• Journal of the Institute of Electronics Engineers of Korea SC
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• v.42 no.6
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• pp.9-14
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• 2005

In this paper, we consider the synthesis of non-fragile $H_{\infty}$ state feedback controllers for singular systems and static state feedback controller with multiplicative uncertainty. The sufficient condition of controller existence, the design method of non-fragile $H_{\infty}$ controller, and the measure of non-fragility in controller are presented via LMI(linear matrix inequality) technique. Also, the sufficient condition can be rewritten as LMI form in terms of transformed variables through singular value decomposition, some changes of variables, and Schur complements. Therefore, the obtained non-fragile $H_{\infty}$ controller guarantees the asymptotic stability and disturbance attenuation of the closed loop singular systems within a prescribed degree. Moreover, the controller design method can be extended to the problem of robust and non-fragile $H_{\infty}$ controller design method for singular systems with parameter uncertainties. Finally, a numerical example is given to illustrate the design method.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.255-273
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• 2019

In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1181-1188
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• 2017

The unit and fundamental units of number fields are important to number field sieves testing primality of more than 400 digits integers and number field seive factoring the number in RSA cryptosystem, and multiplication of ideals and counting class number of the number field in imaginary quadratic cryptosystem. To minimize the time and space in H/W implementation of cryptosystems using fundamental units, in this paper, we introduce the Dirichlet's unit Theorem and propose our process of generating the fundamental units of the number field. And then we present the algorithm generating our fundamental units of the number field to minimize the time and space in H/W implementation and implementation results using the algorithm over the number field.

• 한국정보교육학회:학술대회논문집
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• 2007.08a
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• pp.273-279
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• 2007

수학은 생활의 기본이 되는 도구 교과이다. 그 중에서 아동들이 가장 중요하지만 어려워하고 후속 학습에까지 영향을 미치는 것은 구구단이다. 고학년이 되어서까지 곱셈 구구를 못 외우는 학생들은 지도가 어려울 뿐만 아니라 이후에도 지속적으로 수학 학습에서 뒤떨어지게 된다. 하지만 암기가 중심이 되는 부분이라 다른 것들보다 학습의 흥미가 떨어지고 시기를 놓치면 학습이 점점 더 어려워지는 단점이 있다. 이에 지금까지 어려웠던 어렵고 암기위주로 흘러가던 구구단을 음악과 연결시켜 보는 것은 어떨까란 생각을 하게 되었다. 여기에서 쓰이는 음악들은 모두 초등학교 교과서에 있는 음악으로 아동들이 친숙하게 느낄 수 있는 음악들이다. 이 소프트웨어는 2학년 뿐만 아니라 구구단을 어렵게 느끼는 고학년의 학습에도 도움이 되도록 제작하였다. 프로그램은 전체 구구단인 2$\sim$9단을 다루도록 하였으며, 각 단은 4개의 파트로 구성되어 있다. 1단계에서는 1-각 수까지 반복해서 세는 연습을 하였고, 2단계에서는 반복했던 수를 연결하여 띄어세기 연습, 3단계에서는 2단계에서 했던 띄어세기를 확장하여 구구단 연습을 해 볼 수 있도록 하였다. 정리단계에서는 각단의 구구단을 랜덤으로 배치하여 구구단의 복습이 될 수 있도록 하였다. 2,4,5,6,8단은 각기 박자에 맞춰서 구구단을 외우는 것이고 5,7 단은 박자에 맞추기 어려우므로 글자수에 맞춰서 구구단을 외우도록 하였다. 박자에 맞추는 것이 주가 아니라 수학을 배우는 것이 중심이므로 틀린 박자에 맞는 숫자를 누르는 것은 반응하지 않도록 하였다. 구구단 중간에 있는 수까지를 전부 제시함으로써 큰수와 띄어세기 그리고 구구단과의 관계를 이해할 수 있도록 하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.1A
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• pp.99-106
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• 2004

In this Paper, the matched filter for searching initial synchronization in DSSS (direct sequence spread spectrum) receiver is studied. The matched filter with a single data flow path is described which can be presented by HDL (Hardware Description Language). In order to improve the processing time of operations for the filter, equations are arranged to represent two data flow paths and the associated hardware model is proposed. The model has an architecture based on parallelism and pipeline for fast processing, in which two data flow paths with a series of memory, multiplier and accumulator are placed in parallel. The performance of the model is analyzed and compared with the matched filter with a single data flow path.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.615-631
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• 2010

Exercise is still an important method for mathematics learning and teaching, but there is only a few researches which involve the effectiveness of exercise in mathematics learning. This study is designed for giving some implications to researchers who are interested in developing mathematics exercise books for low achievers with respect to effectiveness. For this, 'Suhak-Ikhimchaek', the Korean elementary mathematics workbook, is chosen and in particular, 'multiplication number fact', one of the units of the book, is analyzed with the following respects: achievement levels of learners, arrays of exercise, the amounts and period of exercise, exercise type. Finally, this study proposes composing principles for developing exercise books for low achievers in mathematics.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.101-122
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• 2010

Chinese Taipei won the first place at the mathematics achievement of TIMSS 2007. Especially, there was a significant difference in the percentage of correct answers between Chinese Taipei and Korea, and Chinese Taipei' percentage of correct answers was higher than Korea. This study compared the education system, mathematics instruction environment, and instructional activities of two countries. And for algebra, curriculum and textbooks were compared between two countries based on TIMSS 2007 framework. It was found that Chinese Taipei emphasized homework and test, and MCFL of that was low. Their textbook was formal, and induced the hasty abstraction, Also, some themes were introduced earlier than Korea and repeated across different grades.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).