• Honam Mathematical Journal
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• v.41 no.4
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• pp.683-695
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• 2019

In the present paper, we study curves in 𝔼³ with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.129-133
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• 2000

It is reasonable to use the stereo vision and image processing technique to digitize 3D coordinates of grid points and to evaluate surface strains on a sheet metal parts. However this method has its intrinsic problems such as the difficulty in enhancement of bad images inevitable error due to digital image resolution of camera and frame grabber unreliability of strains and thickness evaluated from coarse grid on the corner area with large curvature and the limitation of the area that can be measured at a time. Therefore it is still hard to measure strain distribution over the entire surface of a medium,- or large-sized stamped part at a time even by using an automated strain measurement system. In this study the curvature correction algorithm based on the grid refinement and the geometry assembling algorithm based on the global error minimization (GEM) scheme are suggested. Several applications are presented to show the reliability and efficiency of these algorithms.

• Membrane and Water Treatment
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• v.8 no.6
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• pp.553-562
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• 2017

In the present study, the water desalination across the penta-graphene has been explored by using molecular dynamics simulation. The penta-graphene, a new carbon allotrope, introduced theoretically in 2015. It was shown that this carbon nanostructure is slightly stiffer against buckling in comparison with the graphene nanoribbons. The effect of radius of curvature (ROC) of the membrane, pore size, and applied pressure, on water flow rate, and salt rejection is investigated. It is shown that salt rejection, and the shape of the oxygen density distribution inside the pore can be influenced by the ROC of membrane. Finally, it is shown that the ROC, and pore size of 2D membranes, play an important role in the salt rejection.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.493-511
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• 2008

In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let $\varphi:(M^n,g)\rightarrow(N^m,h)$ be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of $\varphi$. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, $\varphi^{-1}$(P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.4
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• pp.439-444
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• 2011

Purpose: To represent the shape of toric corea in the elliptical function for the determination of curvature distribution and lacrimal thickness between cornea and contact lens when the lens is fitted. Methods: Topography measurements of corneal curvature and curvature equation derived from the assumed elliptical function were evaluated using the Excel program which included the necessary equation derived. Results: Mathematical expressions for the cornea whose ribbon shaped-topography image, in which the center does not coincide with the corneal apex, can be determined. Conclusions: For the application where the higher accuracy on the cornea is not required, such as higher order aberration, the cornea cal be expressed in the simple elliptical function.

• Transactions of Materials Processing
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• v.25 no.3
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• pp.182-188
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• 2016

Flexibly-reconfigurable roll forming (FRRF) is a novel sheet metal forming technology conducive to producing multi-curvature surfaces by controlling the strain distribution along longitudinal direction. In FRRF, a sheet metal is shaped into the desired curvature by using reconfigurable rollers and gaps between the rollers. As FRRF technology and equipment are under development, a simulation model corresponding to the physical FRRF would aid in investigating how the shape of a sheet varies with input parameters. To facilitate the investigation, the current study exploits regression analysis to construct a predictive model for the longitudinal curvature of the sheet. Variables considered as input parameters are sheet compression ratio, radius of curvature in the transverse direction, and initial blank width. Samples were generated by a three-level, three-factor full factorial design, and both convex and saddle curvatures are represented by a quadratic regression model with two-factor interactions. The fitted quadratic equations were verified numerically with R-squared values and root mean square errors.

• Transactions of Materials Processing
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• v.26 no.6
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• pp.341-347
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• 2017

Flexibly-reconfigurable roll forming (FRRF) is a novel sheet metal forming technology conducive to produce multi-curvature surfaces by controlling strain distribution along longitudinal direction. Reconfigurable rollers could be arranged to implement a kind of punch die set. By utilizing these reconfigurable rollers, desired curved surface can be formed. In FRRF process, three-dimensional surface is formed from two-dimensional curve. Thus, it is difficult to predict the forming result. In this study, a regression analysis was suggested to construct a predictive model for a longitudinal curvature of FRRF process. To facilitate investigation, input parameters affecting the longitudinal curvature of FRRF were determined as maximum compression value, curvature radius in the transverse direction, and initial blank width. Three-factor three-level full factorial experimental design was utilized and 27 experiments using FRRF apparatus were performed to obtain sample data of the regression model. Regression analysis was carried out using experimental results as sample data. The model used for regression analysis was a quadratic nonlinear regression model. Determination factor and root mean square root error were calculated to confirm the conformity of this model. Through goodness of fit test, this regression predictive model was verified.

• Journal of Korean Medicine Rehabilitation
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• v.19 no.4
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• pp.115-126
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• 2009

Objectives : The aim of this study was to evaluate whether the foot pressure distribution correlates with the lumbo-sacral curvature, and the Oswestry Disability Index in chronic low back pain patients. Methods : We measured the fore foot pressure and the rare foot pressure using the foot analyzer in 28 women subjects with chronic low back pain. The lumbo-sacral curvature and the Oswestry Disability Index(ODI) were also measured. Results : 1. Subjects with higher ODI(%) had significantly lower Fore foot pressure/Rare foot pressure ratio(F/R ratio) (p<0.01). 2. Lumbar lordotic angle and Ferguson angle were inversely related to ODI(%) (p<0.05, p<0.01). 3. Lumbar lordotic angle and Ferguson angle were positively related to F/R ratio (all p<0.05). Conclusions : Using the Foot Analyzer(FA-48S, Tech storm Inc.) we have shown that F/R ratio has significant correlation with the lumbo-sacral curvature and the Oswestry Disability Index. These result suggest that the Foot analyzer may be used in assessing back pain in chronic low back pain patients.

• Journal of the Korean Society for Precision Engineering
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• v.1 no.3
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• pp.71-84
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• 1984

This paper examined strain distribution and radius of curvature of the bulge by finite element method and investigated limit polar thickness strain to predict the formability of sheet metal as we substituted effective strain and the radius of curvature obtained by FEM into instability condition equation successively. In experiment, the radius of curvature and limit polar thickness strainwere obtained by Moire method. Also, a concent- ric set of photogrid circles was used to measure the strain of arbitrary point and mild steel was used as material. This results obtained are as follows: 1) The radius of curvature obtained by FEM is in good agreement with the Moire experimental value. 2) The polar thickness strain is getting larger as the inside is approached from the edge. This means that fracture occurred near the ploe. 3) The circumferential strains agree closely with the meridian strains and the polar thickness strain is about twice the circumferential (or meridian) strain. This result agrees with the fact that anisotropy coefficient (R-value) obtained by tensile test is about one. 4) The theoretical results of limit polar thickness strain obtained by authors' method are better agreement with experimental results than other theoretical results. Therefore, we can better predict the formability of sheet metal with authors' method.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.85-86
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• 2006

A theoretical model is applied to the analysis of thermomechanical properties of $Al-SiC_p$ FGMs in this study. Functionally graded $Al-SiC_p$ composites ($Al-SiC_p$ FGMs) consisted with 10 layers gradually changing volume fractions of Al and $SiC_p$ were fabricated using the pressureless infiltration technique. $Al-SiC_p$ FGMs plates of total thickness of 3mm, 5mm and 7mm with fairly uniform distribution and compositional gradient of $SiC_p$ reinforcement in the Al matrix throughout the thickness was successfully fabricated. The curvature of $Al-SiC_p$ FGM plates was measured to check the internal stress distribution predicted via a theoretical model for the analysis of thermo-mechanical deformation. The evolution of curvature and also internal stresses in response to temperature variations could be predicted for the different combinations of geometric thickness of FGM plates. Theoretical prediction of thermally induced stress distribution makes it possible to design FGM structures without any critical failure during the usage of them.