• 대한수학회보
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• 제33권2호
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• pp.267-275
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• 1996

• 대한수학회지
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• 제33권2호
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• pp.367-379
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• 1996

Let $V = {(z, y) : f(z, y) = z^n + Ay^\alpha z^p + y^\beta z^q + y^k = 0}$ and $W = {(z, y) : g(z, y) = z^n + By^\gamma z^s + y^\delta z^t + y^k = 0}$ be germs of analytic irreducible subvarieties of a polydisc near the origin in $C^2$ with n < k and (n, k) = 1 where A and B are complex numbers. Assume that V and W are topologically equivalent near the origin.

• 대한수학회논문집
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• 제1권1호
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• pp.71-79
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• 1986

• 대한수학회지
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• 제29권2호
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• pp.281-295
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• 1992

• 대한수학회지
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• 제30권2호
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• pp.385-397
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• 1993

• 대한수학회지
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• 제26권2호
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• pp.181-188
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• 1989

• 대한수학회지
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• 제31권2호
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• pp.309-317
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• 1994

• 대한수학회논문집
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• 제9권4호
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• 대한수학회지
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• 제53권2호
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• pp.461-473
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• 2016

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.

• Journal of Welding and Joining
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• 제24권3호
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• pp.27-33
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• 2006

Structural stress approach is well known as a mesh-size insensitive fatigue assessment method by using finite element analyses. It is, however, difficult to estimate the structural stress (SS) at weld end points due to stress singularities when shell elements are used. In this study, fatigue evaluations with longitudinal load carrying box fillet weldment under out-of-plane bending load have been performed by using virtual node method (VNM) in order to avoid the problem, which is called the weld end effect. Various combinations of virtual node parameters, such as reference point and virtual node locations, are investigated for the estimation of proper structural stress values applying VNM in a systematic manner. The appropriate guidance of virtual node parameter has been offered for the fillet weldment considered in the study. The structural stress values obtained by VNM have also been validated by comparing the result with finite element model including weld bead. Moreover, the fatigue strength of the fillet weldment based on the equivalent structural stress is shown to be consistent with the master S-N curve.