• School Mathematics
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• v.11 no.4
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• pp.745-771
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• 2009

To acquire the hints of the development of children's multiplication strategies, this study tried to find the differences between the students who learned multiplication and the students who didn't. And we also tried to explore their acquired computational resources. As a result, we confirm that there is a certain direction on the development of children's multiplication strategies according to their grades and the level of acquirement of mathematical knowledge. Moreover, we comprehend that commutative law is an important part of the strategies on two-digit multiplication and that acquisition of the computational resources must precede the learning of multiplication strategies. In the end part, this article proposes a new taxonomy of strategies for multiplication. To support our proposal, we integrated the prior researches with our findings.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.59-72
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• 2007

There are three kinds of order of instruction in mathematics, that is, historical order, theoretical organization and lecturing organization-order. Simply speaking, each lecturing organization-order is a combination of two preceding orders. The problem is how to combine between them. In a recent paper, we concretely considered this problem for the case of the concept of angle. The present paper analogously discuss with the concept of vectors. To begin with, we investigate theoretical organization and historical order of the concept of vectors as materials for the construction of its lecturing organization-order. It enables us to establish 4 stages in historical order of the concept of vectors proper to its theoretical organization. As a consequence, we suggest several criteria and forms for constructing its lecturing organization-order.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.77-105
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• 2014

Medical imaging techniques have evolved to expand our ability to visualize new contrast information of electrical, optical, and mechanical properties of tissues in the human body using noninvasive measurement methods. In particular, electrical tissue property imaging techniques have received considerable attention for the last few decades since electrical properties of biological tissues and organs change with their physiological functions and pathological states. We can express the electrical tissue properties as the frequency-dependent admittivity, which can be measured in a macroscopic scale by assessing the relation between the time-harmonic electric field and current density. The main issue is to reconstruct spectroscopic admittivity images from 10 Hz to 1 MHz, for example, with reasonably high spatial and temporal resolutions. It requires a solution of a nonlinear inverse problem involving Maxwell's equations. To solve the inverse problem with practical significance, we need deep knowledge on its mathematical formulation of underlying physical phenomena, implementation of image reconstruction algorithms, and practical limitations associated with the measurement sensitivity, specificity, noise, and data acquisition time. This paper discusses a number of issues in electrical tissue property imaging modalities and their future directions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.11
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• pp.5625-5641
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• 2017

Certificateless public key cryptography resolves the certificate management problem in traditional public key cryptography and the key escrow problem in identity-based cryptography. In recent years, some good results have been achieved in speeding up the computation of bilinear pairing. However, the computation cost of the pairing is much higher than that of the scalar multiplication over the elliptic curve group. Therefore, it is still significant to design cryptosystem without pairing operations. A multi-signer universal designated multi-verifier signature scheme allows a set of signers to cooperatively generate a public verifiable signature, the signature holder then can propose a new signature such that only the designated set of verifiers can verify it. Multi-signer universal designated multi-verifier signatures are suitable in many different practical applications such as electronic tenders, electronic voting and electronic auctions. In this paper, we propose a certificateless multi-signer universal designated multi-verifier signature scheme and prove the security in the random oracle model. Our scheme does not use pairing operation. To the best of our knowledge, our scheme is the first certificateless multi-signer universal designated multi-verifier signature scheme.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.10B
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• pp.876-884
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• 2008

In this paper, we propose an asynchronous MAC protocol to minimize energy usage and to maximize data throughput for a wireless sensor network in multi channel environments. Our proposed SPMC-MAC (Slim Preamble Multi-Channel Media Access Control) adopts the preamble sliming mechanism proposed in [6] that takes advantage of the knowledge about the wakeup time of the receiver node. The preamble contains the receiver's ID and a randomly selected channel ID for data communication, and it is transmitted over a dedicated common channel. The power control has the benefit of keeping an appropriate number of nodes with the communication range, resulting in reduced collision and interference. We compare our SPMC-MAC and X-MAC extensively in terms of energy consumption and throughput using mathematical analysis and simulation.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.506-514
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• 2008

