• School Mathematics
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• v.9 no.1
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• pp.1-12
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• 2007

The purpose of this study is searching for the problems and alternatives on teaching for repeating decimal. To accomplish the purpose, we have analyzed the fifth, sixth, and seventh Korean national curriculums, textbooks and examinations for the eighth grade about repeating decimal. W also have analyzed textbooks from USA to find for alternatives. As the results, we found followings. First, the national curriculums blocked us verifying the relation between rational number and repeating decimal. Second, definitions of terminating decimal, infinite decimal, and repeating decimal are slightly different in every textbooks. This leads seriously confusion for students examinations. The alternative on these problems is defining the terminating decimal as following; decimal which continually obtains only zeros in the quotient. That is, we have to avoid the representation of repeating decimal repeated nines under a declared system which apply an infinite decimal continually obtaining only zeros in the quotient. Then, we do not have any problems to verify the following statement. A number is a rational number if and only if it can be represented by a repeating decimal.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.285-298
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• 2008

According to the 7th curriculum, irrational numbers should be introduced using infinite decimals in 9th grade. To do so, the relation between rational numbers and decimals should be explained in 8th grade. Preceding studies remarked that middle school students could understand the relation between rational numbers and decimals through the division appropriately. From the point of view with the arithmetic handling activity, I analyzed that the integers and terminating decimals was explained as decimals with repeating 0s or 9s. And, I reviewed the equivalent relations between irrational numbers and non-repeating decimals, rational numbers and repeating decimals. Furthermore, I suggested an alternative method of introducing irrational numbers.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.1-17
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• 2004

According to the 7-th curriculum, irrational number should be introduced using repeating decimals in 8-th grade mathematics. To do so, the relation between rational numbers and repeating decimals such that a number is rational number if and only if it can be represented by a repeating decimal, should be examined closely Since this relation lacks clarity in some text books, irrational numbers have only slight relation with repeating decimals in those books. Furthermore, some text books introduce irrational numbers showing that $\sqrt{2}$ is not rational number, which is out of 7-th curriculum. On the other hand, if we use numeral 0 as a repetend, many results related to repeating decimals can be represented concisely. In particular, the treatments of order relation with repeating decimals in 8-th grade text books must be reconsidered.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.08a
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• pp.438-441
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• 1998

최근 미국 내 표준안으로서 많이 사용되고 있는 AC-3 오디오 알고리듬은 그 복잡성으로 인하여 실시간 구현을 위해선 프로세서로 구현하는 것이 적합하다. AC-3 복호화 알고리듬은 많은 부분이 실수연산으로 이루어져 있으므로 소수점을 고려한 연산이 필요한데, 프로세서로 구현할 때는 적은 비용과 빠른 속도로 실수연산을 수행하기 위해서 부동소수점보다는 고정소수점 연산이 유리하다. 그러나 고정소수점 연산시 발생하는 유한 단어길이 효과로 인하여 양자화 오차가 발생하므로 복호화된 오디오 신호의 음질저하를 최소화하기 위해서는 최적화가 필요하다. 본 논문에서는 AC-3 복호화 알고리듬의 부분별 양자화 오차를 분석하고 그 결과 가장 많은 오차를 발생시키는 역 TDAC 변환의 오차를 최적화하였다. Fast TDAC 변환이 FFT로 이루어져 있으므로 고정 소수점 연산시 오차가 적은 FFT 구조를 제안하였다. 제안된 구조를 사용하여 AC-3 고정소수점 복호화기를 C 언어를 사용하여 구현하였으며, AC-3 부동소수점 복호화기와 최종 PCM을 비교하여 그 성능을 평가하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.763-769
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• 2004

It is known that a bent function corresponds to a perfect nonlinear function, which makes it difficult to do the differential cryptanalysis in DES and in many other block ciphers. In this paper, for an odd prime p, quadratic p-ary bent functions defined on finite fields are given from the families of p-ary sequences with optimal correlation properly. And quadratic p-ary bent functions, that is, perfect nonlinear functions from the finite field F $_{p^{m}}$ to its prime field $F_{p}$ are constructed by using the trace functions. trace functions.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2513-2515
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• 2001

