• The KIPS Transactions:PartB
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• v.14B no.7
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• pp.541-548
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• 2007

Due to the mathematical convergence property, Simulated Annealing (SA) has been one of the most popular optimization algorithms. However, because of its problem of slow convergence in the practical use, many variations of SA like Fast SA (FSA) have been developed for faster convergence. In this paper, we propose and prove that Greedy SA (GSA) also finds the global optimum in probability in the continuous space optimization problems. Because the greedy selection does not allow the cost to become worse, GSA is expected to have faster convergence than the conventional FSA that uses Metropolis selection. In the computer simulation, the proposed method is shown to have as good performance as FSA with Metropolis selection in the viewpoints of the convergence speed and the quality of the found solution. Furthermore, the greedy selection does not concern the cost value itself but uses only dominance of the costs of solutions, which makes GSA invariant to the problem scaling.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2008.10a
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• pp.297-302
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• 2008

The positioning technology for a moving object is an important and essential component of ubiquitous computing environment and applications, for which Radio Frequency Identification(RFID) has been considered as a core technology. RFID-based positioning system calculates the position of moving object based on k-nearest neighbor(k-nn) algorithm using detected k-tags which have known coordinates and kcan be determined according to the detection range of RFID system. In this paper, RFID-based positioning system determines the position of moving object not using weight factor which depends on received signal strength but assuming that tags within the detection range always operate and have same weight value. Because the latter system is much more economical than the former one. The geometries of tags were determined with considerations in huge buildings like office buildings, shopping malls and warehouses, so they were determined as the line in I-Dimensional space, the square in 2-Dimensional space. In 1-Dimensional space, the optimal detection range is determined as 125% of the tag spacing distance through the analytical and numerical approach. Here, the analytical approach means a mathematical proof and the numerical approach means a simulation using matlab. But the analytical approach is very difficult in 2-Dimensional space, so through the numerical approach, the optimal detection range is determined as 134% of the tag spacing distance in 2-Dimensional space. This result can be used as a fundamental study for designing RFID-based positioning system.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2008.10a
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• pp.270-271
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• 2008

The positioning technology for a moving object is an important and essential component of ubiquitous communication computing environment and applications, for which Radio Frequency IDentification Identification(RFID) is has been considered as also a core technology for ubiquitous wireless communication. RFID-based positioning system calculates the position of moving object based on k-nearest neighbor(k-nn) algorithm using detected k-tags which have known coordinates and k can be determined according to the detection range of RFID system. In this paper, RFID-based positioning system determines the position of moving object not using weight factor which depends on received signal strength but assuming that tags within the detection range always operate and have same weight value. Because the latter system is much more economical than the former one. The geometries of tags were determined with considerations in huge buildings like office buildings, shopping malls and warehouses, so they were determined as the line in 1-Dimensional space, the square in 2-Dimensional space and the cubic in 3-Dimensional space. In 1-Dimensional space, the optimal detection range is determined as 125% of the tag spacing distance through the analytical and numerical approach. Here, the analytical approach means a mathematical proof and the numerical approach means a simulation using matlab. But the analytical approach is very difficult in 2- and 3-Dimensional space, so through the numerical approach, the optimal detection range is determined as 134% of the tag spacing distance in 2-Dimensional space and 143% of the tag spacing distance in 3-Dimensional space. This result can be used as a fundamental study for designing RFID-based positioning system.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1393-1410
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• 2015

An original sensor system based on Fiber Bragg Gratings (FBG) for the strain monitoring of an adaptive wing element is presented in this paper. One of the main aims of the SARISTU project is in fact to measure the shape of a deformable wing for performance optimization. In detail, an Adaptive Trailing Edge (ATE) is monitored chord- and span-wise in order to estimate the deviation between the actual and the desired shape and, then, to allow attaining a prediction of the real aerodynamic behavior with respect to the expected one. The integration of a sensor system is not trivial: it has to fit inside the available room and to comply with the primary issue of the FBG protection. Moreover, dealing with morphing structures, large deformations are expected and a certain modulation is necessary to keep the measured strain inside the permissible measure range. In what follows, the mathematical model of an original FBG-based structural sensor system is presented, designed to evaluate the chord-wise strain of an Adaptive Trailing Edge device. Numerical and experimental results are compared, using a proof-of-concept setup. Further investigations aimed at improving the sensor capabilities, were finally addressed. The elasticity of the sensor structure was exploited to enlarge both the measurement and the linearity range. An optimisation process was then implemented to find out an optimal thickness distribution of the sensor system in order to alleviate the strain level within the referred component.

