• 대한수학회논문집
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• 제28권3호
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• pp.425-432
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• 2013

Let S be a minimal surface of general type with $p_g(S)=q(S)=0$ having an involution ${\sigma}$ over the field of complex numbers. It is well known that if the bicanonical map ${\varphi}$ of S is composed with ${\sigma}$, then the minimal resolution W of the quotient $S/{\sigma}$ is rational or birational to an Enriques surface. In this paper we prove that the surface W of S with $K^2_S=5,6,7,8$ having an involution ${\sigma}$ with which the bicanonical map ${\varphi}$ of S is composed is rational. This result applies in part to surfaces S with $K^2_S=5$ for which ${\varphi}$ has degree 4 and is composed with an involution ${\sigma}$. Also we list the examples available in the literature for the given $K^2_S$ and the degree of ${\varphi}$.

• 충청수학회지
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• 제27권4호
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• 대한수학회보
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• 제54권5호
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• pp.1779-1801
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• 2017

Let X be a minimal del Pezzo surface of degree 2 over a finite field ${\mathbb{F}}_q$. The image ${\Gamma}$ of the Galois group Gal(${\bar{\mathbb{F}}}_q/{\mathbb{F}}_q$) in the group Aut($Pic({\bar{X}})$) is a cyclic subgroup of the Weyl group W($E_7$). There are 60 conjugacy classes of cyclic subgroups in W($E_7$) and 18 of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree 2 can be achieved for given q.

• The Korean Journal of Physiology
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• 제4권2호
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• pp.53-60
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• 1970

In an attempt to clarity the effect of X-irradiation on the activity of surfactant in rabbits, and also to observe the possible difference when the irradiation was made in single or fractionated dose, X-ray in dose of 900 r was irradiated to rabbits either in single or fractionated dose of 300 r each day for three day, Tension-area diagram of lung extract was recorded automatically by a modified Langmuir-Wilhelmy balance with a synchronized recording system designed in this department. The surface tension of lung extract was measured at 1,3,5,24, and 48 hours post-irradiation, and the results were compared with the non-irradiated normal group. The result obtained are summerized as follows: 1) The maximal surface tension, minimal surface tension, width of the tension-area diagram at the surface area of 40% in lung extract, and stability index of the normal rabbit lung extracts were 40.73 dynes/cm, 8.96 dynes/cm. 20.71 dynes/cm, and 1.28 respectively. 2) Activity of surfactant was significantly depressed by X-irradiation, and the pattern of depression was more prominent in the single irradiation group than in the fractionated group. 3) It was found that the changes of the width of the tension-area diagram at the surface area of 40% in lung extract and stability indices corresponded well with that of the maximal or minimal surface tension.

• 대한수학회지
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• 제13권1호
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• pp.79-86
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• 1976

• 호남수학학술지
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• 제5권1호
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• pp.267-272
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• 1983

• 호남수학학술지
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• 제38권1호
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• pp.151-167
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• 2016

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.

• 대한수학회지
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• 제54권2호
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• pp.545-561
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• 2017

The signature of a surface bundle over a surface is known to be divisible by 4. It is also known that the signature vanishes if the fiber genus ${\leq}2$ or the base genus ${\leq}1$. In this article, we construct new smooth 4-manifolds with signature 4 which are surface bundles over surfaces with small fiber and base genera. From these we derive improved upper bounds for the minimal genus of surfaces representing the second homology classes of a mapping class group.

• 호남수학학술지
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• 제28권4호
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• pp.549-558
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• 2006

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

• 호남수학학술지
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• 제31권2호
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• pp.177-183
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• 2009

In this article, we study ruled surfaces in a Lorentzian space-time, which have finite type immersion. We give a condition for bi-finite type surfaces to be of finite type.