• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.337-357
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• 2003

This paper introduces new measures for the stability of slope estimation on the second order response surface at a point and on a sphere. As a measure of point stability of slope estimation, we suggest a point dispersion measure of slope variances over all directions at a point. A spherical dispersion measure is also proposed as a measure of spherical stability of slope estimation on each sphere. Some designs are studied to explore the usefulness of the proposed measures. Using the point dispersion measure, another concept of slope rotatability called equally-stable slope rotatability is proposed as a useful property of response surface designs. We provide a set of conditions for a design to have equally-stable slope rotatability.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Current Optics and Photonics
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• v.7 no.4
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• pp.443-448
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• 2023

The ±1-order Kelly sidebands with dispersion-dependent spacing of mode-locking fiber lasers are investigated for frequency-tunable terahertz signal generation. The principle of dispersion dependence of Kelly sidebands is analyzed. A new method, which is a dispersion-management mechanism introduced into the fiber-laser cavity, is proposed to generate Kelly sidebands with widely tunable wavelength spacing. A spacing tuning range of up to 28.46 nm of the ±1-order Kelly sidebands is obtained in simulation. Using the data of the optical spectrum with dispersion-dependent Kelly sidebands, the frequency spectrum of generated terahertz signals is calculated. Consequently, the signal frequency can be changed from 0.09 to 2.27 THz.

• Journal of the Optical Society of Korea
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• v.13 no.1
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• pp.112-115
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• 2009

We investigate the effect of polarization-mode dispersion (PMD) on the optimum dispersion compensation (ODC) monitoring and nonlinear penalty in optical transmission systems. We report that PMD may reduce the fiber nonlinearity. We also report that the monitoring error of the clock-based ODC monitoring technique decreases after the first-order PMD compensation. A simple explanation of this phenomenon is shown.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.22-27
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• 2006

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.

• Journal of electromagnetic engineering and science
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• v.13 no.3
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• pp.158-164
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• 2013

This paper expands a previously proposed optimized higher order (2, 4) finite-difference time-domain scheme (H(2, 4) scheme) for use with lossy material. A low dispersion error is obtained by introducing a weighting factor and two scaling factors. The weighting factor creates isotropic dispersion, and the two scaling factors dramatically reduce the numerical dispersion error at an operating frequency. In addition, the results confirm that the proposed scheme performs better than the H(2, 4) scheme for wideband analysis. Lastly, the validity of the proposed scheme is verified by calculating a scattering problem of a lossy circular dielectric cylinder.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.233-245
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• 2003

A time fractional advection-dispersion equation is Obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order ${\alpha}$(0 < ${\alpha}$ $\leq$ 1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-dispersion equation.

• Journal of the Optical Society of Korea
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• v.12 no.4
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• pp.240-243
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• 2008

Using the well-known Fokker-Planck method, this paper presents a standard way to find the joint-characteristic function for the first- and second-order polarization-mode-dispersion vectors originally derived by Foschini and Shepp. Compared with the Foschini and Shepp's approach, the Fokker-Planck approach gives a more accurate and straightforward way to find the joint-characteristic function.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.6
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• pp.16-23
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• 2001

Spray dispersion in high pressure diesel engines have been simulated experimentally with a special emphasis on the effect of swirl by using a liquid injection technique. A constant volume chamber was designed to be rotatable in order to generate a continuous swirl and to have the flow field closely resembling a solid body rotation. Emulsified fuel was injected into the chamber and the developing process of fuel sprays was visualized. The effect of swirl on the spray dispersion was quantified by calculating non-dimensionalized dispersion area according to the spray tip penetration length. The results show that the effect of swirl on the spray dispersion is different between short and long spray penetrations. For short range of spray tip penetration, the effect of swirl on spray dispersion is quite small. However, as the spray tip is penetrated into longer distance in spray chamber, the effect of swirl on spray dispersion becomes larger. These results can be used as a basic data for designing combustion chamber and injection system of direct injection diesel engine.