• 대한수학회논문집
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• 제11권2호
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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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권8호
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• pp.3585-3601
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• 2016

The error rate performance of circularly distributed antenna system is studied over Nakagami-m fading channels, where a dual-channel receiver is employed for the quadrature phase shift keying signals detection. To mitigate the Co-Channel Interference (CCI) caused by the adjacent cells and to save the transmit power, this work presents remote antenna unit selection transmission based on the best channel quality and the maximized path-loss, respectively. The commonly used Gaussian and Q-function approximation method in which the CCI and the noise are assumed to be Gaussian distributed fails to depict the precise system performance according to the central limit theory. To this end, this work treats the CCI as a random variable with random variance. Since the in-phase and the quadrature components of the CCI are correlated over Nakagami-m fading channels, the dependency between the in-phase and the quadrature components is also considered for the error rate analysis. For the special case of Rayleigh fading in which the dependency between the in-phase and the quadrature components can be ignored, the closed-form error rate expressions are derived. Numerical results validate the accuracy of the theoretical analysis, and a comparison among different transmission schemes is also performed.

• 호남수학학술지
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• 제27권2호
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• pp.317-332
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• 2005

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

• East Asian mathematical journal
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• 제14권1호
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• 대한수학회보
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• 제51권3호
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• 대한수학회보
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• 제44권3호
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• pp.523-536
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• 2007

Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

• 한국전자파학회논문지
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• 제15권12호
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• pp.1184-1189
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• 2004

본 논문에서는 직교신호를 발생할 수 있는 새로운 구조의 전압제어 발진기를 설계 제작하였다. 정확한 직교 신호 특성과 낮은 위상잡음 특성을 동시에 얻기 위하여 결합 증폭기의 source단자에 저항 궤환을 이용하여 차동 발진기를 결합시켰다. 발진기는 0.18 um 표준 CMOS 공정을 이용하여 제작하였다. 제작한 발질기의 위상잡음 특성은 -120 dBc/Hz @ 1 MHz 0$\~$1.8 V 전압을 가변하였을 때, 2.34 GHz$\~$2.55 GHz의 210 MHz 주파수 가변을 얻었다. 또한 낮은 IF 주파수 혼합기와 결합하여 측정한 결과 직교신호의 위상 오차는 0.5도, 진폭 오차는 0.2 dB 이하를 보였다. 바이어스 전류는 1.8 V 공급전압에 대해 전압제어발진기의 Core 부분 5 mA를 포함하여 전체적으로는 19 mA를 요구한다.

• 대한수학회보
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• 제39권1호
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• pp.9-22
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• 2002

We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\Omega$ in $R^{2}.$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $G_{p}= {I_{m}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $I_{m}{\in}G_{p}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}'$.

• Journal of information and communication convergence engineering
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• 제2권2호
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• pp.102-105
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• 2004

A Quadrature phase detector for high-speed delay-locked loop is introduced. The proposed Quadrature phase detector is composed of two nor gates and it determines if the phase difference of two input clocks is 90 degrees or not. The delay locked loop circuit including the Quadrature phase detector is fabricated in a 0.18 um Standard CMOS process and it operates at 5 GHz frequency. The phase error of the delay-locked loop is maximum 2 degrees and the circuits are robust with voltage, temperature variations.

• 한국통신학회논문지
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• 제9권1호
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• pp.18-24
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• 1984

이온충 신틸레이션 채널(transionospheric scintillation channel)에서 PSK通信시스템의 誤率을 가우스 쿼드러처積分(Gauss quadrature integration)公式의 方法을 利用하여 계산하였다. 使用한 채널 모델은 Rino의 모델로 交信信號의 포락선이 相關가우스 랜덤 과정으로 천천히 변하는 페이딩 채널이다. 신틸레이션 채널에 대한 誤率은 UHF帶의 傳送에서 실제 이온중 신틸레이션 데이터를 使用하여 계산하였다.