• Journal of Science Education
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• v.46 no.1
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• pp.109-120
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• 2022

Fraction division is the content that is important but difficult to learn because it includes the process of finding a numerical expression in the real-world context, the process of making a context that matches a numerical expression, how to solve division, and the justification of standard algorithm. This study analyzes the word problems and problem solving methods about fraction division which elementary pre-service teachers represented. Pre-service teachers have more difficulty in making word problem where the dividend is less than the divisor and they also show typical errors in making the word problems. There were differences in the methods presented according to the contexts of division in problem solving. Through this study, it is necessary to rethink the teaching methods for fraction division instruction in the curriculum for pre-service teachers and analyze the formation process of 'knowledge for content and teaching' because of the differences in responses between grades.

• School Mathematics
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• v.7 no.2
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• pp.103-121
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• 2005

This article compares and analyzes mathematics textbooks of North Korea, South Korea, China and Japan and draws meaningful ways for introducing the division algorithm of fractions. The analysis is based on the five contexts: 'measurement division', 'determination of a unit rate', 'reduction of the quantities in the same measure', 'division as the inverse of multiplication or Cartesian product', 'analogy with multiplication algorithm of fractions'. The main focus of the analysis is what context is used to introduce the algorithm and how much it can appeal to students. This analysis supports that there is a few differences of introducing methods the division algorithm of fractions among those countries and more meaningful way can be considered than ours. It finally suggests that we teach the algorithm in a way which can have students easily see the reason of multiplying the reciprocal of a divisor when they divide with fractions. For this, we need to teach the meaning of a reciprocal of fraction and consider to use the context of determination of a unit rate.

• Proceedings of the Korean Society for Rock Mechanics Conference
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• 2002.03a
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• pp.37-44
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• 2002

터널의 초기 변형결과를 역해석에 적용하기 위하여 초기 값들과 최종변위의 상관관계를 연구하였다 Panet의 지수함수와 분수함수는 경암 터널의 내공변위 예측에 잘 맞았다. ID지점의 초기 계측변위는 선형적으로 적합시킬 수 있으나 계측 전 변형의 추정식으로는 부적합하였다. 초기 계측 결과들과 최종 변형결과는 선형적인 비례관계를 보였으며 이로써 초기 계측결과로부터 추정한 최종변형치를 이용한 역해석이 가능함을 보였다.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.12
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• pp.75-82
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• 2010

This paper presents a wideband ${\Delta}{\Sigma}$ fractional-N frequency synthesizer for a multi-band single chip CMOS RFIC transceivers. A wideband VCO utilizes a 6-bit switched capacitor array bank for 2340~3940 MHz frequency range. VCO frequency calibration circuit is designed for optimal capacitor bank code selection before phase locking process. It finishes the calibration process in $2{\mu}s$ over the whole frequency band. The LO generation block has selectable multiple division ratios of ${\div}2$, ${\div}16$, and ${\div}32$ to generate LO I/Q signals for T-DMB/DAB/FM Radio systems in L-Band (1173~1973 MHz), VHF-III (147~246 MHz), VFH-II (74~123 MHz), respectively. The measured integrated phase noise is quite low as it is lower than 0.8 degree RMS over the whole frequency band. Total locking time of the ${\Delta}{\Sigma}$ frequency synthesizer including VCO frequency calibration time is less than $50{\mu}s$. The wideband ${\Delta}{\Sigma}$ fractional-N frequency synthesizer is fabricated in $0.13{\mu}m$ CMOS technology, and it consumes 15.8 mA from 1.2 V DC supply.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.2
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• pp.191-198
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• 2011

In this paper, a method to approximate a multi-layer Green's function is proposed based on a FDTD scheme and a rational function approximation. For a given horizontal propagation wavenumber, time domain response is calculated and then Fourier transformed to the spectral domain Green's function. Using the rational function approximation, the pole and residue of the Green's function can be estimated, which are crucial for a calculation of a path loss. The proposed method can provide a wideband Green's function, while the conventional normal mode method can be applied to a single frequency problem. To validate the proposed method, We consider two problems, one of which has a analytical solution. The other is about multi-layer case, for which the proposed method is compared with the known normal mode solution, Kraken.

• The Mathematical Education
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• v.58 no.1
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• pp.1-20
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• 2019

As the importance of algebraic thinking in elementary school has been emphasized, the links between fraction knowledge and algebraic thinking have been highlighted. In this study, we analyzed the solution methods and characteristics of thinking by fifth graders who have not yet learned fraction division when they solved 'reverse fraction problems' (Pearn & Stephens, 2018). In doing so, the contexts of problems were extended from the prior study to include the following cases: (a) the partial quantity with a natural number is discrete or continuous; (b) the partial quantity is a natural number or a fraction; (c) the equivalent fraction of partial quantity is a proper fraction or an improper fraction; and (d) the diagram is presented or not. The analytic framework was elaborated to look closely at students' solution methods according to the different contexts of problems. The most prevalent method students used was a multiplicative method by which students divided the partial quantity by the numerator of the given fraction and then multiplied it by the denominator. Some students were able to use a multiplicative method regardless of the given problem contexts. The results of this study showed that students were able to understand equivalence, transform using equivalence, and use generalizable methods. This study is expected to highlight the close connection between fraction and algebraic thinking, and to suggest implications for developing algebraic thinking when to deal with fraction operations.

