• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.119-139
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• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• Journal of Electrochemical Science and Technology
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• v.12 no.2
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• pp.188-203
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• 2021

The specific benefits of the modified films formed on preliminary anodized aluminum, including the versatility of their potential applications impose the need for evaluation of the exploitation reliability of these films. In this aspect, the durability of Cu and Ni modified anodized aluminum oxide (AAO) films on the low-doped AA1050 alloy was assessed through extended exposure to a 3.5% NaCl model corrosive medium. The electrochemical measurements by means of electrochemical impedance spectroscopy (EIS) and potentiodynamic scanning (PDS) after 24 and 720 hours of exposure have revealed that the obtained films do not change their obvious barrier properties. In addition, supplemental analyses of the coatings were performed, in order to elucidate the impact of the AC-deposition of Cu and Ni inside the pores. The scanning electron microscopy (SEM) images have shown that the surface topology is not affected and resembles the typical surface of an etched metal. The subsequent energy dispersive X-ray spectroscopy (EDX) tests have revealed a predominance of Cu in the combined AAO-Cu/Ni layers, whereas additional X-ray photoelectron (XPS) analyses showed that both metals form oxides with different oxidation states due to alterations in the deposition conditions, promoted by the application of AC-polarization of the samples.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.239-247
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• 2022

Let C₀[0, T] denote the Wiener space, the space of continuous functions x(t) on [0, T] such that x(0) = 0. Define a random vector $Z_{\vec{e},k}:C_0[0,\;T] {\rightarrow}{\mathbb{R}}^k$ by $$Z_{\vec{e},k}(x)=({\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;e_1(t)dx(t),\;{\ldots},\;{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^T}\;ek(t)dx(t))$$ where e_j ∈ L₂[0, T] with e_j ≠ 0 a.e., j = 1, …, k. In this paper we study the conditional Fourier-Feynman transform and a conditional convolution product for a cylinder type functionals defined on C0[0, T] with a general vector valued conditioning functions $Z_{\vec{e},k}$ above which need not depend upon the values of x at only finitely many points in (0, T] rather than a conditioning function X(x) = (x(t₁), …, x(t_n)) where 0 < t₁ < … < t_n = T. In particular we show that the conditional Fourier-Feynman transform of the conditional convolution product is the product of conditional Fourier-Feynman transforms.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.285-301
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• 2022

In this paper, we mainly study the random sampling and reconstruction of signals living in the subspace V^p(𝚽, 𝚲) of L^p(ℝ^d), which is generated by a family of molecules 𝚽 located on a relatively separated subset 𝚲 ⊂ ℝ^d. The space V^p(𝚽, 𝚲) is used to model signals with finite rate of innovation, such as stream of pulses in GPS applications, cellular radio and ultra wide-band communication. The sampling set is independently and randomly drawn from a general probability distribution over ℝ^d. Under some proper conditions for the generators 𝚽 = {𝜙_λ : λ ∈ 𝚲} and the probability density function 𝜌, we first approximate V^p(𝚽, 𝚲) by a finite dimensional subspace V^p_N (𝚽, 𝚲) on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in V^p(𝚽, 𝚲) whose energy concentrate on a cube when the sampling size is large enough. Finally, a reconstruction algorithm based on random samples is given for signals in V^p_N (𝚽, 𝚲).

• Research in Mathematical Education
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• v.26 no.2
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• pp.45-61
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• 2023

Number talks as a brief instructional routine benefits students and teachers. In general, the routines consist of four steps- introducing, posing questions, collecting answers, sharing ideas. This paper focuses on the sharing ideas step in which multiple strategies are shared by students because teachers sometimes do not know what to do with these multiple ideas. One way is to support students to engage in comparison given that teachers are expected to support students to compare strategies in number talks. This paper explores whether and how 15 prospective teachers supported students in their practicum classroom to compare different strategies in their enacted number talk. In this paper, 15 videos of number talks enacted by the prospective teachers were collected. Analyzing the videos produced multiple episodes in relation to comparing strategies, including 1) where prospective teachers created pre-conditions for comparison, 2) where they invited students for comparison, 3) where they pressed students to compare, and 4) where they offered their own way to compare. There were two patterns that might limit the potential of having multiple strategies as conditions for comparison. Additionally, this paper found that even though the prospective teachers missed opportunities to support students to compare different strategies, there were two ways for teachers to support students to engage in comparison. These findings can be used for mathematics teacher educators to support prospective teachers.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.257-275
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• 2023

In this study, we designed and implemented a instruction emphasizing mathematical argument for fifth-grade students and analyzed the teaching practices. Through a literature review related to instruction emphasizing mathematical argument, we organized a teaching model of five phases that explain why the general claim that the sum of consecutive odd numbers equals a square number is true: 1) noticing patterns, 2) articulating conjectures, 3) representing through visual model, 4) arguing based on representation, 5) comparing and contrasting. Then, we analyzed the argumentation stream by phases to observe how the instruction emphasizing mathematical argument is implemented in the elementary classroom. Based on the results of this study, we discuss the implications of teaching a mathematical argument in elementary school.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.9
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• pp.387-396
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• 2020

