• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.251-261
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• 2023

In this paper, we extend the definition of the Jacobi operator of smooth maps, and biharmonic maps via the variation of bienergy between two Riemannian manifolds. We construct an example of (p, f)-biharmonic non (p, f)-harmonic map. We also prove some Liouville type theorems for (p, f)-biharmonic maps.

• 한국안광학회지
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• 제14권4호
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• pp.83-87
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• 2009

목적: 본 연구는 눈에 영향을 미칠 수 있는 마스카라에 함유되어 있는 중금속과 휘발성유기화합물과 같은 다양한 화학물질을 검출하기 위하여 수행되었으며, 가장 많이 쓰이는 마스카라 5가지를 분석하였다. 방법: 시중에 유통되는 5개 제품을 구입하여 각각에 함유된 금속원소와 휘발성유기화합물을 분석하였다. 결과: 일부 시료에서 알루미늄과 망간 등의 금속원소가 다소 높은 농도로 검출되었으며 다양한 휘발성유기화합물이 검출되었다. 결론: 마스카라는 눈에 영향을 줄 수 있는 금속원소와 유기화합물을 포함하고 있다.

• Structural Engineering and Mechanics
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• 제49권2호
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• pp.225-235
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• 2014

Cold expansion is an efficient way to improve the fatigue life of an open hole. In this paper, three finite element models have been established to bind the crack growth from an expanded hole and simulated. Expansion and its degree influence are studied using a numerical analysis. Stress intensity factors are determined and used to evaluate the fatigue life. Residual stress field is evaluated using a nonlinear analysis and superposed with the applied stresses field in order to estimate fatigue crack growth. Experimental tests are conducted under constant loading. Results of this investigation indicate expansion and its degree are beneficial to fatigue life and a good agreement was observed between FEM simulations and experimental results.

• Steel and Composite Structures
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• 제26권5호
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• pp.557-572
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• 2018

In this paper, a refined higher-order shear deformation theory including the stretching effect is developed for the analysis of bending analysis of the simply supported functionally graded (FG) sandwich plates resting on elastic foundation. This theory has only five unknowns, which is even less than the other shear and normal 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 numerical model are performed to demonstrate the efficacy of the model.

• 대한수학회논문집
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• 제30권4호
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.571-589
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• 2019

This paper aims to develop a quasi-3D shear deformation theory for the study of bending, buckling and free vibration responses of functionally graded (FG) sandwich thick plates. For that, in the present theory, both the components of normal deformation and shear strain are included. The displacement field of the proposed model contains undetermined integral terms and involves only four unknown functions with including stretching effect. Using Navier's technique the solution of the problem is derived for simply supported sandwich plate. Numerical results have been reported, and compared with those available in the open literature were excellent agreement was observed. Finally, a detailed parametric study is presented to demonstrate the effect of the different parameters on the flexural responses, free vibration and buckling of a simply supported sandwich plates.

• 호남수학학술지
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• 제45권2호
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• pp.300-315
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• 2023

In this article, we deal with the biharmonicity of a vector field X viewed as a map from a pseudo-Riemannian manifold (M, g) into its tangent bundle TM endowed with the Sasaki metric g_S. Precisely, we characterize those vector fields which are biharmonic maps, and find the relationship between them and biharmonic vector fields. Afterwards, we study the biharmonicity of left-invariant vector fields on the three dimensional Heisenberg group endowed with a left-invariant Lorentzian metric. Finally, we give examples of vector fields which are proper biharmonic maps on the Gödel universe.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.497-502
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• 2006

An asymmetric Fuglede-Putnam theorem for $p$-hyponormal operators and class ($\mathcal{Y}$) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

• 대한수학회논문집
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• 제36권1호
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• pp.135-147
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• 2021

In this paper, we introduce the harmonicity of a covector field on a Riemannian manifold (M, g) to its cotangent bundle T∗ M equipped with g-natural metric. Afterward we also construct some examples of harmonic covector fields.

• Steel and Composite Structures
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• 제22권2호
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• pp.257-276
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• 2016

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.