• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.399-406
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• 2024

We point out an error appeared in the paper of Yuan et al. [3] and present a correction of their result under a more general assumption. Moreover, we discuss the validity of the conditions imposed on the sequences of error terms.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.301-315
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• 2024

Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.645-658
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• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

• Korean Journal of Remote Sensing
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• v.10 no.2
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• pp.133-160
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• 1994

In this paper, we propose a comprehensive geometric correction algorithm of Along Track Scanning Radiometer(ATSR) images. The procedure consists of two cascaded modules; precorrection and fine co-location. The pre-correction algorithm is based on the navigation model which was derived in mathematical forms. This model was applied for correction raw(un-geolocated) ATSR images. The non-systematic geometric errors are also introduced as the limitation of the geometric correction by this analytical method. A fast and automatic algorithm is also presented in the paper for co-locating nadir and forward views of the ATSR images by using a binary cross-correlation matching technique. It removes small non-systematic errors which cannot be corrected by the analytic method. The proposed algorithm does not require any auxiliary informations, or a priori processing and avoiding the imperfect co-registratio problem observed with multiple channels. Coastlines in images are detected by a ragion segmentation and an automatic thresholding technique. The matching procedure is carried out with binaty coastline images (nadir and forward), and it gives comparable accuracy and faster processing than a patch based matching technique. This technique automatically reduces non-systematic errors between two views to .$\pm$ 1 pixel.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.31-49
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• 2009

Utilizing the mathematical materials in elementary mathematics education is known to increase the learners' creativity and interests for mathematics. Although the effects of mathematical materials have been frequently researched, a practical plan and a process to utilize the mathematical materials has been rarely researched. The dependence on the mathematical materials is tested by the students' responses to the mathematical problems in the class that allowed to use mathematical materials. The activities in the text book are reorganized to seven chapters for utilizing the mathematical materials. The dependence on the mathematical materials when solving the mathematical problems is investigated by the textbook, students' answers, and handouts. The conclusions of this study are: First of all, the activities using mathematical materials are reorganized within the mathematics education curriculum. The high interests are also investigated in all the learning level of learners. Second, the learners in the high learning level use the mathematical materials for their needs and the correction of their mistakes. The dependence on mathematical materials is lowest compared to the other level learners. Third, the learners in the mid learning level also use the mathematical materials for their needs and their mistakes, but are often confused when utilizing the materials. Fourth, the learners in the low learning level show their interests, and enthusiasm in the mathematical materials themselves. Their interests help to solve mathematical problems. The dependence on the materials is higher than the other level learners, but the dependence is not shown only for the low level learners.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.117-133
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• 2013

Mathematical misconception is one of the big obstacles of the underachieving students to learn mathematics correctly. This study aims to develop the instruction materials for secondary school students who are underachieving in mathematics to reduce the occurrence of the misconception and to help them to build the correct concept in the mathematical learning. Before developing the material, we tried to collect the misconception cases occurring in common mathematics lesson. This materials tries to provide key educational contents for mathematics teachers who is responsible for teaching underachieving student and help them to creative interesting ideas for lessons. The materials could be used not only as an teaching materials for underachieving students or students with the misconceptions, but also could be used as training materials for mathematics teachers.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1543-1546
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• 2008

The purpose of this study was to investigate factors affecting the change of tibial posterior slope and introduce a mathematical model which calculate, through 3-dimensional analysis of the proximal tibia, how the angle of the opening wedge along the anteromedial tibial cortex influences the tibial posterior slope and valgus correction when performing a medial open wedge osteotomy. This mathematical model with navigation system can be guidelines which provide surgeons on preoperative and intraoperative measurements to maintain or correct the tibial slope and to obtain the desired valgus correction of the lower limb during an opening wedge osteotomy.

• East Asian mathematical journal
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• v.30 no.4
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• pp.451-474
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• 2014

The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.59-69
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• 2009

The element reduction of a multiset S is to reduce the number of repetitions of an element in S by a predetermined number. Privacy-preserving element reduction of a multiset is an important tool in private computation over multisets. It can be used by itself or by combination with other private set operations. Recently, an efficient privacy-preserving element reduction method was proposed by Kissner and Song [7]. In this paper, we point out a mathematical flaw in their polynomial representation that is used for the element reduction protocol and provide its correction. Also we modify their over-threshold set-operation protocol, using an element reduction with the corrected representation, which is used to output the elements that appear over the predetermined threshold number of times in the multiset resulting from other privacy-preserving set operations.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.469-473
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• 2013

Let G = (V, E) be a graph and k be a positive integer. A $k$-dominating set of G is a subset $S{\subseteq}V$ such that each vertex in $V{\backslash}S$ has at least $k$ neighbors in S. A Roman $k$-dominating function on G is a function $f$ : V ${\rightarrow}$ {0, 1, 2} such that every vertex ${\upsilon}$ with $f({\upsilon})$ = 0 is adjacent to at least $k$ vertices ${\upsilon}_1$, ${\upsilon}_2$, ${\ldots}$, ${\upsilon}_k$ with $f({\upsilon}_i)$ = 2 for $i$ = 1, 2, ${\ldots}$, $k$. In the paper titled "Roman $k$-domination in graphs" (J. Korean Math. Soc. 46 (2009), no. 6, 1309-1318) K. Kammerling and L. Volkmann showed that for any graph G with $n$ vertices, ${{\gamma}_{kR}}(G)+{{\gamma}_{kR}(\bar{G})}{\geq}$ min $\{2n,4k+1\}$, and the equality holds if and only if $n{\leq}2k$ or $k{\geq}2$ and $n=2k+1$ or $k=1$ and G or $\bar{G}$ has a vertex of degree $n$ - 1 and its complement has a vertex of degree $n$ - 2. In this paper we find a counterexample of Kammerling and Volkmann's result and then give a correction to the result.