements physically. Furthermore, the memory usage of the proposed algorithm is adjusted adaptively to the size of confined memory space by flexibly resizing the size of a unit cell. As a result, the confined memory space can be fully utilized to generate the result of clustering as accurately as possible. The proposed algorithm is analyzed by a series of experiments to identify its various characteristics

• Journal of KIISE:Databases
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• v.36 no.3
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• pp.226-234
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• 2009

A data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. Due to the characteristics of a data stream, it is impossible to save all the data elements of a data stream. Therefore it is necessary to define a new synopsis structure to store the summary information of a data stream. For this purpose, this paper proposes a cuboid prefix tree that can be effectively employed in evaluating an iceberg query over data streams. A cuboid prefix tree only stores those itemsets that consist of grouping attributes used in GROUP BY query. In addition, a cuboid prefix tree can compute multiple iceberg queries simultaneously by sharing their common sub-expressions. A cuboid prefix tree evaluates an iceberg query over an infinitely generated data stream while efficiently reducing memory usage and processing time, which is verified by a series of experiments.

• Journal of Radiation Protection and Research
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• v.9 no.2
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• pp.90-96
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• 1984

Estimated dose rates in spent fuel pool storage with the extended fuel cycle core management were reviewed and compared with design limit after calculation with the aid of DLC-23/CASK(22 n, 18 g) nuclear data and ANISN code. Radioactivity and gamma spectrum within spent fuel assemblies were calculated with ORIGEN code by extended fuel cycle model. In the calculation of dose rate, the fuel pool geometry was assumed to be infinite slab. Also, composition materials and radiation source within assemblies which are being stored in pool storage were assumed to be uniformly distributed throughout all the assemblies. As a result of culculation of dose rate from stored assemblies and waterborne radionuclides in pool water, the calculated dose rates appear to be lower than design basis limit under normal condition as well as abnormal condition.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.