• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.375-385
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• 2014

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.3
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• pp.355-359
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• 2003

We investigate the properties of fuzzy (semi-)topogenous orders in the framework of fuzzy (supra) topologies and fuzzy (supra) interior operators. We study the relationship between fuzzy (semi-)topogenous structures, fuzzy (supra)topologies and fuzzy (supra)interior operators.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.45-58
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• 1982

The problem of comparing k normal populations with a control (or a standard) in terms of the absolute values of their means is considered. Under the framework of indifference-zone formulation a single-state and a two-stage procedures for selecting the best are proposed, according to their commom vairances known or unknown respectively. The procedures guarantee that the probability of correct selection is not less than some preassigned lower limit. Selected tables necessary to implement the procedures are provided.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.353-364
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• 2011

Duality in the optimal harvesting for a nonlinear age-spatial structured population dynamic model is studied in the framework of optimal control problem. In this paper the duality theory that displays the conjugacy of the primal problem is established and an application is given. Duality theory plays an important role in both optimization theory and methodology and the results may be applied to a realistic biological system on the point of optimal harvesting.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.603-619
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• 2006

One of the most important aims in mathematics education is to enhance students' problem-solving abilities. To achieve this aim, in real school classrooms, many educators have examined and developed effective teaching methods, learning strategies, and practical problem-solving techniques. Among those trials, it is noticeable that Engel, Zeits, Shapiro and other not a few mathematicians emphasized 'Invariance Principle' as a mean of solving problems. This study is to consider the basic concept of 'Invariance Principle', analyze 'Invariance' concept in secondary Mathematics contents on the basis of framework of 'Invariance Principle' shown by Shapiro and discuss some instructional issues to occur in the process of it.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.665-678
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• 2022

The aim of this paper is to introduce a new iterative process and show that our iteration scheme is faster than other existing iteration schemes with the help of numerical examples. Next, we have established convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some convergence results for the approximation of the fixed points of a nonexpansive mapping.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.17-34
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• 2016

The purpose of this study was to analyze the contents on statistics in elementary mathematics textbook according to 2009 school curriculum. And we analyzed the elementary mathematics textbook in the light of data collection, graph understanding level suggested by Cursio. Specially, we analyzed the contents within the framework of evaluation norm suggested in 2015 school curriculum. We expect that this study will be a fundamental reference for the development of textbook according to 2015 school curriculum.

• Research in Mathematical Education
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• v.5 no.1
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• pp.13-24
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• 2001

Using computer technology in teaching school mathematics creates new instructional environments. The emphases on the use of computer technology in the classrooms and in particular the use of computer-based exploration as a context of mathematics instruction have been reflected in the recommendation of the NCTM (Curriculum and Evaluation Standards for School Mathematics, 1989). Although the power of using computer technology in the exploration of mathematical problems has been recognized and stressed by many educators, we do not have many research studies on mathematics in computer-based explorations. Especially research has failed to clarify how computer technology can contribute to the construction of procedural and conceptual knowledge of mathematics. Up to now most researches on procedural and conceptual knowledge in computer environments have only focused on classifying programming languages which program language has more random access and rich interrelationship characteristic in relation to conceptual knowledge in humans, and which computer language has more characteristic flavor of procedural knowledge. How computer-based explorations affect the knowledge construction of mathematics, therefore, emerges as an issue of research on teacher education program for theoretical framework. This situation leads to do research on the effectiveness of using computer explorations in pre-service teacher education in terms of procedural and conceptual knowledge construction.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.453-473
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• 2018

In this study, we analyzed the contents of speed concept presented in Korean, Japanese, Singapore, and American elementary mathematics textbooks, and drew implications for the teaching of speed concept in elementary schools. We developed a textbook analysis framework by theoretical discussions on the characteristics of the speed concept based on the proportional relationship and the previous researches on the speed in elementary mathematics. We analyzed the textbooks of four countries and drew some suggestions for improving the teaching of speed concept in Korean elementary schools.