• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1599-1622
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• 2013

We show many examples of curves on the unit 2-sphere $S^2(1)$ in $\mathbb{R}^3$ and the unit 3-sphere $S^3(1)$ in $\mathbb{R}^4$. We study whether its curves are Bertrand curves or spherical Bertrand curves and provide some examples illustrating the resultant curves.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.395-402
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• 2004

The extended finite element scheme applied to crack problems is reviewed in this paper. As the enrichments of the solution space and the basic formulation are discussed, several examples of the application of the method are given. The examples include a LEFM crack, a cohesive crack, multiple LEFH cracks and dynamic crack propagation problems. It is shown that the extended finite element method is one of the powerful tools to study crack problems.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.939-950
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• 2003

Control charts are very useful tool for monitoring of process characteristics. This paper discusses the problem of design of control limits when the subgroups are composed by cluster sampling type. As an alternative method of design of control limits XbBar chart is proposed, which uses the control limits based on the variation between subgroups instead of using classical variation within subgroups. Two examples are presented for reasonable design of control limits and conditions of subgroups based on the cluster sampling. Through examples the guidelines for making proper control limits are proposed.

• Proceedings of the KSR Conference
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• 2000.11a
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• pp.396-401
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• 2000

There are three examples of noise reduction test by rail welding. One of them is tested at electric car running area and another is tested at expansion joint and long welded rail and the third is tested at open deck bridge. We can know from the result that the noise reduction effect of rail welding is very different to the type of track and the car. The condition of the test has some differences, but it may be useful reference of noise reduction.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1013-1015
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• 2005

Liu[Fuzzy Optimization and Decision Making, 2(2003), 87-100] proved that convergence in credibility does not imply convergence a.s. and convergence in mean does not imply convergence a.s. by giving counter-examples. But these examples are not true. In this note, we prove that convergence in credibility implies convergence a.s. and convergence in mean implies convergence a.s.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1195-1209
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• 2009

In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.137-148
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• 2012

Recently Ding [4, 5, 8] gives examples of his FC-spaces which are not L-spaces due to Ben-El-Mechaiekh et al. [1]. We show that they are actually L-spaces. We also clarify that all statements in [5] can be stated in corrected and generalized forms for the class of abstract convex spaces beyond FC-spaces.

• East Asian mathematical journal
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• v.26 no.2
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• pp.219-232
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• 2010

The main purpose of this work is to suggest a new approach to teaching general topology to undergraduate students. First, we change the order of contents. Usually, we introduce definitions, examples, theorems, and problems in this order. But, showing familiar examples of some concept of topology prior to the definition of one is the best method so far as I know from teaching experience of topology, which students feel very hard because of its abstractness. For more efficiency, mathematics-clubs each consisting of three or four students in topology course are established. This makes students very positive in topology class.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.899-924
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• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.489-503
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• 2007

In this paper, we define signed interval-valued Choquet integrals which have numerous applications in mathematical economics, informatiom theory, expected utility theory, and risk analysis on interval-valued random variables, for examples: interval-valued random payments and interval-valued random profiles, etc. And we discuss axiomatic characterizations of them. Furthermore, we fine some condition that comonotonic additivity of symmetric Choquet integrals on interval-valued random payments is satisfied and give two examples related the main theorem.