• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.133-143
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• 2014

A new three-step quadraparametric family of eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear equation. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.741-748
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• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.663-676
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• 2016

In this paper we propose a new family of eighth order optimal methods for solving nonlinear equations by using weight function methods. The methods of the family require three function and one derivative evaluations per step and has order of convergence eight, and so they are optimal in the sense of Kung-Traub hypothesis. Precise analysis of convergence is given. Some members of the family are compared with several existing methods to show their performance and as a result to confirm that our methods are as competitive as compared to them.

• Research in Mathematical Education
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• v.15 no.4
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• pp.357-371
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• 2011

In mathematical problem solving, students may make various errors. In order to draw useful lessons from the errors, and then correct them, we surveyed 24 eighth-grade students' performances in geometrical problem solving according to Casey's hierarchy of errors. It was found that: 1. Students' effect can lead to errors at the stage of "comprehension", "strategy selection", and "skills manipulation"; and 2. Students' geometric schemas also influenced their strategy selection".

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.165-175
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• 2010

In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.

• International conference on construction engineering and project management
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• 2017.10a
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• pp.1-7
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• 2017

Korea's domestic construction market and overseas construction order environment are experiencing a decreasing trend, and this trend is expected to continue. Therefore, domestic construction companies are seeking to enter the global construction market. This study analyzes the global construction market and the global competitiveness for global construction companies and provides the results. To this end, this study has developed a model to evaluate the global construction competitiveness level and to evaluated global construction competitiveness in 2016. The evaluation of global construction competitiveness was analyzed based on the competitiveness of construction infrastructure by country, and the evaluation results of competitiveness of construction companies. These assessments were based on 20 detailed international statistics (ENR, Global Insight, Compass, etc.). The evaluation results are as follows. First, in regard to the comprehensive global construction competitiveness by country, America ranked first among 20 countries, followed by China. European countries like Spain, Germany and the Netherlands ranked third to fifth, respectively. Korea ranked sixth, one rank higher than that of the previous year. America and European countries remain strong. Second, in regard to the comprehensive building infrastructure competitiveness by country, America ranked first followed by Germany. Korea ranked twelfth, which is the same rank as that of the previous year. When it comes to stability in the construction market, China ranked first and Korea eighth. For construction systems, Sweden ranked first and Korea thirteenth, and for infrastructure, Japan ranked first and Korea tenth. Third, according to the construction company's capability evaluation by country, America ranked first followed by China. Korea ranked fourth, two ranks higher than that of the previous year because of its building competitiveness (fifth → fourth) and design competitiveness (eleventh → eighth) which has improved. When it comes to building competitiveness, China ranked first and Korea fourth. For design competitiveness, America ranked first and Korea eighth, and for price competitiveness, India ranked first and Korea seventh. However, Korea is still in the middle of the pack rank among the 20 countries considered when it comes to design competitiveness. It is ranked eleventh for design productivity and thirteenth for foreign sales against the total sales (internationalization). Thus, Korea needs to improve technical power and tap into new markets for improved competitiveness, including increased productivity. To do so, more R&D investment is required.

• Journal of the Korean Society of Earth Science Education
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• v.12 no.2
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• pp.119-130
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• 2019

The TIMSS assessment is conducted every four years, and Korean fourth grade cohort in TIMSS 2011 participated in TIMSS 2015 again as eighth graders, which produced the first achievement data of the cohort group of elementary and middle schools. In this study, in order to investigate the causes of the decline in Korean students' science achievement with grade changes from the fourth to the eighth grade, we analyzed educational context variables such as characteristics of students, teachers, and classroom instructions of the top 5 achievement countries participated in both TIMSS 2011 and TIMSS 2015. According to the results, students' sense of school belonging increased, whereas students' positive attitudes toward science teaching decreased with the grade change from the fourth to the eighth. As for the teacher characteristics, the teacher's professional development activity increased, and the teacher's confidence in science teaching showed similar tendency to the international average. Regarding classroom instruction characteristics, the frequency of inquiry-related science activities was highest at the fourth grade, and lower than the international average at the eighth grade. Based the results, we suggested implications for science teaching and learning as well as further studies including development of differentiated strategy by the school level to improve students' achievement, the necessity of converting into more student-engaging science classes, and the necessity of in-depth study on the teacher related educational contextual variables.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.22-25
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• 1999

A dynamic explicit finite element code for simulating sheet forming processes has been developed The code utilises the discrete Kirchhoff shell element and contact force is treated by a conventional penalty method. In order to reduce the computational cost a new and robust contact searching algorithm has been developed and implemented into the code. in the method a hierarchical structure of tool segments called a tree structure is built for each tool at the initial stage of the analysis Tree is built in a way to divide a trunk to 8 sub-trunk 2 in each direction until the lowest level of the tree(leaf) contains exactly one segment of the tool. In order to have a well-balanced tree each box on each sub level contains one eighth of the segments. Then at each time step contact line from a node comes out of the surface of the tool. Simulation of various sheet forming processes were performed to verify the validity of the developed code with main focus on he usefulness of the developed contact searching algorithm.