본 논문에서는 유한비트 근사화를 통하여 고정소수점 연산을 이용하여 DCT구현시 발생하는 오차 영향에 대한 해석을 수행하였다. 고정소수점 연산을 위해서는 유한 비트 근사화를 실시하여야 하는데 이 과정에서 수치 표현범위의 제약으로 인한 오차가 발생하게 되고, 특히 순환 연산구조를 가지는 DCT등의 알고리즘 구현시 급격한 성능의 감소를 가져오게 된다. 본 논문에서는 순환 연산식을 유한비트 근사화를 통하여 구현시 발생되는 에러에 대한 분석을 수행하고, 해석식을 도출하였다.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.11b
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• pp.587-592
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• 2002

본 논문에서는 De Bruijn 그래프에 기초한 다중처리기구성의 한 가지 방법을 제안하였다. 제안한 방법에서는 유한체상의 수학적 성질과 그래프의 성질을 사용하여 변환연산자를 제한하였으며, 이들 변환연산자를 이용하여 De Bruijn 그래프의 변환표를 도출하였다. 그리고, 이 변환표로부터 유한체상의 De Bruijn 그래프를 도출하였다. 제안한 다중처리기는 유한체상의 임의의 소수와 양의 정수에 대해 구성할 수 있으며 고장허용컴퓨팅시스템, 파이프라인 시스템, 병렬처리 네트워크, 스위칭 함수와 이의 회로, 차세대 디지털논리시스템 및 컴퓨터구조 중의 하나인 다치디지털논리시스템 등에 적용할 수 있으리라 전망된다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.3
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• pp.511-514
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• 2019

Elliptic Curves Cryptosystem(ECC) provides the same level of security with relatively small key sizes, as compared to the traditional cryptosystems. The performance of ECC over GF(2m) and GF(p) depends on the efficiency of finite field arithmetic, especially the modular multiplication which is based on the reduction algorithm. In this paper, we propose a new modular reduction algorithm which provides high-speed ECC over NIST prime P-256. Detailed experimental results show that the proposed algorithm is about 25% faster than the previous methods.

• Journal of Internet of Things and Convergence
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• v.6 no.4
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• pp.49-57
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• 2020

In this paper, I provided an approximation function Li*2,10(x) using logarithm integral for the counting function π*2,10(x) of consecutive deca primes. Several personal computers and Mathematica were used to validate the approximation function Li*2,10(x). I found the real value of π*2,10(x) and approximate value of Li*2,10(x) for various x ≤ 1011. By the result of theses calculations, most of the error rates are margins of error of 0.005%. Also, I proved that the sum C2,10(∞) of reciprocals of all primes with difference 10 between primes is finite. To find C2,10(∞), I computed the sum C2,10(x) of reciprocals of all consecutive deca primes for various x ≤ 1011 and I estimate that C2,10(∞) probably lies in the range C2,10(∞)=0.4176±2.1×10-3.

• The Mathematical Education
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• v.50 no.3
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• pp.309-327
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• 2011

In this paper, we extended the division algorithm for the integers to the finite decimals. Though the remainder for the finite decimals is able to be defined as various ways, the remainder could be defined as 'the remained amount' which is the result of the division and as "the remainder" only if 'the remained amount' is decided uniquely by certain conditions. From the definition of "the remainder" for the finite decimal, it could be inferred that 'the division by equal part' and 'the division into equal parts' are proper for the division of the finite decimal concerned with the definition of "the remainder". The finite decimal, based on the unit of measure, seemed to make it possible for us to think "the remainder" both ways: 1" in the division by equal part when the quotient is the discrete amount, and 2" in the division into equal parts when the quotient is not only the discrete amount but also the continuous amount. In this division context, it could be said that the remainder for finite decimal must have the meaning of the justice and the completeness as well. The theorem of the division algorithm for the finite decimal could be accomplished, based on both the unit of measure of "the remainder", and those of the divisor and the dividend. In this paper, the meaning of the division algorithm for the finite decimal was investigated, it is concluded that this theory make it easy to find the remainder in the usual unit as well as in the unusual unit of measure.