• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.105-122
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• 2014

In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.371-391
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• 2016

Long division was one of the major issues in math war II started from 1990's in US. In this paper, we investigated this concretely and examined present teaching condition of long division in Korea. Firstly, Long division is not only a mechanical way to get the answer but also a realization of core conception in elementary mathematics. Futhermore it is a connecting link between elementary and middle mathematics education. Secondly, it is needed to use the term 'long division' to provide the concrete teaching guidelines. Thirdly, a minor algorithm, like an 'partial quotient method', is necessary to introduce in order to help understanding long division.

• ETRI Journal
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• v.26 no.1
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• pp.53-56
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• 2004

In this letter, we propose a novel design scheme for an optimal non-uniform planar array geometry in view of maximum side-lobe reduction. This is implemented by a thinned array using a genetic algorithm. We show that the proposed method can maintain a low side-lobe level without pattern distortion during beam steering.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.5A
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• pp.501-508
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• 2006

Orthogonal frequency division multiplexing-code division multiplexing access(OFDM-CDMA) systems without guard interval can enhance the bandwidth performance more efficiently than the systems with guard interval. In this paper, a new technique for an OFDM-CDMA system without guard interval, which can eliminate inter-symbol interference(ISI) and inter-channel interference(ICI), is presented. The proposed algorithm is a new demodulation technique, based on the Pseudo-Decorrelator, and it is named PD algorithm. Simulation results show that the PD algorithm can combat ISI and ICI efficiently for an OFDM-CDMA system without guard interval. The BER performance of the PD algorithm is much better than that of a conventional OFDM-CDMA system without guard interval.

• School Mathematics
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• v.12 no.3
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• pp.439-454
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• 2010

This study presents how two eighth grade students generated their own algorithms in the context of fraction measurement division situations by modifications of unit-segmenting schemes. Teaching experiment was adopted as a research methodology and part of data from a year-long teaching experiment were used for this report. The present study indicates that the two participating students' construction of reciprocal relationship between the referent whole [one] and the divisor by using their unit- segmenting schemes and its strategic use finally led the students to establish an algorithm for fraction measurement division problems, which was on par with the traditional invert-and-multi- ply algorithm for fraction division. The results of the study imply that teachers' instruction based on understanding student-generated algorithms needs to be accounted as one of the crucial characteristics of good mathematics teaching.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.5
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• pp.17-23
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• 2004

In this paper, we proposed a mixed algerian to improve decimal division speed. In the binary number system, nonrestoring algorithm has a smaller number of operation than restoring algorithm. In decimal number system however, the number of operations differs with respect to quotient values. Since one digit ranges 0 to 9 in decimal, the proposed mixed algerian employs both nonrestoring and restoring algorithm considering current partial remainder values. The proposed algorithm chooses either restoring or nonrestoring algerian based on the remainder values. The proposed algorithm improves computation speed substantially over a single algorithm decreasing the number of operations.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.4
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• pp.31-39
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• 2004

The ARM7 TDMI microprocessor employ a software routine iteration method in order to handle integer division operation, but this method has long execution time and many execution instruction. In this paper, we proposed ARM7 TDMI microprocessor with integer division instruction. To make this, we additionally defined UDIV instruction for unsigned integer division operation and SDIV instruction for signed integer division operation, and proposed ARM7 TDMI microprocessor data Path to apply division algorithm. Applied division algorithm is nonrestoring division algorithm and additive hardware is reduced using existent ARM data path. To verify the proposed method, we designed proposed method on RTL level using HDL, and conducted logic simulation. we estimated the number of execution cycles and the number of execution instructions as compared proposed method with a software routine iteration method, and compared with other published integer divider from the number of execution cycles and hardware size.

• Korean Journal of Remote Sensing
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• v.37 no.1
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• pp.153-160
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• 2021

Land Surface Temperature (LST) is the radiological surface temperature which observed by satellite. It is very important factor to estimate condition of the Earth such as Global warming and Heat island. For these reasons, many countries operate their own satellite to observe the Earth condition. South Korea has many landcovers such as forest, crop land, urban. Therefore, if we want to retrieve accurate LST, we would use high-resolution satellite data. In this study, we made LSTs with 4 LST retrieval algorithms which are used widely with Landsat-8 data which has 30 m spatial resolution. We retrieved LST using equations of Price, Becker et al. Prata, Coll et al. and they showed very similar spatial distribution. We validated 4 LSTs with Moderate resolution Imaging Spectroradiometer (MODIS) LST data to find the most suitable algorithm. As a result, every LST shows 2.160 ~ 3.387 K of RMSE. And LST by Prata algorithm show the lowest RMSE than others. With this validation result, we choose LST by Prata algorithm as the most suitable LST to South Korea.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.385-403
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• 2018

Fraction division can be categorized as partitive division, measurement division, and the inverse of a Cartesian product. In the contexts of quotitive division and the inverse of a Cartesian product, the multiply-by-the-reciprocal algorithm is drawn well out. In this study, I analyze the potential and significance of the method of using $1{\div}$(divisor) as an alternative way of developing the multiply-by-the-reciprocal algorithm in the context of quotitive division. The method of using $1{\div}$(divisor) in quotitive division has the following advantages. First, by this method we can draw the multiply-by-the-reciprocal algorithm keeping connection with the context of quotitive division. Second, as in other contexts, this method focuses on the multiplicative relationship between the divisor and 1. Third, as in other contexts, this method investigates the multiplicative relationship between the divisor and 1 by two kinds of reasoning that use either ${\frac{1}{the\;denominator\;of\;the\;divisor}}$ or the numerator of the divisor as a stepping stone. These advantages indicates the potential of this method in understanding the multiply-by-the-reciprocal algorithm as the common structure of fraction division. This method is based on the dual meaning of a fraction as a quantity and the composition of times which the current elementary mathematics textbook does not focus on. It is necessary to pay attention to how to form this basis when developing teaching materials for fraction division.

• Journal of IKEEE
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• v.24 no.4
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• pp.961-968
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• 2020

This paper describes a design of high performance modular multiplier that is essentially used for elliptic curve cryptography. Our modular multiplier supports modular multiplications for five field sizes over GF(p), including 192, 224, 256, 384 and 521 bits as defined in NIST FIPS 186-2, and it calculates modular multiplication in two steps with integer multiplication and reduction. The Karatsuba-Ofman multiplication algorithm was used for fast integer multiplication, and the Lazy reduction algorithm was adopted for reduction operation. In addition, the Nikhilam division algorithm was used for the division operation included in the Lazy reduction. The division operation is performed only once for a given modulo value, and it was designed to skip division operation when continuous modular multiplications with the same modulo value are calculated. It was estimated that our modular multiplier can perform 6.4 million modular multiplications per second when operating at a clock frequency of 32 MHz. It occupied 456,400 gate equivalents (GEs), and the estimated clock frequency was 67 MHz when synthesized with a 180-nm CMOS cell library.