• Journal of The Korean Association of Information Education
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• v.18 no.4
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• pp.559-566
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• 2014

This is to understand the neurological dynamic cognitive processes of math learning based on the abstract mappings( level A2), abstract systems(level A3), and single principles(level A4), which are principles of Fischer's cognitive development theory. Math learning requires flexibility to adapt existing brain function in selecting new neurophysiological activities to learn desired knowledge. This study suggests a general statistical framework for the identification of neurological patterns in different abstract learning change with optimal support. We expected that functional brain networks derived from a simple math learning would change dynamically during the supportive learning associated with different abstract levels. Task based patterns of the brain structure and function on representations of underlying connectivity suggests the possible prediction for the success of the supportive learning.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.285-291
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• 1997

In this paper, we obtain an abstract formulation of a fixed point theorem for nonexpansive mappings. Our theorem is a non-metric version of Kirk's original theorem.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• Journal of Korean Philosophical Society
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• v.141
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• pp.43-62
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• 2017

The main purpose of this paper is to survey the debates between Searle and Smith over the problem of "freestanding Y terms" in Searle's conception of social reality, and offer a viable solution, drawing on the experientialist conception of symbolic experience. Smith raises the problem of "freestanding Y term" against Searle's formula "X counts as Y in C" that there may be some cases where we cannot identify an X term to which an Y term refers. In case of an abstract concept such as equity, we may not find exactly what it stands for. That is, we cannot identify exactly what(X term) counts as equity. If there is nothing like an X for Y term, we can regard anything as equity, which may disrupt Searle's formula. Understandably, Smith does not say that the problem dismantles Searle's whole conception of social reality. Instead, Smith intends to show that Searle's formula is neither complete nor specific enough. Apparently, Searle admits that there may be freestanding Y terms and tries to articulate it within his formula, which does not seem to work. I suggest that the experientialist account of symbolic experience may serve to dissolve Smith's challenge, without modifying Searle's original formula. According to the experientialist conception of symbolization, we symbolically map some portion of our experience onto a physical object, which serves as a signifier, and we then understand and experience the signifier "in terms of" the mapped portion of experience. Thus, we experience certain buildings and some relevant people, say students, staffs, and professors in terms of "university." The status functions of university have been created by means of symbolic mappings, which change the way we understand and experience the buildings and people. In this picture, there need not be any notions such as "one-to-one correspondence" between X terms and Y terms. In this way, Searle may maintain his original formula, while dissolving, not answering, Smith's challenge. What Searle needs is a more appropriate theory of symbolization, part of which has been articulated by the experientialist account of symbolic experience.