• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.8
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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.

• Honam Mathematical Journal
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• v.27 no.2
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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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• v.14 no.1
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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 ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.12 s.91
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• pp.1184-1189
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• 2004

A new schematic of quadrature voltage controlled oscillator(QVCO) is designed and fabricated. To obtain quadrature characteristic and low phase noise simultaneously, two differential VCOs are forced to un in quadrature mode by using coupling amplifier with a source degeneration resistor, which is optimized to obtain quadrature accuracy with minimum phase noise degradation. The designed QVCO was fabricated in standard CMOS technology. The measured performance showed the phase noise of below -120 dBc/Hz at 1 MHEz frequency offset, tuning bandwidth of 210 MHz from 2.34 GHz to 2.55 GHz with a tuning voltage varying form 0 to 1.8 V Quadrature error of 0.5 degree and amplitude error of 0.2 dB was measured with conjunction with low-lF mixer. The fabricated QVCO requires 19 mA including 5 mA in the VCO core part fiom a 1.8 V supply.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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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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• v.2 no.2
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.9 no.1
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• pp.18-24
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• 1984

Calculation of error probabilities for a coherent phase-shilft keyed communication system operating in a transionospheric scintillation channel is accomplished by means of the Gauss-quadrature integration formula. The channel model used, patterned after Rino's work, is slowly flat fading wherein the envelope of the received signal is modeled as the envelope of correlated Gaussian quadrature random processes. The error probability for the scintillation channel is calculated using actual ionospheric scintillation data for transmission in the UHF region(30-300MHz).