• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

• Archives of Plastic Surgery
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• v.44 no.1
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• pp.26-33
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• 2017

Background The purpose of this study was to assess the correlation between the 2-dimensional (2D) extent of orbital defects and the 3-dimensional (3D) volume of herniated orbital content in patients with an orbital wall fracture. Methods This retrospective study was based on the medical records and radiologic data of 60 patients from January 2014 to June 2016 for a unilateral isolated orbital wall fracture. They were classified into 2 groups depending on whether the fracture involved the inferior wall (group I, n=30) or the medial wall (group M, n=30). The 2D area of the orbital defect was calculated using the conventional formula. The 2D extent of the orbital defect and the 3D volume of herniated orbital content were measured with 3D image processing software. Statistical analysis was performed to evaluate the correlations between the 2D and 3D parameters. Results Varying degrees of positive correlation were found between the 2D extent of the orbital defects and the 3D herniated orbital volume in both groups (Pearson correlation coefficient, 0.568-0.788; $R^2=32.2%-62.1%$). Conclusions Both the calculated and measured 2D extent of the orbital defects showed a positive correlation with the 3D herniated orbital volume in orbital wall fractures. However, a relatively large volume of herniation (>$0.9cm^3$) occurred not infrequently despite the presence of a small orbital defect (<$1.9cm^2$). Therefore, estimating the 3D volume of the herniated content in addition to the 2D orbital defect would be helpful for determining whether surgery is indicated and ensuring adequate surgical outcomes.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.195-200
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• 2010

Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.675-682
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• 2010

The flood impact pressure acting on a vertical wall resulting from a dam-breaking problem is simulated using a navier-Stokes(N-S) solver. The N-S solver uses Eulerian Finite Volume Method(FVM) along with Volume Of Fluid(VOF) method for 2-D incompressible free surface flows. A Split Lagrangian Advection(SLA) scheme for VOF method is implemented in this paper. The SLA scheme is developed based on an algorithm of Piecewise Linear Interface Calculation(PLIC). The coupling between the continuity and momentum equations is affected by using a well-known Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Several two-dimensional numerical simulations of the dam-breaking problem are presented to validate the accuracy and demonstrate the capability of the present algorithm. The significance of the time step and grid resolution are also discussed. The computational results are compared with experimental data and with computations by other numerical methods. The results showed a favorable agreement of water impact pressure as well as the global fluid motion.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.215-241
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• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1990.10a
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• pp.23-25
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• 1990

In this paper, a system to measure tree degradation of three dimensional phenomena in organic insulating materials using image processing system is discussed. Using a computerized tomography method, volume of tree immediately after tree initiation, as well as changes in the configuration of the tree were measured, which up to now have been difficult to measure. The specimens used an acrylic acid resin. As a result, it was possible to record the cross sections of the tree, and to describe the volume of the tree by the three dimensional measurement.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.101-121
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• 2010

This article includes an introduction, a history of Pick's theorem on lattice polyhedron and its proof, Reeve's theorem on 3-dimensional lattice polyhedrons extended from the Pick's theorem and Ehrhart polynomial generalized as an n-dimensional lattice polyhedron, and then shows the relationship between the volume of 3-dimensional polyhedron and the number of its lattice points by means of Reeve's theorem. It is aimed to apply the relationship to the visualization of sums in sequences.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.3
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• pp.149-157
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• 2000

Tool wear in the shearing process such as blanking, piercing and trimming is very important, because it has great effects on the dimensional accuracy, working efficiency and economy. Most of tools in the shearing process have the coated layer at surface fur good wear and corrosion resistance. When the surface of tool is teated, the wear Phenomena of coated surface layer and inner layer may be different. This paper describes a computer modelling technique by the finite element method in order to investigate the wear mechanism and to predict the wear profile of Ti-N coated tool in piercing process according to the volume of Production. Wear coefficients of the coated layer and inner layer are obtained through Pin-on-Disk wear test, respectively. To verify the effectiveness of the suggested technique, the technique is applied to wear analysis in piercing recess of piston pin and simulation results are compared with experimental ones.

• Archives of Plastic Surgery
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• v.32 no.5
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• pp.589-592
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• 2005

Since G.N. Hounsfield's clinical use of computed tomography in 1971, digital imaging technique using computers has shown an eye opening progress. Progress has made 3-dimensional understanding of not only facial bones but muscles and other connective tissues possible through 3-dimensional reconstruction of preexisting tomographical images. Also, quantitative analysis of density, distance, volume has become possible, allowing objective analysis of preoperative and postoperative states through imaging. The authors measured the masseter muscle volume of 20 normal individuals and 8 female patients through 3-D reconstructive CT imaging and made a statistical analysis of the measurements. The method used in our study may be applied to the diagnosis of disease causing the change of the facial volume and presurgical design as a useful tool to provide objective information on the evaluation of surgery outcome.

• Nuclear Engineering and Technology
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• v.39 no.4
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• pp.313-326
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• 2007

In this paper, an algorithm to reconstruct two orthogonal images into a three-dimensional image is developed in order to measure the bubble size and volume in a two-phase boiling flow. The central-active contour model originally proposed by P. $Szczypi\'{n}ski$ and P. Strumillo is modified to reduce the dependence on the initial reference point and to increase the contour stability. The modified model is then applied to the algorithm to extract the object boundary. This improved central contour model could be applied to obscure objects using a variable threshold value. The extracted boundaries from each image are merged into a three-dimensional image through the developed algorithm. It is shown that the object reconstructed using the developed algorithm is very similar or identical to the real object. Various values such as volume and surface area are calculated for the reconstructed images and the developed algorithm is qualitatively verified using real images from rubber clay experiments and quantitatively verified by simulation using imaginary images. Finally, the developed algorithm is applied to measure the size and volume of vapor bubbles condensing in a subcooled boiling flow.