• Structural Engineering and Mechanics
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• v.83 no.1
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• pp.67-77
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• 2022

In this study, frictionless continuous and discontinuous contact problems of a magneto-electro-elastic layer in the presence of the body force were discussed. The layer was indented by a rigid cylindrical insulating punch and supported by a rigid substrate without bond. Applying the Fourier integral transform technique, the general expressions of the problem were derived in the presence of body force. Thanks to the boundary conditions, the singular integral equations were obtained for both the continuous and the discontinuous contact cases. Gauss-Chebyshev integration formulas were used to transform the singular integral equations into a set of nonlinear equations. Contact width under the punch, initial separation distance, critical load, separation regions and contact stress under the punch and between the layer, and substrate were given as a result.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.53-57
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• 2002

In this paper we give an example of energy minimizing harmonic maps for which the set of singular points are two or more lines intersecting at a point.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.273-280
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• 1996

In this paper we extend the concept of the Sobolev wave front set of a distribution to the one of the generalized Sobolev wave front set of a generalized distribution, and we investigate the relations among these concepts. Finally, we prove the local property of these sets.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.345-358
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• 1998

Let (p/q,n) denote the orbifold with its underlying space $S^3$ and a rational knot or link p/q as its singular set with a cyclic isotropy group of order n. In this paper we shall show the geometrical realization for the case (7/3,n) for all $n \geq 3$.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.39-46
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• 1996

Let $\alpha > 0$ and $\zeta$ be a point on the unit circle $T= {$\mid$z$\mid$ = 1}$ of the complex plane C.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.107-127
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• 2014

The goal of this note is to describe the asymptotic behaviour of problems set in cylinders when the size of them is becoming infinite. This leads to consider problems in unbounded domains as well as new singular perturbations issues.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11C
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• pp.1118-1122
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• 2003

In this paper, we propose a new invisible digital watermarking scheme based on wavelet transform using singular value decomposition. Embedding process is started by decomposing the lowest frequency band image with 3${\times}$3 block among which we define the watermark block chosen by a key set; entropy and condition number of the block. A watermark is embedded in the singular values of each watermark blocks. This provides a robust watermarking in lowest possible time-frequency domain. To detect the watermark, we are locally modeling an attack as 3${\times}$3 matrices on the watermark blocks. Combining with the SVD and the attack matrices, we estimate watermark set corresponding to the watermark blocks. In each watermark block, we determine an optimal watermark which is justified by the T-testing. A numerical experiment shows that the proposed watermarking scheme efficiently detects the watermarks from several JPEG attacks.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.545-565
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• 2016

In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = and ${\Omega}$ = stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.

• Structural Engineering and Mechanics
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• v.14 no.2
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• pp.151-170
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• 2002

Moving force identification is a very important inverse problem in structural dynamics. Most of the identification methods are eventually converted to a linear algebraic equation set. Different ways to solve the equation set may lead to solutions with completely different levels of accuracy. Based on the measured bending moment responses of the bridge made in laboratory, this paper presented the time domain method (TDM) and frequency-time domain method (FTDM) for identifying the two moving wheel loads of a vehicle moving across a bridge. Directly calculating pseudo-inverse (PI) matrix and using the singular value decomposition (SVD) technique are adopted as means for solving the over-determined system equation in the TDM and FTDM. The effects of bridge and vehicle parameters on the TDM and FTDM are also investigated. Assessment results show that the SVD technique can effectively improve identification accuracy when using the TDM and FTDM, particularly in the case of the FTDM. This improved accuracy makes the TDM and FTDM more feasible and acceptable as methods for moving force identification.