• Journal of the Korean earth science society
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• v.27 no.6
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• pp.591-605
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• 2006

The purpose of this study is to investigate the relationship between lunar and earth rotation, by quantitatively describing the rotation of lunar configuration which is observed during the lunar diurnal motion. Our research suggests that observation of the lunar diurnal motion could be used as a study topic in the earth science courses. The rotation of the lunar configuration is an apparent phenomenon that can be seen when an observer. standing on the ground. looks at the moon as if the lunar dark configuration rotates on the basis of horizontal line. In spite its competence as a study topic because it is observable by naked eyes, there are only few major textbooks that introduce this phenomenon with regard to the earth rotation. Therefore, this study induced the mathematical principle of the lunar rotation in detail and proposed that this could be developed as a scientific inquiry through practical observation. In addition, an analytical proof and qualitative method of explanation of the lunar reverse rotation were also presented.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.63-80
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• 2006

Along with natural and algebraic languages, schema is a fundamental component of mathematical language. The principal purpose of this present study is to focus on this point in detail. Schema was already in use during Pythagoras' lifetime for making geometrical inferences. It was no different in the case of Oriental mathematics, where traces have been found from time to time in ancient Chinese documents. In schma an idea is transformed into something conceptual through the use of perceptive images. It's heuristic value lies in that it facilitates problem solution by appealing directly to intuition. Furthermore, introducing schema is very effective from an educational point of view. However we should keep in mind that proof is not replaceable by it. In this study, various schemata will be presented from a diachronic point of view, We will show with emaples from the theory of categories, Feynman's diagram, and argand's plane, that schema is an indispensable tool for constructing new knowledge.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.379-398
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• 2011

In learning environment at mathematics education, prove and refute are essential abilities to demonstrate whether and why a statement is true or false. Learning proofs and counter examples within the domain of limit of sequence is important because preservice teacher encounter limit of sequence in many mathematics courses. Recently, a number of studies have showed evidence that pre service and students have problem with mathematical proofs but many research studies have focused on abilities to produce proofs and counter examples in domain of limit of sequence. The aim of this study is to contribute to research on preservice teachers' productions of proofs and counter examples, as participants showed difficulty in writing these proposition. More importantly, the analysis provides insight and understanding into the design of curriculum and instruction that may improve preservice teachers' learning in mathematics courses.

• School Mathematics
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• v.11 no.2
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• pp.261-280
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• 2009

This study was motivated by recognizing the weakness of teaching and learning about the concepts of statements in high school mathematics curriculum. To report the reality of students' understanding about statements, this study investigated the 33 first-year undergraduate students' understanding about the concepts of statements by giving them 22 statement problems. The problems were selected based on the conceptual framework including five types of statement concepts which are considered as the key ideas for understanding mathematical reasoning and proof in college level mathematics. The analysis of the participants' responses to the statement problems found that their understanding about the concepts of prepositions are very limited and extremely based on the instrumental understanding applying an appropriate remembered rule to the solution of a preposition problem without knowing why the rule works. The results from this study will give the information for effective teaching and learning of statements in college level mathematics, and give the direction for the future reforming the unite of statements in high school mathematics curriculum as well.

• Journal of the Korean Geotechnical Society
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• v.33 no.12
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• pp.59-73
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• 2017

Numerical analysis using 3D finite element program (PLAXIS 3D) evaluated the interaction of soil - pile structure under dynamic surface loading. The dynamic p-y curve of the 1-g shaking table experiment by numerical analysis was calculated, and the parametric studies were presented by considering the pile-soil condition, the pile tip condition, and the loading condition. The frequency of 1.4 Hz is almost equal to the natural frequency of the pile - soil system. The p and y values of resonance phenomenon are significantly different from the results of other frequencies. The results can be summarized by a third order polynomial function representing the trend line in the p-y curve. In the case of a single pile, the shape of the dominant curve was found to be an ellipse by mathematical proof. The elliptic equation can be used for the dynamic design or analysis of soil-pile system.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.