• 대한수학회보
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• 제49권4호
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• pp.705-714
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• 2012

In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any ${\lambda}$ < ${\lambda}^*$ and no solution for any ${\lambda}$ > ${\lambda}^*$. We show that when ${\lambda}$ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.

• 대한수학회논문집
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• 제21권4호
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• pp.701-717
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• 2006

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.

• 대한수학회논문집
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• 제33권3호
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• pp.871-888
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• 2018

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

• 대한수학회보
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• 제57권2호
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• pp.355-369
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• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.

• Structural Engineering and Mechanics
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• 제13권3호
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• pp.299-312
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• 2002

In this paper, a new method to solve the dynamic response problem for structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an optimum scheme is adopted when there are many interval structural parameters. With the interval algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are developed. Based on the matrix perturbation theory and interval extension of function, the upper and lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to illustrate the validity of the present method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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• pp.304-311
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• 2004

In this paper, three dimensional dynamic infinite elements are developed for the soil-structure interaction analysis in multi-layered halfspace. For the efficient discretization of 3-D for field regions, five types of dynamic infinite elements are developed. They are the horizontal, vertical, upper horizontal conner, lower vertical conner and conner of conner infinite elements. The shape functions of the infinite elements are based on the approximate expressions of the analytical solutions of the propagating waves in the infinite region. Numerical example analyses are presented for demonstrating the effectiveness of the proposed infinite elements.

• Transactions on Electrical and Electronic Materials
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• 제11권5호
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• pp.212-215
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• 2010

$BiFeO_3/Pb(Zr_{0.95}Ti_{0.05})O_3$ (BFO/PZT) heterolayered thin films were fabricated by the spin coating method on a Pt/Ti/$SiO_2$/Si substrate using metal alkoxide solutions. The coating and heating procedure was repeated 6 times to form the heterolayered films. The thickness of the BFO/PZT films after one cycle of drying/sintering is about 30-40 nm. All BFO/PZT films show a void free uniform grain structure without the presence of rosette structures. It can be assumed that the crystal growth of the upper BFO layers can be influenced by the lower PZT layers. As the number of coatings increased, the dielectric constant increased, so that the value for the 6-layer film was 1360 at 1 KHz.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1133-1138
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• 2006

This paper considers a hybrid flow shop scheduling problem for the objective of minimizing the number of tardy jobs. The hybrid flow shop consists of two stages in series, each of which has multiple identical parallel machines, and the problem is to determine the allocation and sequence of jobs at each stage. A branch and bound algorithm that gives the optimal solutions is suggested that incorporates the methods to obtain the lower and upper bounds. Dominance properties are also derived to reduce the search space. To show the performance of the algorithm, computational experiments are done on randomly generated problems, and the results are reported.

• Structural Engineering and Mechanics
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• 제57권6호
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• pp.1143-1156
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• 2016

This paper presents a comparative study of finite element method (FEM) and analytical method for the plane problem of a layered composite containing an internal perpendicular crack in literature. The layered composite consists of two elastic layers having different elastic constants and heights. External load is applied to the upper elastic layer by means o a rigid punch and the lower elastic layer rests on two simple supports. Numerical simulations are realized by the world wide code ANYS software. Two dimensional analysis of the problem is carried out and the results are verified by comparison with solutions reported in literature. Main goal of the numerical simulation is to investigate the normal stress ${\sigma}_x$(0, y), stress intensity factors at the crack factor and the crack opening displacements.

• 한국레이저가공학회지
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• 제11권3호
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• pp.16-20
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• 2008

The lap Joint welding of 6K21 aluminum sheets by Nd:YAG laser were performed with an aluminum 5183 filler wire or without a filler wire. The porosity of laser welding beads were observed through an optical microscope and X-ray photography with various levels of welding speed and gap size. The porosity was observed in the gap between upper and lower sheet near a heat affected zone when autogenous welding. Decrease of welding speed and use of AA5183 filler wire reduced porosity significantly.