• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.10a
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• pp.165-168
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• 2001

It is possible to classify image data into two types according to the internal representation: one is bitmap, the other is vector. A bitmap image is represented by the two dimensional pixels whereas a vector image is represented by mathematical functions to draw vector objects such as line, rectangle and circle on the two or three dimensional space. So it is necessary for users to use a individual application program for each different image. In this paper, we present a method for designing and implementation of image editing tool based on combining of bitmap and vector image.

• Journal of Navigation and Port Research
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• v.36 no.7
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• pp.571-575
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• 2012

Berthing and unberthing maneuver is essential work for marine pilots and securing the safety against risks during the maneuver is more important than anything else. Moreover, the maneuvering environment in ports and harbors has changed rapidly and got worse due to development of a new port, the advent of a new type or large-sized ship, and the rapid increase in harbor traffic. As one of measures taken to cope with such changes in the maneuvering environment and for each pilot to improve his own maneuvering ability, this paper developed laptop-based ship-handling simulator which is readily available anytime and anywhere. This paper is to develop a conning display for ship's maneuvering and electronic chart based display widely used nowadays to represent a model ship's movement. The displays were arranged appropriately considering pilot age, easy handling by mouse, using a maximum screen, proper arrangement of rudder, engine, thruster, tug etc and representation of information. Up to now thirteen (13) model ships were developed based on real-ship, whose mathematical model is Japanese MMG & pilots' low speed maneuver.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1269-1286
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• 2017

This paper presents a newly developed resonance self-shielding method based on Tone's method in $APOLLO3^{(R)}$ for fast and thermal reactor calculations. The new method is based on simplified models, the narrow resonance approximation for the slowing down source and Tone's approximation for group collision probability matrix. It utilizes mathematical probability tables as quadrature formulas in calculating effective cross-sections. Numerical results for the ZPPR drawer calculations in 1,968 groups show that, in the case of the double-column fuel drawer, Tone's method gives equivalent precision to the subgroup method while markedly reducing the total number of collision probability matrix calculations and hence the central processing unit time. In the case of a single-column fuel drawer with the presence of a uranium metal material, Tone's method obtains less precise results than those of the subgroup method due to less precise heterogeneous-homogeneous equivalence. The same options are also applied to PWR UOX, MOX, and Gd cells using the SHEM 361-group library, with the objective of analyzing whether this energy mesh might be suitable for the application of this methodology to thermal systems. The numerical results show that comparable precision is reached with both Tone's and the subgroup methods, with the satisfactory representation of intrapellet spatial effects.

• Proceedings of the KOR-KST Conference
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• 2000.02a
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• pp.25-47
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• 2000

In route guidance systems fastest-path routing has typically been adopted because of its simplicity. However, empirical studies on route choice behavior have shown that drivers use numerous criteria in choosing a route. The objective of this study is to develop computationally efficient algorithms for identifying a manageable subset of the nondominated (i.e. Pareto optimal) paths for real-time vehicle routing which reflect the drivers' preferences and route choice behaviors. We propose two pruning algorithms that reduce the search area based on a context-dependent linear utility function and thus reduce the computation time. The basic notion of the proposed approach is that ⅰ) enumerating all nondominated paths is computationally too expensive, ⅱ) obtaining a stable mathematical representation of the drivers' utility function is theoretically difficult and impractical, and ⅲ) obtaining optimal path given a nonlinear utility function is a NP-hard problem. Consequently, a heuristic two-stage strategy which identifies multiple routes and then select the near-optimal path may be effective and practical. As the first stage, we utilize the relaxation based pruning technique based on an entropy model to recognize and discard most of the nondominated paths that do not reflect the drivers' preference and/or the context-dependency of the preference. In addition, to make sure that paths identified are dissimilar in terms of links used, the number of shared links between routes is limited. We test the proposed algorithms in a large real-life traffic network and show that the algorithms reduce CPU time significantly compared with conventional multi-criteria shortest path algorithms while the attributes of the routes identified reflect drivers' preferences and generic route choice behaviors well.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.123-129
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• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.309-322
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• 2024

