• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.503-514
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• 1996

We consider non-constant coefficient elliptic equations of the type -div(a \bigtriangledown u) = f$, and employ the P-version of the finite element method as a numerical method for the approximate solutions. To compute the integrals in the variational form of the discrete problem we need the numerical quadrature rule scheme. In practice the integrations are seldom computed exactly. In this paper, we give an $L_2(\Omega)$-error estimate of $\Vert u = \tilde{u}_p \Vert_{0,omega}$ in comparison with $\Vert u = \tilde{u}_p \Vert_{1,omega}$, under numerical quadrature rules which are used for calculating the integrations in each of the stiffness matrix and the load vector.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.905-915
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• 2000

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.993-1002
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• 2017

Let ${\Omega}$ be a bounded, uniformly totally pseudoconvex domain in ${\mathbb{C}}^2$ with the smooth boundary b${\Omega}$. Assuming that ${\Omega}$ satisfies the negative ${\bar{\partial}}$ property. Let M be a positive, finite area divisor of ${\Omega}$. In this paper, we will prove that: if ${\Omega}$ admits a maximal type F and the ${\check{C}}eck$ cohomology class of the second order vanishes in ${\Omega}$, there is a bounded holomorphic function in ${\Omega}$ such that its zero set is M. The proof is based on the method given by Shaw [27].

• Tunnel and Underground Space
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• v.19 no.6
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• pp.558-566
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• 2009

Time-dependent behavior is a basic mechanical property of rocks. Predicting the failure time of rock structures by analyzing the time-dependent characteristic is important and problematic. It is tried to predict the failure time of tunnel, slope & laboratory creep test specimen from measured displacement(or strain) and rate with relationship suggested by Voight($\ddot{\Omega}=A\dot{\Omega}^\alpha$, where $\Omega$ is a measurable quantity such as strain & displacement and A & $\alpha$ are constants). A & $\alpha$ are estimated through applying the nonlinear least square method to the single and double integrated Voight's equations and utilized to predict the failure time. Predicted failure time is in accordance with real one except minor error. Linear inverse rate method applied to creep strain and rate yields a poor linear correlation of data and precision of predicted failure time is not better than methods using strain and rate.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1711-1721
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• 1992

A nonlinear dissipative dynamical system can often have multiple attractors. In this case, it is important to study the global behavior of the system by determining the global domain of attraction of each attractor. In this paper we study the global behavior of a forced beam with two mode interaction. The governing equation of motion is reduced to two second-order nonlinear nonautonomous ordinary differential equations. When .omega. /=3.omega.$_{1}$ and .ohm.=.omega $_{1}$, the system can have two asymptotically stable steady-state periodic solutions, where .omega./ sub 1/, .omega.$_{2}$ and .ohm. denote natural frequencies of the first and second modes and the excitation frequency, respectively. Both solutions have the same period as the excitation period. Therefore each of them shows up as a period-1 solution in Poincare map. We show how interpolated mapping method can be used to determine the two four-dimensional domains of attraction of the two solutions in a very effective way. The results are compared with the ones obtained by direct numerical integration.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.6 no.4
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• pp.493-500
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• 1996

AZO transparent conducting thin films were fabricated by reactive DC magnetron sputtering method using Zn metla target containing 2 wt% of Al, and electrical and optical properties were investigated after heattreatment. Electrical resistivity was reduced 50% and had reached $1{\times}10^{-3}~3.5{\times}10^{-4}\;{\Omega}cm$ by heat treatment. In the case of oxide AZO films, the resistivity of $10^{3}\;{\Omega}cm$ was also decreased to $2{\times}10^{-3}\;{\Omega}cm$ after heat treatment. The optical transmittance of AZO films deposited in the transition range was increased from 59.4 % to 77.4 % by $400^{\circ}C$, 30 min heat treatment.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.16-17
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• 2006

In order to obtain spherical fine powder, we have developed a new method of high-pressure water atomization system using swirl water jet with the swirl angle $(\omega)$. The effect of nozzle apex angle $(\theta)$ upon the morphology of atomized powders was investigated. Molten copper was atomized by this method, with $\omega=0.2$ rad (swirl water jet) and $\omega=0$ rad (conical water jet). It was found that the median diameter $(D_{50})$ of atomized powders decreased with decreasing $(\theta)$ down to 0.35 rad in each $\omega$, but under ${\theta}<\;0.35$ rad, $D_{50}$ increased abruptly with decreasing $\theta$ for $\omega=0$ rad, while it was still decreased with decreasing $(\theta)$ for $\omega=0.2$ rad.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.17-28
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• 2018

In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.329-339
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• 1995

Let us consider the Neumann problem for a quasilinear equation $$ (I_\varepsilon) {\varepsilon^m div($\mid$\nabla_u$\mid$^{m-2}\nabla_u) - u$\mid$u$\mid$^{m-2} + f(u) = 0 in \Omega {\frac{\partial\nu}{\partial u} = 0 on \partial\Omega. $$ where $1 < m < N, N \geq 2, \varepsilon > 0, \Omega$ is a smooth bounded domain in $R^n$ and $\nu$ is the unit outer normal vector to $\partial\Omega$.