• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.521-539
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• 2016

The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.10C
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• pp.1460-1468
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• 2004

In this paper, we developed a low-area and low-cost SIMD MAC/MAS(Single Instruction Multiple Data Multiply and ACcumulate/Multiply And Subtract) for multimedia that is used much in real life. We compared the result of this research with a previously developed more large and high performance SIMD MAC/MAS. This paper is consist of 5 parts, which are an introduction, the contents of designing SIMD MAC/MAS hardware, a special qualities for previous works, the result of synthesis and conclusion. The design result reduced by size 32% of whole hardware than 64 bit SIMD MAC/MAS block of designed for high performance. This improved ISA (Instruction Set Architecture) to be suitable to embedded DSP(Digital Signal Processor), and shortened bit range of 64-bit data to 32-bit and implement more optimally.

• 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 electromagnetic engineering and science
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• v.6 no.2
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• pp.110-116
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• 2006

A reflective array type surface acoustic wave(SAW) dispersive delay line(DDL) with high time-bandwidth at the V/UHF-band is designed and fabricated for compressive receiver applications. This type of the SAW DDL has the properties of the relative bandwidth of 20 %, the time delay of 49.89 usec, the insertion loss of 38.5 dB and the side lobe rejection of 39 dB. In comparison with a commercial SAW DDL, the insertion loss, amplitude ripple and side lobe rejection are improved by $1.5dB{\pm}0.6dB$ and 4 dB respectively. Using the fabricated SAW DDL, the prototype of the compressive receiver is developed. It is composed of RF converter, fast tunable LO, chirp LO, A/D converter, signal processing unit and control unit. This prototype system shows a fine frequency resolution of below 30 kHz with high scan rate.

• Smart Structures and Systems
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• v.21 no.4
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• pp.469-477
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• 2018

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.167.1-167.1
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• 2016

The interaction between adsorbed water and hydrogen on metallic surfaces is important for fundamental understanding of heterogeneous catalysis and electrode surface reactions in acidic environment. Here, we explore a long-standing question of whether hydronium ion can exist or not on a Pt surface coadsorbed with atomic hydrogen and water. Studies based on mass spectrometry and infrared spectroscopy show clear evidence that hydrogen atoms are converted into hydrated protons on a Pt(111) surface. The preferential structures of hydrated protons are identified as multiply hydrated $H_5O_2{^+}$ and $H_7O_3{^+}$ species rather than as hydronium ions. The multiply hydrated protons may be regarded as two dimensional zundel ($H_5O_2{^+}$) and Eigen cation ($H_7O_3{^+}$) in water-metal interface. These surface-bound hydrated protons may be key surface intermediates of the electrochemical interconversion between adsorbed hydrogen atoms and solvated protons.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2496-2498
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• 2005

The transmission characteristics of multiply cascaded phase-shifted long-period fiber gratings (LPFGs) will be investigated theoretically and experimentally. Their passband can be changed by increasing the number of ${\pi}$ -shifted LPFGs. When two ${\pi}$ -shifted LPFGs with different grating lengths are cascaded in series, the bandwidth of the rejection band and passband can be controlled by the pristine characteristics of two gratings.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.860-863
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• 2002

Realizations of multirate converters are proposed using periodically time-varying (PTV) structures. By exploiting the computational redundancy of the filtering operation in a multirate filter, it is possible to implement the filter with much less hardware. In the proposed implementations, several coefficients time-share in a periodic fashion the hardware of one multiply-and-add. Therefore, each multiply-and-add circuit performs different coefficient scalings at different time instants within a period. Compared to the direct form realization, the proposed realizations reduce the hardware of an interpolator and a decimator by a factor of approximately U and M, respectively, while retaining the same processing speed, where U and M are the upsampling and downsampling factors, respectively. The approach can be used to obtain realizations for sampling rate conversion by a rational factor of U/M, where U and M are relatively prime, in which case hardware reduction by a factor of approximately UM can be achieved.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.349-352
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• 2000

In this paper, a SIMD 64bit MAC (Multiply -Accumulate) unit is designed. It is composed of two 32bit MAC unit which supports SIMD 16bit operations. As a result, It can process two 32bit MAC operations or four 16bit operations in one cycle. Proposed MAC unit is described in Verilog HDL. After functional verification is performed, MAC unit is synthesized and optimized with 0.35$\mu\textrm{m}$ standard cell library. The synthesis result shows that this MAC unit can operate at 80㎒ of clock frequency in 85$^{\circ}C$, 3.0V, worst case process and 125㎒ of clock frequency at 25$^{\circ}C$, 3.3V, typical case process. It achieves 320Mops of performance, and is suitable for embedded DSP processors.

• Advances in Computational Design
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• v.5 no.3
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• pp.277-289
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• 2020

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.