Identifying algae in water is important for managing algal blooms which have great impact on drinking water supply systems. There have been various microscopic approaches developed for algae classification. Many of them are based on the morphological features of algae. However, there have seldom been mathematical frameworks for comparing the shape of algae, represented as a planar continuous curve obtained from an image. In this work, we describe a recent framework for computing shape distance between two different algae based on the elastic metric and a novel functional representation called the square root velocity function (SRVF). We further introduce statistical procedures for multiple shapes of algae including computing the sample mean, the sample covariance, and performing the principal component analysis (PCA). Based on the shape distance, we classify six algal species in watersheds experiencing algal blooms, including three cyanobacteria (Microcystis, Oscillatoria, and Anabaena), two diatoms (Fragilaria and Synedra), and one green algae (Pediastrum). We provide and compare the classification performance of various distance-based and model-based methods. We additionally compare elastic shape distance to non-elastic distance using the nearest neighbor classifiers.

• School Mathematics
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• v.10 no.4
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• pp.603-623
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• 2008

The purpose of this research was to gain a better understanding of the characteristics of students' mathematical representations using additive strategy in ratio and proportion tasks. The additive strategy is the erroneous one used most often among the strategies reported in solving ratio and proportion tasks. It is a problem solving strategy that preserves the difference from one ratio to another. Students' additive strategies were categorized into four parts: subtracting without considering units of quantities, comparing the numbers that represent the whole subtracted from the part and same part, adding the difference, and subtracting the difference. In order to change from additive strategy to multiplicative strategy, the researcher asked to find out the unit quantity and found the characteristics of students' mathematical notations in the following: Firstly, the students made the number which they wanted by multiplying and adding same numbers. Secondly, they represented the mid-points between natural numbers. Thirdly, they related $a{\div}b$ to decimal number, not $\frac{a}{b}$. Fourthly, they were inclined to divide the larger number with the smaller number without understanding the context of the problem. These results are interpreted as showing that lower level of performance in the dividing operation with the notations of fraction hinders the transformation from additive strategy to multiplicative strategy.

• Communications of Mathematical Education
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• v.38 no.2
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• pp.121-144
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• 2024

This study analyzes how the academic achievement of students in Korea changes as they transition from 4th grade of elementary school to 2nd grade of middle school, considering that the 4th graders in the previous TIMSS cycle become 2nd graders in the next cycle. In particular, this study selects and compares the eight main countries in the TIMSS math evaluation (Korea, Singapore, Taiwan, Japan, USA, UK, Australia, and Russia) to analyze the trend of change in academic achievement of Korean students according to school grade transition. The trend of change in academic achievement of students was analyzed not only overall but also by content area (number, geometry and measurement, data representation (data and probability/data and probability), gender, and regional scale. The analysis focused on the average score and the proportion of students by achievement level. The results of the study are as follows. First, there was no significant change in the average score of Korean students' academic achievement as the school grade transitioned, but the achievement gap widened in terms of the proportion by achievement level. Second, there were differences in students' academic achievement by content area according to school grade transition, and the pattern differed depending on the evaluation cycle. Third, there was a significant gap in students' math academic achievement depending on gender and regional scale of school location. This study reveals that the achievement gap among students in our country widens as they transition between school levels. The gap is found to vary in terms of achievement level, math content area, student gender, and school location. To alleviate these disparities, more substantial research and support are proposed in addition to policy implementation by the government or provincial offices of education.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.213-235
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• 2013

The purpose of this study is to analyze how the teaching activities which used EXCEL influence the specialized high school underachieved students. They have difficulties in making use of various representations for better understanding of function. EXCEL is helpful for learning function because it enables the students to use real life materials in math learning as well as formulates Tabular, Algebraic and Graphical which represent function. Furthermore, the students in specialized high school also have the experience of using EXCEL while studying other subjects. For that reason they have no burdens and fears on using EXCEL in learning activities. Utilizing EXCEL in the classroom gives an expectation that it helps to have interests on studying function and prepare for the next learning in the end. Research classes were conducted in a group of five students who have different hopes of career and a variety of mathematical interests. Though the students couldn't transfer Algebraic to Graphical in the diagnostic evaluation, they could resolve the problem of connections between Graphical, Tabular and Algebraic in the process perspectives, and could also express graphical representation by linking object perspectives with process perspectives. Therefore, they solved the connection problem of Tabular, Algebraic and Graphical in the object perspectives. As a result, the students could make transitions between Algebraic and Graphical in object perspectives through the classes applying EXCEL. Consequently, teaching the students with underachievement utilizing EXCEL enables them to recover their interests on math and it helps them to complete their following curriculum.