• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.891-910
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• 1999

We classify analytically surface singularities defined by some weighted homogeneous polynomials which are topologically equivalent to the type {{{{ { z}`_{0 } ^{n } }}}} + {{{{ { z}`_{k } ^{1 } }}}} + {{{{ { z}`_{2 } ^{1 } }}}} = 0.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1213-1223
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• 2015

We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1173-1246
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• 2019

We find all P-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces (a corrected version of) Jan Steven's list [Manuscripta Math. 1993] of the numbers of P-resolutions of each singularities. We then compute the dimensions and Milnor numbers of the corresponding irreducible components of the reduced base spaces of versal deformations of each singularities. Furthermore we realize Milnor fibers as complements of certain divisors (depending only on the singularities) in rational surfaces via the semi-stable minimal model program for 3-folds. Then we compare Milnor fibers with minimal symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya Math. J. 2012]. As an application, we show that there are 6 pairs of entries in the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each pairs represent diffeomorphic minimal symplectic fillings.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.221-230
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• 2008

In the study of normal (complex analytic) surface singularities, it is interesting to investigate the invariants. The purpose of this paper is to give a characterization of the vanishing of ${\delta}_2$. In [11], we gave characterizations of minimally elliptic singularities and rational triple points in terms of th.. second plurigenera ${\delta}_2$ and ${\gamma}_2$. In this paper, we also give a characterization of rational triple points in terms of a certain computation sequence. To prove our main theorems, we give two formulae for ${\delta}_2$ and ${\gamma}_2$ of rational surface singularities.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1655-1667
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• 2017

We consider del Pezzo surfaces with du Val singularities. We'll prove that a del Pezzo surface X with du Val singularities has a $-K_X-polar$ cylinder if and only if there exist tiger such that the support of this tiger does not contain anti-canonical divisor. Also we classify all del Pezzo surfaces X such that X has not any cylinders.

• 한국기계연구소 소보
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• v.4 no.1
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• pp.29-42
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• 1981

In this paper, it is demonstrated that, with the distribution of lowestorder concentrated (discrete) singularities of delta function nature, the solution to the linear free surface problem can be obtaianed with a remarkable degree of accuracy. The linearized bounday valve problem is formulated subject to boundary conditions for the determination of strengths of singularities; the simple sources above (not on) the free surface and the vortices on the body surface. Three sample calculations were performed; the flow about a submerged vortex of known strength, the flow past a submerged circular cylinder, and the flow around a hydrofoil section. The convergence of the numerical procedure is achieved with a relatively small number of elements, The final results are compared with those of the publi¬shed works, and are considered very satisfactory.

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.3
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• pp.1-9
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• 1981

In this paper, it is demonstrated that, with the distribution of lowest order concentrated(discrete) singularities of delta function nature, the solution to the linear free surface problem can be obtained with a remarkable degree of accuracy. The linear boundary value problem is formulated subject to boundary conditions for the determination of strengths of singularities; the simple sources above(not on) the free surface and the vortices on the body surface. Three sample calculation were performed` the flow about a submerged vortex of known strength, the flow past a submerged circular cylinder, and the flow around a hydrofoil section. The convergence of the numerical procedure is achieved with a relatively small number of elements. The final results are compared with those of the published works, and are considered very satisfactory.

• Journal of Mechanical Science and Technology
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• v.20 no.7
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• pp.1043-1050
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• 2006

The aerodynamic interaction between a wing and a rail is investigated using a boundary-element method. The source and doublet singularities are distributed on the wing and its guide-way rail surface. The unknown strengths of the singularities are determined by inverting the aerodynamic influence coefficient matrices. Present method is validated by comparing computed results with the other numerical data. Rail width and rail height affect the aerodynamic characteristics of the wing only if the rail is narrower than the wing span. Although the present results are limited to the inviscid, irrotational flows, it is believed that the present method can be applied to the conceptual design of the high speed ground transporters moving over the rail.

• Journal of Sensor Science and Technology
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• v.32 no.5
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• pp.300-306
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• 2023

A hull-cleaning robot sticks to the surface of a vessel and moves for efficient cleaning. Precise path planning and tracking using the current position is crucial. Many robots rely on the INS algorithm, but errors accumulate. To fix this, GPS, sonar, and USBL are used, though with limitations. Selecting suitable sensors for the surface operation and accurate positioning algorithm are vital. In this study, we developed a robot position estimation algorithm using the structure of a ship. Problems that arise when expanding the 2D position estimation algorithm used in existing wall structures to 3D were evaluated and methods for solving them were proposed. In addition, we aimed to improve performance by deriving singularities that exist in the robot path and proposing an error correction algorithm based on the singularities.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.797-822
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• 2011

Log Enriques surface is a generalization of K3 and Enriques surface. We will classify all the rational log Enriques surfaces of rank 18 by giving concrete models for the realizable types of these surfaces.