• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.10a
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• pp.295-298
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• 2014

In this paper, an efficient design of HEVC Adaptive Loop Filter(ALF) for filter coefficients estimation is proposed. The ALF performs Cholesky decomposition of $10{\times}10$ matrix iteratively to estimate filter coefficients. The Cholesky decomposition of the ALF consists of root and division operation which is difficult to implement in a hardware design because it needs to many computation rate and processing time due to floating-point unit operation of large values of the Maximum 30bit in a LCU($64{\times}64$). The proposed hardware architecture is implemented by designing a root operation based on Cholesky decomposition by using multiplexer, subtracter and comparator. In addition, The proposed hardware architecture of efficient and low computation rate is implemented by designing a pipeline architecture using characteristic operation steps of Cholesky decomposition. An implemented hardware is designed using Xilinx ISE 14.3 Vertex-6 XC6VCX240T FPGA device and can support a frame rate of 40 4K Ultra HD($4096{\times}2160$) frames per second at maximum operation frequency 150MHz.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.10a
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• pp.271-274
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• 2014

This paper proposes high-performance SAO(Sample Adaptive Offset) in HEVC(High Efficiency Video Coding) encoder for Ultra HD video processing in real time. SAO is a newly adopted technique belonging to the in-loop filter in HEVC. The proposed SAO encoder hardware architecture uses three-layered buffers to minimize memory access time and to simplify pixel processing and also uses only adder, subtractor, shift register and feed-back comparator to reduce area. Furthermore, the proposed architecture consists of pipelined pixel classification and applying SAO parameters, and also classifies four consecutive pixels into EO and BO concurrently. These result in the reduction of processing time and computation. The proposed SAO encoder architecture is designed by Verilog HDL, and implemented by 180k logic gates in TSMC $0.18{\mu}m$ process. At 110MHz, the proposed SAO encoder can support 4K Ultra HD video encoding at 30fps in real time.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.675-695
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• 2023

To learn mathematics effectively, understanding vocabulary is essential. Accordingly, as a way to present vocabulary for mathematics education, high-frequency vocabulary was extracted from the 2009 revised 1st and 2nd grade mathematics textbooks and the 2015 revised 1st and 2nd grade mathematics textbooks. At this time, mathematics textbooks were analyzed by grade and semester, and vocabulary with a common frequency of 5 or more was extracted. In order to use it effectively in school settings, common vocabulary for each grade and intensive vocabulary for each semester were presented. As a result of the study, 61 vocabulary words for first grade education and 121 vocabulary words for second grade education were selected. As a result of analysis by vocabulary level, various levels of vocabulary from grades 1 to 5 were used. As a result of analysis by vocabulary type, the proportion of academic words increased similarly, but the proportion of technical words was found to be highest in the first semester of the second year. Based on these results, the extracted vocabulary for mathematics education is used as a resource for vocabulary instruction for students' mathematics education in each grade to help students learn mathematics.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.39-55
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• 2024

Recently, the 2022 revised mathematics curriculum has established achievement standards for equal sign and equality, and efforts have been made to examine teaching methods and student understanding of relational understanding of equal sign. In this context, this study conducted a lesson that emphasized relational understanding in an introduction to equal sign, and compared and analyzed the understanding of equal sign between the experimental group, which participated in the lesson emphasizing relational understanding and the control group, which participated in the standard lesson. For this purpose, two classes of students participated in this study, and the results were analyzed by administering pre- and post-tests on the understanding of equal sign. The results showed that students in the experimental group had significantly higher average scores than students in the control group in all areas of equation-structure, equal sign-definition, and equation-solving. In addition, when comparing the means of students by item, we found that there was a significant difference between the means of the control group and the experimental group in the items dealing with equal sign in the structure of 'a=b' and 'a+b=c+d', and that most of the students in the experimental group correctly answered 'sameness' as the meaning of equal sign, but there were still many responses that interpreted the equal sign as 'answer'. Based on these results, we discussed the implications for instruction that emphasizes relational understanding in equal sign introduction lessons.

• Journal of the Korean Geographical Society
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• v.41 no.2 s.113
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• pp.212-226
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• 2006

Surface data generally represent continuous distribution of geographical or social phenomena of a region in urban analysis. Instances include distribution of temperature, population of region, and various distributions related to human activities. When spatial data are given in the form of surface, surface comparison is required as a way of comprehending the surface change or the relationship between two surfaces. As for previous approaches of surface comparison, there are visualization, quantitative methods and qualitative method. All those approaches, however, show the difference between two surfaces in a limited way. Especially, they are not able to distinguish spatial difference between two surfaces. To overcome such problem, this paper proposes a method of comparing two surfaces in terms of their spatial structure. Main concept of the method comes from earth moving problem and the method is named minimum surface transformation, here. When a surface is transformed into another, total surface volume moved in the process of transformation should be the minimum. Both quantitative and spatial differences between two surfaces are evaluted by total surface volume moved and the distribution of moved surface volume of each cell respectively. The method is applied to hypothetical and actual data. From the former, it is understood that the method explains how two surfaces are quantitatively and spatially different. The result of the latter shows that moved total surface volume decreases as time goes by which fits the actual situation that population change rate gets smaller. Concerning the other measure of surface difference, the distribution of $X_{ij}$ describes detailed flow of surface volume than that of simply subtracting surface volume by indicating to what direction the population change occurs.

• Journal of the Korean School Mathematics Society
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• v.18 no.1
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• pp.1-14
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• 2015

In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.5_6
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• pp.324-329
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• 2003

The public-key cryptosystems such as Diffie-Hellman Key Distribution and Elliptical Curve Cryptosystems are built on the basis of the operations defined in GF(2$^{m}$ ):addition, subtraction, multiplication and multiplicative inversion. It is important that these operations should be computed at high speed in order to implement these cryptosystems efficiently. Among those operations, as being the most time-consuming, multiplicative inversion has become the object of lots of investigation Formant's theorem says $\beta$$^{-1}$ =$\beta$$^{2}$sup m/-2/, where $\beta$$^{-1}$ is the multiplicative inverse of $\beta$$\in$GF(2$^{m}$ ). Therefore, to compute the multiplicative inverse of arbitrary elements of GF(2$^{m}$ ), it is most important to reduce the number of times of multiplication by decomposing 2$^{m}$ -2 efficiently. Among many algorithms relevant to the subject, the algorithm proposed by Itoh and Tsujii[2] has reduced the required number of times of multiplication to O(log m) by using normal basis. Furthermore, a few papers have presented algorithms improving the Itoh and Tsujii's. However they have some demerits such as complicated decomposition processes[3,5]. In this paper, in the case of 2$^{m}$ -2, which is mainly used in practical applications, an efficient algorithm is proposed for computing the multiplicative inverse at high speed by using both the factorization formula x$^3$-y$^3$=(x-y)(x$^2$＋xy＋y$^2$) and normal basis. The number of times of multiplication of the algorithm is smaller than that of the algorithm proposed by Itoh and Tsujii. Also the algorithm decomposes 2$^{m}$ -2 more simply than other proposed algorithms.