• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.621-633
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• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.233-243
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• 2013

The Erlangen program is a scholastic plan by German mathematician Felix Klein, in which he, based on group theory, made a reassessment of geometry as well as an attempt to generally organize it. In this paper, I will introduce the historical and scholastic background of the Erlangen program, overview the process of its formation, and provide some comments regarding its historical significance.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-13
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• 1999

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

• East Asian mathematical journal
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• v.36 no.1
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• pp.55-60
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• 2020

We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for modeling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumulative function via a change of measure technique and a multidimensional Girsanov's theorem.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.159-172
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• 2004

A map is singular if each edge is on the same face on a surface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper po-vides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enumerating functions of such maps are also derived.

• Journal of Korean Society for Quality Management
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• v.19 no.1
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• pp.28-42
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• 1991

For a series or parallel system, though the component lifetimes have the absolutely continuous bivariate exponential distributions(ACBVE) by Block and Basu(1974), the common assumption that the component lifetimes are independent is used. The purpose of this paper, in this case, is to investigate the magnitude of the error caused by erroneous assumption, using the measure proposed by Klein and Moeschberger(1986). Estimation of the measure is conducted by maximum likelihood estimator(MLE) and those estimators are compared with corresponding jackknifed MLE through the Monte Carlo study.

• 한국초전도학회:학술대회논문집
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• 2008.08a
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• pp.15-15
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• 2008

• Proceedings of the Korean Society of Applied Entomolohy Conference
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• 2003.10a
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• pp.51-51
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• 2003

• Bulletin of the Korean Chemical Society
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• v.20 no.12
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• pp.1479-1482
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• 1999

We have studied the behavior of interdiffusion between partially miscible polymer pair from a theoretical viewpoint by applying the reptation model for collective interdiffusion and spinodal decomposition in polymer mixtures with different molecular weights. We find that our predictions agree well with the experiments of Klein and co-workers, where the exponent α of the initial increase of interfacial width with time in $t^{\alpha}$ is significantly lower than 0.5 for free diffusion.

• Tuberculosis and Respiratory Diseases
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• v.84 no.4
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• pp.335-337
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• 2021