This paper presents an intelligent model; named as free model, approach for a closed-loop system identification using input and output data and its application to design a power system stabilizer (PSS). The free model concept is introduced as an alternative intelligent system technique to design a controller for such dynamic system, which is complex, difficult to know, or unknown, with input and output data only, and it does not require the detail knowledge of mathematical model for the system. In the free model, the data used has incremental forms using backward difference operators. The parameters of the free model can be obtained by simultaneous perturbation stochastic approximation (SPSA) method. A linear transformation is introduced to convert the free model into a linear model so that a conventional linear controller design method can be applied. In this paper, the feasibility of the proposed method is demonstrated in a one-machine infinite bus power system. The linear quadratic regulator (LQR) method is applied to the free model to design a PSS for the system, and compared with the conventional PSS. The proposed SPSA-based LQR controller is robust in different loading conditions and system failures such as the outage of a major transmission line or a three phase to ground fault which causes the change of the system structure.

• Journal of Veterinary Clinics
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• v.27 no.4
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• pp.427-434
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• 2010

Correlation is a technique used to measure the strength or the degree of closeness of the linear association between two quantitative variables. Common misuses of this technique are highlighted. Linear regression is a technique used to identify a relationship between two continuous variables in mathematical equations, which could be used for comparison or estimation purposes. Specifically, regression analysis can provide answers for questions such as how much does one variable change for a given change in the other, how accurately can the value of one variable be predicted from the knowledge of the other. Regression does not give any indication of how good the association is while correlation provides a measure of how well a least-squares regression line fits the given set of data. The better the correlation, the closer the data points are to the regression line. In this tutorial article, the process of obtaining a linear regression relationship for a given set of bivariate data was described. The least square method to obtain the line which minimizes the total error between the data points and the regression line was employed and illustrated. The coefficient of determination, the ratio of the explained variation of the values of the independent variable to total variation, was described. Finally, the process of calculating confidence and prediction interval was reviewed and demonstrated.

• Journal of the Korea Society of Computer and Information
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• v.11 no.1 s.39
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• pp.11-18
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• 2006

The logical analysis of data(LAD) is a Boolean-logic based data mining tool. A critical step in analyzing data by LAD is the pattern generation stage where useful knowledge and hidden structural information in data is discovered in the form of patterns. A conventional method for pattern generation in LAD is based on term enumeration that renders the generation of higher degree patterns practically impossible. In this paper, we present a novel optimization-based pattern generation methodology and propose two mathematical programming models, a mixed 0-1 integer and linear programming (MILP) formulation and a well-studied set covering problem (SCP) formulation for the generation of optimal and heuristic patterns, respectively. With benchmark datasets, we demonstrate the effectiveness of our models by automatically generating with ease patterns of high complexity that cannot be generated with the conventional approach.

• Education of Primary School Mathematics
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• v.19 no.4
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• pp.291-311
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• 2016

Researcher was interested in circumference of plane figure problem. Meanwhile, researcher found some difficulty in solving circumference problem with stair like plane figure. In this phenomenon, researcher felt to find the teaching method to help students with circumference of plane figure. For this, researcher analyzed many students' recording paper and had interview with few students. As a result researcher found that students had some difficulty in recognizing essential information and prior knowledge base was not made up. From these responses, this paper proposed teaching method for helping students about circumference related problems.

• JSTS:Journal of Semiconductor Technology and Science
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• v.14 no.4
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• pp.391-406
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• 2014

The performance of General-Purpose computation on Graphics Processing Units (GPGPU) is heavily dependent on the memory access behavior. This sensitivity is due to a combination of the underlying Massively Parallel Processing (MPP) execution model present on GPUs and the lack of architectural support to handle irregular memory access patterns. Application performance can be significantly improved by applying memory-access-pattern-aware optimizations that can exploit knowledge of the characteristics of each access pattern. In this paper, we present an algorithmic methodology to semi-automatically find the best mapping of memory accesses present in serial loop nest to underlying data-parallel architectures based on a comprehensive static memory access pattern analysis. To that end we present a simple, yet powerful, mathematical model that captures all memory access pattern information present in serial data-parallel loop nests. We then show how this model is used in practice to select the most appropriate memory space for data and to search for an appropriate thread mapping and work group size from a large design space. To evaluate the effectiveness of our methodology, we report on execution speedup using selected benchmark kernels that cover a wide range of memory access patterns commonly found in GPGPU workloads. Our experimental results are reported using the industry standard heterogeneous programming language, OpenCL, targeting the NVIDIA GT200 architecture.