• 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.58 no.1
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.385-391
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• 2016

We consider Jacobi filds as the first derivatives for ${\varepsilon}$, the energy of harmonic extensions, in a given manifold. In this paper we see that the Jacobi fild is bounded by the given boundary map. Here we give no restriction concerned with the curvature for the given manifold.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.12-37
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• 2024

The paper introduces a set of new ruled surfaces such that the base curve is taken to be the striction curve of N, C and W ruled surfaces from the alternative frame, and the generating line is taken to be one of the vectors of Sannia frame. The characterizations for each ruled surface such as fundamental forms, the Gaussian and mean curvature are also examined to provide the conditions for each surface to be developable or minimal.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.8
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• pp.46-59
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• 1998

This paper presents shape design, surface construction, and cutting path generation for the surface of marine ship propeller blades. A propeller blade should be designed to satisfy performance constraints that include operational speed which impacts rotations per minutes, stresses related to deliverable horst power, and the major length of the marine ship which impacts the blade size and shape characteristics. Primary decision variables that affect efficiency in the design of a marine ship propeller blade are the blade diameter and the expanded area ratio. The blade design resulting from these performance constraints typically consists of sculptured surfaces requiring four or five axis contoured machining. In this approach a standard blade geometry description consisting of blade sections with offset nominal points recorded in an offset table is used. From this table the composite Bezier surface geometry of the blade is created. The control vertices of the Hazier surface patches are determined using a chord length fitting procedure from tile offset table data. Cutter contact points and path intervals are calculated to minimize travel distance and production time while maintaining a cusp height within tolerance limits. Long path intervals typically generate short tool paths at the expense of increased however cusp height. Likewise, a minimal tool path results in a shorter production time. Cutting errors including gouging and under-cut, which are common errors in machining sculptured surfaces, are also identified for both convex and concave surfaces. Propeller blade geometry is conducive to gouging. The result is a minimal error free cutting path for machining propeller blades for marine ships.

• Journal of Chest Surgery
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• v.19 no.2
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• pp.225-231
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• 1986

Pericardial adhesions following open heart surgery pose a special problems, increasing the risk of cardiac reoperation because of the danger of damaging the heart, coronary artery and veins, or grafts and also the fibrous tissue may obliterate the pericardial space and eventually constrict the heart. This study was undertaken to evaluate the effect of intrapericardial urokinase and dextran 40 on the formation of pericardial adhesions in an animal model. latrogenic traumas on the pericardium were surgically induced in 30 rabbits, simulating injuries possible during actual surgery. In all rabbits, blood [1 ml] was obtained from an ear vessel and injected into the pericardium. Control group of ten rabbits did not receive any further medication, urokinase group of ten received 15, 000-20, 000 IU of urokinase, and remained ten received 1 ml of 10% dextran 40. All rabbits were sacrificed at 4 weeks. At autopsy, the development of adhesions were graded as none [Grade I], minimal [Grade II], moderate [Grade III], and severe [Grade IV]. Histological studies of the parietal pericardium and epicardium were performed. The results were as follows: 1. Group 1[Control group] showed minimal adhesion in 40%, moderate in 50%, and severe in 10% of the group. Sharp dissections were necessary in 60% of adhesions. 2. Group II [Dextran group] showed no adhesions in 20%, minimal in 60%, and moderate in 20% of the group. 3. Group III [Urokinase group] showed no adhesions in 40%, minimal in 40%, and moderate in 20% of the group. Considering in this group, the adhesion activity was significantly suppressed [60% adhesions] compared to the control group [100% adhesions] [P < 0.05]. 4. Histological findings revealed mild serosal fibrosis in none adherent group, loose fibrous connections between two layers of pericardium in minimal adhesion group, tight fibrous connections in moderate adhesion group, and marked fibrous thickening and close attachment of two surfaces were noted in severe adhesion group. These data have revealed the decreased incidence of pericardial adhesions with urokinase and dextran 40.

• Journal of Biomedical Engineering Research
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• v.28 no.6
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• pp.791-797
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• 2007

This paper proposes a semiautomatic vertebra segmentation method that overcomes limitations of both manual segmentation requiring tedious user interactions and fully automatic segmentation that is sensitive to initial conditions. The proposed method extracts fence surfaces between vertebrae, and segments a vertebra using fence-limited region growing. A fence surface is generated by a deformable model utilizing valley information in a valley emphasized Gaussian image. Fence-limited region growing segments a vertebra using gray value homogeneity and fence surfaces acting as barriers. The proposed method has been applied to ten patient data sets, and produced promising results accurately and efficiently with minimal user interaction.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1320-1323
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• 1996

This paper describes an interpolation method for a parametric surface. A parametric surface is approximated to triangular mesh surfaces and then the basic paths are achieved. As the generated path is a series of linear segments, this algorithm can be easily adapted to general NC controllers. The generated paths have minimal transfer length and are gouge-free within the approximation tolerance. The problems, induced when the paths are represented by linear segments, are overcome without making any path deviation by this algorithm. This algorithm saves machining time by eliminating overdetermined tool paths and keeping the desired average feedrate, which improve productivity and lead to lower production costs.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.2
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• pp.146-153
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• 1998

NC machines with 4 or 5 axes are capable of various tool approach motions, which makes interference-free and high machinablity machining possible. This paper deals with how to integrate these two advantages (interference-free and high machinability machining) in multi-axes NC machining with a ball-end mill. Feasible tool approach region at a point on a surface is first computed, then among which an approach direction is determined so as to minimize the cutting force required. Tool and spindle volumes are considered in computing the feasible tool approach region, and the computing time is improved by trans-forming surface patches into minimal enclosing spheres. A cutting force prediction model is used for estimating the cutting force. The algorithm is developed so as to be applied to 4- or 5-axes NC machining in common.

• Korean Journal of Computational Design and Engineering
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• v.6 no.4
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.