• 대한수학회논문집
• /
• 제9권2호
• /
• pp.423-438
• /
• 1994

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) ＋ $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f ＋ Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$ ⊂ $L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.9-9
• /
• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• 전자공학회논문지D
• /
• 제35D권1호
• /
• pp.8-15
• /
• 1998

An analysis of the microstripline is started as an assumption of the axial & transveral current distribution. Applying the boundary conditions to the scalar wave equations of a electric & magnetic potential, the two simultaneous coupled integral equations are produced. The electronmagnetic fields in microstrip line can be obtained by solving these two coupled integral equaltion. In general, either a numerical analysis method or a Galerkin method was used to solve them. In this paper, a residue theorem is proposed to solve them. The electromagnetic fields are expressed as integral equations for LSE and LSM mode in the spectral domain. Applying a residue theorem to the Fourier transformed equation and Fourier inverse transformed equation which is necessary for interchanging the space domain and the spectral domain, the electromagnetic fields are expressed as algebraic equations whichare relatively easier to handle. the distributions of the electromagnetic field are shown at the range of -5w/2.leq.x.leq.5w/2, 0.lep.y.leq.4h for z=0. It agrees well with the results of the Quasi-TEM mode analysis.

• Journal of the Optical Society of Korea
• /
• 제15권2호
• /
• pp.187-195
• /
• 2011

We have designed two photonic crystal waveguide (PCW) structures with output focused beams in order to achieve more coupling between photonic devices and decrease the mismatch losses in photonic integrated circuits. PCW with coupled resonator optical waveguide (CROW) termination has been optimized by both one dimensional (1D) and seven dimensional (7D) particle swarm optimization (PSO) algorithms by evaluating the fitness function by the finite difference time domain (FDTD) method. The 1D and 7D-optimizations caused the factors of 2.79 and 3.875 improvements in intensity of the main lobe compared to the non-optimized structure, whereas the FWHM in 7D-optimized structure was increased, unlike the 1D case. It has also been shown that the increment of focusing causes decrement of the bandwidth.

• Journal of information and communication convergence engineering
• /
• 제13권1호
• /
• pp.50-55
• /
• 2015

We report design and simulation of a two-dimensional (2D) silicon-based nanophotonic crystal as an optical insulator to enhance the light emission efficiency of light-emitting diodes (LEDs). The device was designed in a manner that a triangular array silicon photonic crystal light insulator has a square trench in the middle where LED can be placed. By varying the normalized radius in the range of 0.3-0.5 using plane wave expansion method (PWEM), we found that the normalized radius of 0.45 creates a large band gap for transverse electric (TE) polarization. Subsequently a series of light propagation simulation were carried out using 2D and three-dimensional (3D) finite-difference time-domain (FDTD). The designed silicon-based light insulator device shows optical characteristics of a region in which light propagation was forbidden in the horizontal plane for TE light with most of the visible light spectrum in the wavelength range of 450 nm to 600 nm.

• East Asian mathematical journal
• /
• 제19권1호
• /
• pp.73-80
• /
• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• Bulletin of the Korean Chemical Society
• /
• 제26권6호
• /
• pp.952-958
• /
• 2005

Angiotensin-converting enzyme (ACE) is known to be primarily responsible for hypertension. Threedimensional quantitative structure-activity relationship (3D-QSAR) models have been constructed using the comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) for a series of 28 ACE inhibitors. The availability of ACE crystal structure (1UZF) provided the plausible biological orientation of inhibitors to ACE active site (C-domain). Alignment for CoMFA obtained by docking ligands to 1UZF protein using FlexX program showed better statistical model as compared to superposition of corresponding atoms. The statistical parameters indicate reasonable models for both CoMFA ($q^2$ = 0.530, $r^2$ = 0.998) and CoMSIA ($q^2$ = 0.518, $r^2$ = 0.990). The 3D-QSAR analyses provide valuable information for the design of ACE inhibitors with potent activity towards C-domain of ACE. The group substitutions involving the phenyl ring and carbon chain at the propionyl and sulfonyl moieties of captopril are essential for better activity against ACE.

• 대한전자공학회논문지TC
• /
• 제45권8호
• /
• pp.121-127
• /
• 2008

본 논문은 원통형 확산기를 사용한 전자파 잔향실내의 전기장 분포에 관하여 다루었다. $1{\sim}3$ GHz 주파수 대역의 QRD(Quadratic Residue Diffuser)와 원통형 확산기(Cylindrical Diffuser)를 설계 후 각각의 전기장 분포 특성을 비교하였다. 전기장 분포 특성 및 전기장 균일도를 조사하기 위해 FDTD(Finite-Difference Time-Domain) 수치 해석 방법을 사용하였으며, 2 GHz에서 수치해석 결과 원통형 확산기를 사용하였을 경우 기존의 QRD를 사용한 경우에 비하여 표준편차와 공차는 각각 0.11 dB, 0.43 dB 개선되었고, 전기장 세기는 QRD의 36.6 dBmV/m보다 높은 43.2 dBmV/m로 나타났으며, 편파 특성면에서도 QRD보다 개선되었음을 확인 할 수 있었다. 따라서 원통형 확산기를 사용한 전자파 잔향실이 소형 전자기기의 전자파 장해 및 복사 내성 측정을 위한 대용시험 시설로 사용될 수 있음을 확인하였다.

• 한국광학회지
• /
• 제4권1호
• /
• pp.1-8
• /
• 1993

축소배율(5$\times$)을 갖고, Seidel 1차 수차중 4개의 비축수차인 코마(coma), 비점수차(astigmatism), 상면만곡(field curvature) 그리고 왜곡수차(distortion)가 제거된 마이크로 리소그라피를 위한 4-구면 반사경 광학계를 해석적으로 구하였다. 이때, $t=d_1+d_2+d_3$<0, (di는 반사거울 $c_i$와 $c_{i+1}$ 사이의 거리)이고, 축상 수차인 구면수차와 잔류고차수차는 반사거울 $c_3$와 $c_4$를 비구면화 하므로서 제거하였다. 이렇게 설계된 4-반사경 광학계의 N.A.는 0.4로서 Rayleigh분해능은 0.38 $\mu\textrm{m}$이다.

• Wind and Structures
• /
• 제5권2_3_4호
• /
• pp.379-392
• /
• 2002

Numerical flow computations around an aeroelastic 3D square cylinder immersed in the turbulent boundary layer are shown. Present computational code can be characterized by three numerical aspects which are 1) the method of artificial compressibility is adopted for the incompressible flow computations, 2) the domain decomposition technique is used to get better grid point distributions, and 3) to achieve the conservation law both in time and space when the flow is computed a with moving and transformed grid, the time derivatives of metrics are evaluated using the time-and-space volume. To provide time-dependant inflow boundary conditions satisfying prescribed time-averaged velocity profiles, a convenient way for generating inflow turbulence is proposed. The square cylinder is modeled as a 4-lumped-mass system and it vibrates with two-degree of freedom of heaving motion. Those blocks which surround the cylinder are deformed according to the cylinder's motion. Vigorous oscillations occur as the vortex shedding frequency approaches cylinder's natural frequencies.