• Communications of the Korean Mathematical Society
• /
• v.16 no.4
• /
• pp.691-701
• /
• 2001

We computed zero mean Gaussian of average error bounds pf Simpsons quadrature with convariances in [2]. In this paper, we compute zero mean Gaussian of average error bounds between Simpsons quadrature and composite Simpsons quadra-ture on four consecutive subintervals. The reason why we compute these on subintervals is because these results enable us to compute a posteriori error bounds on the whole interval in the later paper.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.293-307
• /
• 1997

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ $\mid$R_n(f)$\mid$ \leq \frac{2\pi}{\sqrt{l(\Gamma)}} max_{z\in\Gamma}$\mid$f(z)$\mid$ (\smallint_\Gamma $\mid$K_n(z)$\mid$^2$\mid$dz$\mid$)^\frac{2}{1}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2009.03a
• /
• pp.188-194
• /
• 2009

Consolidation settlement, a crucial parameter in geotechnical design of soft ground, has not been computed in a unique way due to different computation methods in practice. To improve computational error in calculating consolidation settlement, a number of researches has been attempted. Conventional 1-dimensional consolidation theory assumes the center of the clay layer as the representative point to obtain effective stress in calculation, which could resort to erroneous results. To calculate exact solutions considering initial distribution of effective stress, diving a stratum into multi-layers could resort to wasting time and effort. In the study, a novel methodology for calculating consolidation settlement via Guassian quadrature is developed. The method generally is capable of computing settlements in any case of the stress conditions encountered in fields.

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

• Structural Engineering and Mechanics
• /
• v.3 no.2
• /
• pp.135-144
• /
• 1995

Since structural systems may fail in any one of several failure modes, computation of system reliability is always difficult. A method using numerical quadrature for computing structural system reliability with either one or more than one failure mode is presented in this paper. Statistically correlated safety margin equations are transformed into a group of uncorrelated variables and the joint density function of these uncorrelated variables can be generated by using the Maximum Entropy Method. Structural system reliability is then obtained by integrating the joint density function with the transformed safety domain enclosed within a set of linear equations. The Gaussian numerical integration method is introduced in order to improve computational accuracy. This method can be used to evaluate structural system reliability for Gaussian or non-Gaussian variables with either linear or nonlinear safety boundaries. It is also valid for implicit safety margins such as computer programs. Both the theory and the examples show that this method is simple in concept and easy to implement.

• Proceedings of the IEEK Conference
• /
• 2000.07a
• /
• pp.517-520
• /
• 2000

This paper deals with the statistical analysis of an autocalibration procedure for the gain and phase imbalances between the in-phase (I) and quadrature (Q) components in quadrature receivers. In real implementation, the imbalances of the gain and phase exist and degrade the performance of the receiver. In this paper we investigate the statistical characteristic of the estimates in an on-line imbalance estimation method for the receiver under the assumption of an additive white Gaussian noise environment.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.10 no.8
• /
• pp.3585-3601
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.4 no.1
• /
• pp.161-166
• /
• 1989

• Communications of the Korean Mathematical Society
• /
• v.8 no.3
• /
• pp.545-554
• /
• 1993

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.13 no.4
• /
• pp.285-301
• /
• 1988

The symbol error rate equations of multi-level quadrature PRS(QPRS) system have been derived in the individual and composite environment of Gaussian/impulsive noise, cochannel CW interference, carrier offset, phase jitter and fading. And using the derived error rate equations, the probability of error has been evaluated and shown in graphs as functions of carrier to noise power ratio, carrier to interference power ratio, phase error, impulsive index, the ration of Gaussian noise to impulsive noise power component, signal to noise power ration in phase locked loop(PLL), and fading figures. The rseults show that the error rate performances are generally more more degraded by impulsive noise than by Gaussian noise. But on the contrary the erors occurred more frequently by Gaussian noise than impulsive noise in a fading environment.