The purpose of this study is to identify the variables of metropolitan and provincial offices of education that affect the academic achievement of unit schools, and to predict how academic achievements dynamically change with the support of offices of education. The results of academic achievement of 606 general high schools in 16 metropolitan and provincial offices of education(rates of attaining more than normal education in Korean, English, and mathematics subjects) were analyzed using a multi-level model and system dynamics. As a result of the analysis, it was confirmed that the provincial and provincial offices of education's efforts to increase the efficiency of local education finance, the efforts to reduce teacher administration, and the facilitation of faculty training were the variables of the provincial and provincial offices of education. In addition, through policy experiments, efforts to revitalize teacher training were the most influential factors in academic achievement of unit schools, followed by efforts to streamline local education finances and to reduce the administrative work of teachers. In order to improve the academic achievement of unit schools, the functions of the metropolitan and provincial offices of education should be strengthened based on the education accountability, and policies need to be established in the mid- to long-term perspective.

• Journal of Engineering Education Research
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• v.8 no.1
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• pp.84-98
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• 2005

This study is on improving the general engineering education for enhancing the quality of engineers at a local engineering school in which the students are not highly qualified for engineering education. Based on the analysis on the current engineering education by asking questions to professors, students and alumni of Hongik College of Science and Engineering, we have set the basic educational philosophy as educating practical engineers and have decided the goals of basic engineering education as changing to student oriented education, enhancing the field adaptation capability, improving the problem solving ability and introducing engineering design courses. For achieving the foregoing goals, we have changed several basic engineering courses. Mathematics, science courses, computer related courses, English, communication skill related courses are strengthened, but general college education courses are reduced. We also have encouraged students to participate the classes actively and study efficiently, think logically and creatively. For the operational details, we have tried to impose less courses to freshmen and sophomores, to impose the prerequisite courses, to activate summer and winter schools. Finally, we have tried to find the ways to support continuous improvement on the basic engineering education.

• Journal of the Korean BIBLIA Society for library and Information Science
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• v.6 no.1
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• pp.133-160
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• 1984

The main purpose of the present study is to survey the major abstracting bulletins of national nature in Korea, to define such problem areas as lacunae, duplicates and limitation in coverage in the abstracting services currently available in Korea, and to make some suggestions for action for improving the abstracting services in the light of general principles and the tradition and situations unique to Korea. The major conclusions reached at this study are summarised as follows: (A) A new abstracting bulletin of general nature covering the whole field needs to be created in each of the following fields where no established abstracting service is available for the outcome of research and development activities in Korea. (1) Language (2) Religion (3) Art (4) Language (5) Literature (6) History (B) A new specialised abstracting bulletin needs to be created in each of the following fields of science where abstracting services limited in coverage are partially available. (a) Statistics (b) Sociology (c) political science (d) Public administration (e) Law (f) Folk lore (g) Military science (2) Pure sciences (a) Mathematics (b) Chemistry (c) Astronomy (d) Geology (e) Mineralogy (f) Life sciences (g) Botany (h) Zoology (3) Applied sciences (a) Agriculture (b) Architectural engineering (c) Mechanical engineering (d) Electrical engineering (e) Chemical engineering (f) Manufacturing industry (g) Domestic science (C) Publication of the abstracting bulletins suggested in (A) and (B) above may be ideally carried on by a qualified learned society established in the respective field. and should be financially supported by the public fund under the provisions of Art. 27 of the Research Promotion Act of 1979. (D) The current practice of adding the author's abstract and keywords to each of the records of the "Doctoral Theses in Humanities and Social Sciences" part of the" Catalogue of Doctoral and Master's Theses Submitted to the Universities in Korea" published by the National Assembly Library should be applied to all the other parts, i. e. to the parts of the "Master's Theses in Humanities and Social Sciences" and of the "Doctoral and Master's Theses in Natural Sciences': which will not only increase the Catalogue's use value but also discourage appearance of various theses abstracts of individual academic institutions such as the" Abstracts of the Doctoral and Master's Theses Submitted to Korea Advanced Institute of Science and Technology" which will in turn reduce inefficiency involved in the abstracting services at national level. (E) A general abstracting bulletin covering most part of the outcome of research and development activities in Korea other than that covered by the existing abstracts needs to be created to be temporarily. used till the abstracting journals suggested in this study will be fully available. A realistic way of having such a bulletin may be to expand the present coverage of "The Abstracts of the Reports of the Government-sponsored Projects" currently published by Korean Research Foundation.

• Journal of Practical Engineering Education
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• v.15 no.1
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• pp.73-80
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• 2023

The advancement of online technology in the 21st century has increased online courses and web-based communication in higher education. This type of education is not limited by time or location and has made it possible to expand university campuses globally and broaden the reach of university education to the general public and students from other universities. Changes such as a decrease in the school-age population and a reorganization of the university structure have also created an opportunity to change the perception of online education. In this paper, we conducted surveys on K University students, high school seniors, and the general public to assess their satisfaction with online courses, identify areas that require massive online courses, and determine students' needs for the operation of massive online courses. The survey showed that K University students are generally satisfied with online courses. However, improvements are needed to ensure a smooth online course-taking environment, increase system uniformity, and enhance the overall online course environment. High school students have a strong preference for natural science and should be offered online courses in subjects such as mathematics and physics as prerequisites to prepare for their major classes. The general public prefers the humanities, which is evident in the purpose of the liberal arts lectures.