• School Mathematics
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• v.12 no.3
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• pp.411-424
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• 2010

The fractional concept consists of various meaning, so that it is difficult to understand in primary school mathematics. In this article, we intend to analyze the cognition of 54 pre-service elementary teachers about the operations of partitioning and iterating that are based on Steffe's fraction schemes. The following fraction problem is used in this analysis: If the bar $\Box$ represent 3/8, then create a bar that is equivalent to 4/3. In our analysis, the 43% of pre-service elementary teachers can be well to treat the operations of partitioning and iteration. The 33% are use the equivalent fractions. But the 19% is not good. From the our analysis, it is important that pre-service elementary teachers must be have experimental(operational) thinking as the science education. And in this study we apply the operations of partitioning and iterating to the fraction activity of textbooks.

• School Mathematics
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• v.19 no.1
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• pp.59-75
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• 2017

This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.

• The Mathematical Education
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• v.62 no.4
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• pp.457-471
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• 2023

Measurement is an imperative content area of early elementary mathematics, but it is reported that students' understanding of units in measurement situations is insufficient despite its importance. Therefore, this study examined lower-grade elementary students' quantitative reasoning of units in length measurement by identifying the levels of reasoning of units. For this purpose, we collected and analyzed the responses of second-grade elementary school students who engaged in a set of length measurement tasks using an open number line in terms of unitizing, iterating, and partitioning. As a result of the study, we categorized students' quantitative reasoning of unit levels into four levels: Iterating unit one, Iterating a given unit, Relating units, and Transforming units. The most prevalent level was Relating units, which is the level of recognizing relationships between units to measure length. Each level was illustrated with distinct features and examples of unit reasoning. Based on the results of this study, a personalized plan to the level of unit reasoning of students is required, and the need for additional guidance or the use of customized interventions for students with incomplete unit reasoning skills is necessary.

• Journal of Korea Multimedia Society
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• v.4 no.4
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• pp.234-332
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• 2001

For a method improving fractal image segmentation which is a new application of fractal image coding, YST scheme have proposed an image segmentation scheme using labeling based on periodic points of pixel transformation and error-correction of labels by iterating fractal transformation. The scheme generates the high quality segmentation, however, it has the redundancy in the process of labeling and correction of labels. To solve this problem, we propose a labeling algorithm based on orbit of pixel transformation and restricted condition on iterating process of fractal transformation.

• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.5
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• pp.473-481
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• 2013

A fractional folding analog-to-digital converter (ADC) with a novel arithmetic digital encoding technique is discussed. In order to reduce the asymmetry errors of the boundary conditions for the conventional folding ADC, a structure using an odd number of folding blocks and fractional folding rate is proposed. To implement the fractional technique, a new arithmetic digital encoding technique composed of a memory and an adder is described. Further, the coding errors generated by device mismatching and other external factors are minimized, since an iterating offset self-calibration technique is adopted with a digital error correction logic. A prototype 8-bit 1GS/s ADC has been fabricated using an 1.2V 0.13 um 1-poly 6-metal CMOS process. The effective chip area is $2.1mm^2$(ADC core : $1.4mm^2$, calibration engine : $0.7mm^2$), and the power consumption is 88 mW. The measured SNDR is 46.22 dB at the conversion rate of 1 GS/s. Both values of INL and DNL are within 1 LSB.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.1
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• pp.137-147
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• 2013

In this paper, an 1.2V 8b 1GS/s A/D Converter(ADC) based on a folding architecture with a resistive interpolation technique is described. In order to overcome the asymmetrical boundary-condition error of conventional folding ADCs, a novel scheme with an odd number of folding blocks and a fractional folding rate are proposed. Further, a new digital encoding technique with an arithmetic adder is described to implement the proposed fractional folding technique. The proposed ADC employs an iterating offset self-calibration technique and a digital error correction circuit to minimize device mismatch and external noise The chip has been fabricated with a 1.2V 0.13um 1-poly 6-metal CMOS technology. The effective chip area is $2.1mm^2$ (ADC core : $1.4mm^2$, calibration engine : $0.7mm^2$) and the power dissipation is about 350mW including calibration engine at 1.2V power supply. The measured result of SNDR is 46.22dB, when Fin = 10MHz at Fs = 1GHz. Both the INL and DNL are within 1LSB with the self-calibration circuit.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.8 no.3
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• pp.87-92
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• 2008

In this paper, certain scaling functions are generated using the dyadic subband tree structure and applied to a time-hopping, pulse position modulation, ultra-wideband (TH-PPM UWB) system. Scaling functions can be obtained by iterating a lowpass filter at each level using a critically sampled dyadic tree. The performance of the TH-PPM UWB system employing scaling functions as the mono-cycle waveform is evaluated through computer simulations in a Rayleigh fading environment.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2827-2830
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• 2003

Tele manipulator is distingushed from industrial robot by iterating same specified work. Manipulator operator is included in control loop for controlling the telemanipulator because he decide directly during the work and order controllabily reducing the modelling error of telemanipulator which depend on the PID controller. But position-force control method of bidirectional control impose unsafety of vibiration and Analytic Hierachy Method can stabilize for reducing nonlinear modelling error by expert operator because of transformation empirical control rule to linear model.

• East Asian mathematical journal
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• v.31 no.5
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• pp.635-652
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• 2015

It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.