• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1293-1308
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• 2016

In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth 2-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.227-253
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• 2023

In this article, we generalize the results discussed in [6] by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are 3-legged with a bad central vertex.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.483-498
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• 2010

The purpose of this paper is to investigate the dispositions of university students' understanding and reasoning about rational number concept. For this, we surveyed for the subject groups of prospective math teachers(33), engineering major students(35), American engineering and science major students(28). The questionnaire consists of four problems related to understanding of rational number concept and three problems related to rational number operation reasoning. We asked multi-answers for the front four problem and the order of favorite algorithms for the back three problems. As a result, we found that university students don't understand exactly the facets of rational number and prefer the mechanic approaches rather than conceptual one. Furthermore, they reasoned illogically in many situations related to fraction, ratio, proportion, rational number and don't recognize exactly the connection between them, and confuse about rational number concept.

• Hwankyungkyoyuk
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• v.13 no.2
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• pp.38-50
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• 2000

We are evidently Home Economicus, egoistic rational utility maximiger, and all the capitalism economic situation make us adapt to such life, and recognize that it is rational to act like that. This can be demonstrated in Prisoner′s Dilemma(PD) which always select the non-cooperative choice for free rider in rational selection process of public goods. This paper notice the "what is problem\ulcorner"The problem is not in free rider itself but in free rider egoism. The practical behavior of free rider egoism can be explained by way of Prisoner′s Dilemma. In PD situation, the prisoner makes a rational choice, non-cooperative alternative, but he doesn′arrive at preto-optimality. It is dilemma. Why can′t he arrive \ulcorner Because he is isolated from other prisoner. So we call it prisoner′s dilemma. The PD situation can be compared with our real economic life, which, we think, have kept by rational choice of the public goods. We actually have made our life as an individual one although we organized communities of capitalism. Of course, we know each others as members of same society, but each individual being can′t secure the belief, which has composed basis of community. So, it is very similar and common between PD situation and our real economic life in the production of public goods. We conclude that this non-cooperative process of PD situation can be utilized as instrument of EE. So this non-cooperative process can show us the effectiveness of EE as follows. \circled1 Game situation life PD can be used as good instrument for explaining the rational selection dilemma(error) to Homo-Economicus, the rational agent, with the optimal and rational language. \circled2 We can show that the selection result is dilemma, not arrive pareto - optimality. \circled3 The dilemma can be resolved with accomplishing the good communal life based on the belief, not on the isolation.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.63-72
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• 2002

An inverse interpolation problem for rational matrix functions with a certain type of symmetricity in zero-pole structure is studied.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.191-201
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• 2005

In this paper, the existence of periodic positive solution and the attractivity are investigated for the rational recursive sequence $x_{n+1} = (A + ax_{n_k})/(b + x{n-l})$, where A, a and b are real numbers, k and l are nonnegative integer numbers.

• East Asian mathematical journal
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• v.26 no.1
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• pp.69-73
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• 2010

We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.

• East Asian mathematical journal
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• v.32 no.1
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• pp.77-84
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• 2016

We explicitly derive diagrams representing (1,1)-decompositions of rational pretzel knots $K_{\beta}=M((-2,\;1),\;(3,\;1),\;({\mid}6{\beta}+1{\mid},{\beta}))$ from four unknotting tunnels for ${\beta}=1,\;-2$ and 2.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.149-156
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• 1998

We relate the existence of rational curves with the existence of rigid bundles of any even rank on Enriques surfaces and compare with the case of K3 surfaces.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.197-205
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• 2018

In this note we give a relationship between the degree and coprime-ness of matrix-valued rational functions.