• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1061-1075
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• 2019

In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.705-715
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• 2023

In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.33 no.3
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• pp.159-163
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• 2007

The relationship between texture and rheological properties of mascara(oil-in-water emulsion) was analyzed in this study. The final mascara product and gelling agents(2.0 wt%) used therein, such as hydroxyethylcellulose(HC), carboxymethylcellulose(CMC), hectorite, sodium magnesium silicate (SMS), hydroxyethyl acrylate/sodium acryloyldimethyl taurate copolymer(HS), and polyacrylate 13/polyisobutene/polysorbate 20 (PPP), were measured for rheological properties. As a result, HS and PPP showed the highest adhesiveness which were related to the volumizing effect of mascara. The viscosities of HC, SMS, and HS were measured at the stress range of $1{\sim}1,000s^{-1}$. SMS, with the lowest storage modulus range of $100{\sim}1,000s^{-1}$, affected the mascara in terms of smooth texture. The results of this study suggest that the rheology of gelling agents used influences the final texture of the mascara.

• Journal of radiological science and technology
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• v.28 no.1
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• pp.25-32
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• 2005

Purpose : To evaluate the degree of the artifact which is caused by the mascara and the eye shadow when acquiring MR images and compare the difference of the image distortion according to the change of various pulse sequence. Material and Method : The popular domestic mascara and eye shadow products were selected from three different companies respectively and divided into two groups mascara (M1, M2, M3 ), eye shadow (E1, E2, E3). Self-designed quadrature type saddle coil which has 4 cm inside diameter, 8 cm length and which is for both Tx and Rx was used. MR image was acquired respectively after applying the mascara to the tape from study 1, the eye shadow to the tape from study 2 and adding the eye shadow to the mascara from study 3. The FSE(fast spin echo), the SE(spin echo), the GE(gradient echo) were used as pulse sequences. The degree of the image distortion which was measured from each sequence was analyzed in quality and quantity. Result : The mascara and the eye shadow caused the artifacts to the MR images partially and induced the image distortion. There was a little difference in terms of the degree of artifact according to the change of pulse sequence. From the study 3 in which the eye shadow was applied to the mascara, on the axial plane image, the width of artifact was 16.73 mm in the GE pulse sequence, 6.64 mm in the SE pulse sequence, and 6.19 mm in the FSE pulse sequence. The degree of the artifact appeared highly in order of the GE, the SE and the FSE. On the sagittal plane image, the length of artifact was 22.84 mm in the GE, 17.81 mm in the SE and it appeared highly with the SE and the FSE technique order. Conclusion : When examining the eyeball and the brain of a woman with the mascara and the eye shadow, we have to consider that the artifact caused by them can have an effect on the image diagnosis. We concluded that it is more suitable for a brain and a eyeball T2 emphasizing image to use the FSE technique than the GE technique.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.369-383
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• 2018

In this work, a novel hyperbolic shear deformation theory is developed for free vibration analysis of the simply supported functionally graded plates in thermal environment and the FGM having temperature dependent material properties. This theory has only four unknowns, which is even less than the other shear deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical model are performed to demonstrate the efficacy of the model.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.771-781
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• 2019

In this paper, we consider biharmonic submanifolds of a quaternionic space form. We give the necessary and sufficient conditions for a submanifold to be biharmonic in a quaternionic space form, we study different particular cases for which we obtain some non-existence results and curvature estimates.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.157-168
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• 2015

In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f-harmonic. Also we present some properties for the f-biharmonicity of submanifolds of $\mathbb{S}^n$, and we give the classification of f-biharmonic curves in 3-dimensional sphere.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1209-1219
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• 2022

The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.629-641
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• 2023

The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class C₁₂ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between C₁₂ and Kählerian structures. Secondly, we give some basic results for Riemannian curvature tensor of C₁₂-manifolds and then establish equivalent relations among 𝜑-sectional curvature. Concrete examples are given.