• The Mathematical Education
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• v.25 no.1
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• pp.21-23
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• 1986

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.687-693
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• 2003

In this paper, when N is a compact Riemannian manifold, using warped products, we discuss the conformal deformation of a warped product metric on $M\;\;[a,\;\infty)\;\times\;_f\;N$ with specific warping functions.

• Journal of the Korean Physical Society
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• v.80
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• pp.30-36
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• 2022

Holographic model of massive scalar field with its self-interaction λϕⁿ in AdS space is able to give a logarithmic scale dependence to marginal multi-trace deformation couplings on its dual conformal field theory, where λ is the self-interaction coupling of the scalar field, ϕ, and n is an integral number. In arXiv:1501.06664, the authors realize this feature by looking at bulk scalar solutions near AdS boundary imposing a specific boundary condition between the coefficients of non-normalizable and normalizable modes of the scalar field excitations. We study the same holographic model to see scale dependence of marginal deformations on the dual conformal field theory by employing completely different method: holographic Wilsonian renormalization group. We solve Hamilton-Jacobi equation derived from the holographic model of massive scalar with λϕⁿ interaction and obtain the solution of marginal multi-trace deformations up to the leading order in λ. It turns out that the solution of marginal multi-trace deformation also presents logarithmic behavior in energy scale near UV region.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.10
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• pp.1487-1492
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• 2010

The objective of this study is to design the conformal cooling channels for the mould of a plastic drawer of a refrigerator by analysis of three-dimensional injection molding. In order to obtain the desired design of the conformal cooling channels, the influence of the diameter and the position of the conformal cooling channels on the moulding characteristics and the product qualities were quantitatively examined. From the results of the examination, an optimal design of the conformal cooling channels, which ensures uniform cooling and minimum potential deformation of the molded drawers, was estimated. By comparing the designed mould and a conventional mould with linear cooling channels from the viewpoints of the product qualities as well as cooling and cycle times, it was shown that the mould with conformal cooling channels can simultaneously improve the productivity of the injection moulding process and the product qualities.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.9-18
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• 1996

In this paper, we consider the existence of a solution to the elliptic nonlinear partial differential equation ${\Delta}u＋H({\chi})e^{u}$ = 0 (H $\neq$ 0) (1) on a compact manifold without boundary. This equation is related to the problem of a pointwise conformal deformation of metrics on two dimensional compact connected manifolds.(omitted)

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Journal of Sensor Science and Technology
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• v.32 no.6
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• pp.335-339
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• 2023

Skin-compatible electronics have evolved to achieve both conformality and stretchability for stable contact with deformable biological skin. While existing research has largely concentrated on alternative materials, the potential of Parylene-based thin-film electrodes for stretchable on-skin applications remains relatively untapped. This study proposes an engineering strategy to achieve stretchability using the Parylene thin-film electrode. Unlike the conventional Parylene thin-film electrode, we introduce morphological adaptability via controlled microscale slits in the Parylene electrode structure. The slits-containing device enables unprecedented stretchability while maintaining critical electrical insulation properties during mechanical deformation. Finally, the demonstration on human skin shows the mechanical adaptability of these Parylene-based bioelectrodes while their electrical characteristics remain stable during various stretching conditions. Owing to the ultra-thinness of the Parylene coating, the wearable bioelectrode not only achieves stretchability but also conforms to the skin. Our findings broaden the practical use of Parylene thin-film bioelectrodes.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.5
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• pp.404-411
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• 2009

We introduce in this paper a new method for smooth foldover-free warping of images, based on the vector field deformation technique proposed by Von Funck et al. It allows users to specify the constraints in two different ways: positional constraints to constrain the position of a point in the image and gradient constraints to constrain the orientation and scaling of some parts of the image. From the user-specified constraints, it computes in the image domain a C1-continuous velocity vector field, along which each pixel progressively moves from its original position to the target. The target positions of the pixels are obtained by solving a set of partial derivative equations with the 4th order Runge-Kutta method. We show how our method can be useful for texture mapping with hard constraints. We start with an unconstrained planar embedding of a target mesh using a previously known method (Least Squares Conformal Map). Then, in order to obtain a texture map that satisfies the given constraints, we use the proposed warping method to align the features of the texture image with those on the unconstrained embedding. Compared to previous work, our method generates a smoother texture mapping, offers higher level of control for defining the constraints, and is simpler to implement.

• Tribology and Lubricants
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• v.24 no.6
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• pp.326-331
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• 2008

The contact surfaces between mold and target should be in parallel for a proper imprinting process. However, large size of contacting area makes it difficult for both mating surfaces (mold and target planes) to be in all uniform contact with the expected precision level in terms of thickness and position. This is caused by the waviness of mold and target although it is very small relative to the area scale. The gripping force for both mold and target by the vacuum chuck is other major effect to interrupt the uniform contact, which must be avoided in imprinting mechanism. In this study, the cause of non-conformal contact mechanism between mold and target is investigated with the consideration of deformation due to the vacuum gripping for the size $470{\times}370\;mm^2$ LCD panel.

• Korean Journal of Materials Research
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• v.19 no.8
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• pp.437-442
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• 2009

This paper describes an improved strategy for controlling the adhesion force using both the antiadhesion and adhesion layers for a successful large-area transfer process. An MPTMS (3-mercaptopropyltrimethoxysilane) monolayer as an adhesion layer for Au/Pd thin films was deposited on Si substrates by vapor self assembly monolayer (VSAM) method. Contact angle, surface energy, film thickness, friction force, and roughness were considered for finding the optimized conditions. The sputtered Au/Pd ($\sim$17 nm) layer on the PDMS stamp without the anti-adhesion layer showed poor transfer results due to the high adhesion between sputtered Au/Pd and PDMS. In order to reduce the adhesion between Au/Pd and PDMS, an anti-adhesion monolayer was coated on the PDMS stamp using FOTS (perfluorooctyltrichlorosilane) after $O_2$ plasma treatment. The transfer process with the anti-adhesion layer gave good transfer results over a large area (20 mm $\times$ 20 mm) without pattern loss or distortion. To investigate the applied pressure effect, the PDMS stamp was sandwiched after 90$^{\circ}$ rotation on the MPTMS-coated patterned Si substrate with 1-${\mu}m$ depth. The sputtered Au/Pd was transferred onto the contact area, making square metal patterns on the top of the patterned Si structures. Applying low pressure helped to remove voids and to make conformal contact; however, high pressure yielded irregular transfer results due to PDMS stamp deformation. One of key parameters to success of this transfer process is the controllability of the adhesion force between the stamp and the target substrate. This technique offers high reliability during the transfer process, which suggests a potential building method for future functional structures.