• Tunnel and Underground Space
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• v.12 no.2
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• pp.99-106
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• 2002

To use the early measured data of tunnel deformation in but analysis, the relationship between these values find final deformation data were studied. Panet\`s exponential and fraction equations successfully approximate the convergence of the hard rock tunnels. Measured deformation data of ID location, $U_{1D}$ show that they can be lilted to linear equations but should not be used to estimate potential deformation before measurement, $C_{0}$. Early measured data $U_{1D}$ $U_{2D}$ , and final deformation $ U_{L}$ showed linear correlations. It proved that estimated data of final deformation from early measured ones can be used as input parameters for back analysis.

• Journal of Korean Tunnelling and Underground Space Association
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• v.15 no.3
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• pp.357-373
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• 2013

In this paper, a back analysis program for analyzing the behavior of tunnel-ground system and evaluating the material properties and tunnel design parameters was developed. This program was designed to be able to implement the back analysis of underground structure by combination of using FLAC and optimized algorithm as direct method. In particular, Rosenbrock method which is able to do direct search without obtaining differential coefficient was adopted for the back analysis algorithm among optimization methods. This back analysis program was applied to the site to evaluate the design parameters. The back analysis was carried out using field measurement results from 5 sites. In the course of back analysis, nonlinear regression analysis was carried out to identify the optimum function of the measured ground displacement. Exponential function and fractional function were used for the regression analysis and total displacement calculated by optimum function was used as the back analysis input data. As a result, displacement recalculated through the back analysis using measured displacement of the structure showed 4.5% of error factor comparing to the measured data. Hence, the program developed in this study proved to be effectively applicable to tunnel analysis.

• 한국지구과학회:학술대회논문집
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• 2010.04a
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• pp.74-76
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• 2010

영동지방은 서쪽으로는 태백산맥이 남북으로 위치해 있고 동쪽으로 동해와 인접해 있는 지리적인 위치로 전 계절에 걸쳐 지역 특성에 따른 국지적인 기상 현상이 많이 발생하고 있다. 특히, 대설은 영동지방의 기후 특징 중 대표적이라 할 수 있다. 대설 일수가 많고 강설량이 많은 영동지방의 강릉과 속초, 그리고 울릉도는 연 강수량에서 겨울철(12월~2월) 강수량이 각각 약 10%와 20% 이상을 차지하고 있는데 이는 우리나라 다른 지역의 5% 내외에 비하면 매우 높은 것이다. 이 지역의 강설 특징은 좁은 지리적 범위에 국한되어 나타나는 좁고 강한 강수역과 지역적으로 커다란 변화를 보이는 적설량과 강설 일수이다. 해안선으로부터 산맥의 분수계까지의 거리가 중요한 역할을 하고 있으며, 이러한 복잡한 지역에서의 강설의 발생과 강설량의 분포를 이해하기 위해서는 강설의 패턴을 분류하여 연구하는 것이 매우 중요하다. 본 연구에서는 cP 확장 시 영동지방의 강설 패턴을 하층 대류권의 바람장에 따라 산악 강설 패턴, 한기-해안 강설 패턴, 난기-해안 강설 패턴으로 분류하였다. 또한, 각 강설 패턴에 대한 종관적인 대기구조의 특성을 파악한 후 3차원 분석시스템을 이용하여, 2008년 12월 21일부터 22일까지 영동지방에 내린 대설을 한기-해안 강설 패턴으로 분류하고 분석하였다.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.55 no.2
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• pp.195-206
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• 2022

The separation of spectrally overlapped broadband echo signals from free-swimming Japanese needlefish Hypohamphus sajori using the fractional Fourier transform (FrFT) was investigated. The broadband echo signals were measured over frequency ranges of 40-80 and 110-220 kHz. The overlapped echo signals were separated after eliminating noise signals in the smoothed pseudo-Wigner-Ville distribution domain. The echo signal from a 40 mm WC sphere suspended just below a chirp transducer was used to calibrate the broadband of the chirp echo sounder and estimate the frequency dependence of target strength for the separated echo signals. The experimental results show that the proposed FrFT method can analyze the time-frequency image of broadband echo signals from free-swimming individual fish effectively and can be used as a quantitative tool for extracting the acoustic features used for fish species identification.