• School Mathematics
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• v.6 no.3
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• pp.267-281
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• 2004

The purpose of this study is to understand Preservice elementary teachers' knowledge about multiplication of fractions by focusing on their computation abilities, understanding of meanings, generating appropriate problem contexts and representations. A total of 115 preservice elementary teachers participated in the present study. The results of this study indicated that most of preservice elementary teachers have little difficulty in computing multiplication of fractions for right answers, but they have big difficulty in understanding meanings and generating appropriate problem contexts for multiplication of fractions when the multiplier is not an integer, called 'multiplier effect.' Likewise, the rate of appropriate representations surprisingly decreased for multiplication of fractions when the multiplier is not an integer. The findings also point out that an ability to make problem contexts is highly correlated with representations and meanings. This study implies that teacher education programs need to improve preservice elementary teachers' profound understanding of elementary mathematics in order to fundamentally improve the quality of teaching practices in classrooms.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.6
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• pp.1083-1091
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• 2017

This paper describes a design of cryptographic processor supporting 224-bit elliptic curves over prime field defined by NIST. Scalar point multiplication that is a core arithmetic function in elliptic curve cryptography(ECC) was implemented by adopting the modified Montgomery ladder algorithm. In order to eliminate division operations that have high computational complexity, projective coordinate was used to implement point addition and point doubling operations, which uses addition, subtraction, multiplication and squaring operations over GF(p). The final result of the scalar point multiplication is converted to affine coordinate and the inverse operation is implemented using Fermat's little theorem. The ECC processor was verified by FPGA implementation using Virtex5 device. The ECC processor synthesized using a 0.18 um CMOS cell library occupies 2.7-Kbit RAM and 27,739 gate equivalents (GEs), and the estimated maximum clock frequency is 71 MHz. One scalar point multiplication takes 1,326,985 clock cycles resulting in the computation time of 18.7 msec at the maximum clock frequency.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.8
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• pp.1172-1179
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• 2022

This paper describes a design of point scalar multiplier for public-key cryptography based on binary Edwards curves (BEdC). For efficient implementation of point addition (PA) and point doubling (PD) on BEdC, projective coordinate was adopted for finite field arithmetic, and computational performance was improved because only one inversion was involved in point scalar multiplication (PSM). By applying optimizations to hardware design, the storage and arithmetic steps for finite field arithmetic in PA and PD were reduced by approximately 40%. We designed two types of point scalar multipliers for BEdC, Type-I uses one 257-b×257-b binary multiplier and Type-II uses eight 32-b×32-b binary multipliers. Type-II design uses 65% less LUTs compared to Type-I, but it was evaluated that it took about 3.5 times the PSM computation time when operating with 240 MHz. Therefore, the BEdC crypto core of Type-I is suitable for applications requiring high-performance, and Type-II structure is suitable for applications with limited resources.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.3
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• pp.270-276
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• 2018

This paper presents a low area 256-point pipelined FFT architecture, especially for IEEE 802.16a WiMAX systems. Radix-24 algorithm and single-path delay feedback (SDF) architecture are adopted in the design to reduce the complexity of twiddle factor multiplication. A new cascade canonical signed digit (CSD) complex multipliers are proposed for twiddle factor multiplication, which has lower area and less power consumption than conventional complex multipliers composed of 4 multipliers and 2 adders. Also, the proposed cascade CSD multipliers can remove look-up table for storing coefficient of twiddle factors. In hardware implementation with Cyclone 10LP FPGA, it is shown that the proposed FFT design method achieves about 62% reduction in gate count and 64% memory reduction compared with the previous schemes.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.588-592
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• 2004

Scalar multiplication is to compute $textsc{k}$P when an integer $textsc{k}$ and an elliptic curve point f are given. As a general method to accelerate scalar multiplication, Agnew, Mullin and Vanstone proposed to use $textsc{k}$'s with fixed Hamming weights. We suggest a new method that uses $textsc{k}$'s with fixed signed Hamming weights and show that this method is more secure.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.523-533
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• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.477-484
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• 2020

The control rod drive mechanism needs to be debugged after reactor fresh fuel loading. It is of great importance to monitor the subcriticality of this process accurately. A modified method was applied to the subcriticality monitoring process, in which only a single control rod cluster was fully withdrawn from the core. In order to correct the error in the results obtained by Neutron Source Multiplication Method, which is based on one point reactor model, Monte Carlo neutron transport code was employed to calculate the fission neutron distribution, the iterated fission probability and the neutron flux in the neutron detector. This article analyzed the effect of a coarse mesh and a fine mesh to tally fission neutron distributions, the iterated fission probability distributions and to calculate correction factors. The subcriticality before and after modification is compared with the subcriticality calculated by MCNP code. The modified results turn out to be closer to calculation. It's feasible to implement the modified NSM method in large local reactivity addition process using Monte Carlo code based on 3D model.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.683-689
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• 2007

Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

• ETRI Journal
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• v.43 no.4
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• pp.684-693
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• 2021

This paper presents a low-cost two-stage approximate multiplier for bfloat16 (brain floating-point) data processing. For cost-efficient approximate multiplication, the first stage implements Mitchell's algorithm that performs the approximate multiplication using only two adders. The second stage adopts the exact multiplication to compensate for the error from the first stage by multiplying error terms and adding its truncated result to the final output. In our design, the low-cost multiplications in both stages can reduce hardware costs significantly and provide low relative errors by compensating for the error from the first stage. We apply our approximate multiplier to the convolutional neural network (CNN) inferences, which shows small accuracy drops with well-known pre-trained models for the ImageNet database. Therefore, our design allows low-cost CNN inference systems with high test accuracy.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.1
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• pp.143-152
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• 2012

In this paper hardware implementation of GF($2^{191}$) elliptic curve cryptographic coprocessor which supports 7 operations such as scalar multiplication(kP), Menezes-Vanstone(MV) elliptic curve cipher/decipher algorithms, point addition(P+Q), point doubling(2P), finite-field multiplication/division is described. To meet structure resistant against simple power analysis, the ECC processor adopts the Montgomery scalar multiplication scheme which main loop operation consists of the key-independent operations. It has operational characteristics that arithmetic units, such GF_ALU, GF_MUL, and GF_DIV, which have 1, (m/8), and (m-1) fixed operation cycles in GF($2^m$), respectively, can be executed in parallel. The processor has about 68,000 gates and its simulated worst case delay time is about 7.8 ns under 0.35um CMOS technology. Because it has about 320 kbps cipher and 640 kbps rate and supports 7 finite-field operations, it can be efficiently applied to the various cryptographic and communication applications.