• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.109-116
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• 1997

In the present paper we consider an abstract partial dif-ferential equation of the form $\frac{\partial^2u}{{\partial}t^2}-\frac{\partial^2u}{{\partial}x^2}+A(x.t)u=f(x, t)$, where ${A(x, t):(x, t){\epsilon}\bar{G} }$ is a family of linear closed operators and $G=GU{\partial}G$, G is a suitable bounded region in the (x, t)-plane with bound-are ${\partial}G$. It is assumed that u is given on the boundary ${\partial}G$. The objective of this paper is to study the considered Dirichlet problem for a wide class of operators $A(x, t)$. A Dirichlet problem for non-elliptic partial differential equations of higher orders is also considerde.

• Korean Journal of Child Studies
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• 제28권5호
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• pp.19-36
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• 2007

This study explored proverb comprehension and use in elementary school children by familarity and concreteness of proverbs and children's age, sex, experience of living with grandparents. The 529 fourth and sixth grade participants completed a questionnaire probing knowledge of 16 proverbs; 4 each in four categories(familiar-concrete, familiar-abstract, unfamiliar-concrete, and unfamiliar-abstract). Results showed highest comprehension scores for familiar-concrete proverbs. Sixth graders obtained higher comprehension score than fourth graders in all four proverb categories. There was no difference between grades in frequency of proverb usage. An interaction effect between grade and sex showed that female sixth graders had the highest comprehension score. These results suggest a possibility of relationship between figurative language and cognitive development related to abstract thinking in late school-age children.

• Bulletin of the Korean Mathematical Society
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• 제54권4호
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• pp.1229-1240
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• 2017

This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Then we study abstract harmonic analysis of complex measures over the left coset space G/H.

• The Mathematical Education
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• 제42권4호
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• pp.481-501
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• 2003

The main purpose of this work is to propose programs of algebra courses for the department of mathematics education of teacher training universities. Set Theory, Linear Algebra, Number Theory, Abstract Algebra I, Abstract Algebra II, and Philosophy of Mathematics for School Teachers are discussed in this article.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.165-175
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• 2021

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

• Communications of the Korean Mathematical Society
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• 제12권3호
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• pp.579-595
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• 1997

In this paper, we establish an $L_p$ analytic Fourier-Feynman transform theory for a class of cylinder functions on an abstract Wiener space. Also we define a convolution product for functions on an abstract Wiener space and then prove that the $L_p$ analytic Fourier-Feyman transform of the convolution product is a product of $L_p$ analytic Fourier-Feyman transforms.

• Communications of Mathematical Education
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• 제19권4호
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• pp.599-620
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• 2005

There can be two different approaches to introducing Abstract Algebra to undergraduate students: One is to introduce group concept prior to ring concept, and the other is to do the other way around. Although the former is almost conventional, it is worth while to take the latter into consideration in the viewpoint that students are already familiar to rings of integers and polynomials. In this paper, we investigated 16 most commonly used Abstract Algebra undergraduate textbooks and found that 5 of them introduce ring theory prior to group theory while the rest do the other way around. In addition, we interviewed several undergraduate students who already have taken an Abstract Algebra course to look into which approach they prefer. Then we compare pros and cons of two approaches on the basis of the results of the interview and the historico-genetic principle of teaching and learning in Abstract Algebra and suggest that it certainly be one of alternatives to introduce ring theory before group theory in its standpoint.

• The Journal of Korean Institute of Communications and Information Sciences
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• 제32권8B호
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• pp.529-538
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• 2007

In this paper, we have analyzed a simulation model of Slammer worm propagation process which caused serious disruptions on the Internet in the year of 2003 by using NS-2. Previously we had presented and analyzed Abstract Network to Abstract Network(AN-AN) model being modified from the Detailed Network to Abstract Network(DN-AN) of NS-2. However, packet analysis in AN-AN model had a problem of taking 240 hours to simulate the initial 300 seconds of infection. We have reduced the AN-AN model to save the simulation time and analyzed total 3.5 hours of the network congestions within 107 hours. Moreover, we have derived optimal quarantine rate of 0.0022 considering service outage of network devices caused by the heavy infected traffics, which was not taken into consideration in previous works. As the result of simulation, Although the inbound traffic at the Korean international gateway was back in normal conditions at 4,787 second, due to the revese direction saturation was maintained until 12,600 seconds, the service outage was persisted for 3.5 hours.

• Journal of The Korean Association of Information Education
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• 제18권4호
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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.