• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.753-762
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• 2014

A three-step sextic simple-root finder is constructed with the use of weighting functions of derivative-to-derivative ratios. Their convergence and computational properties are investigated along with concrete numerical examples to verify the theoretical analysis.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.31-38
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• 1999

This paper focuses on extracting formants from transfer function, derived from linear prediction analysis of speech signal. The second derivative of the log magnitude spectrum of the transfer function, the first and third derivatives of the phase spectrum of the transfer function in the z-plane are discussed. Their resolutions of detecting formants are analyzed and some comparisons are given. Theoretical analyses and experimental results show that the third derivative of the phase spectrum decays more rapidly around the formant locations than the first derivative of the phase spectrum and the second derivative of the log magnitude spectrum. Compared with the second derivative of the log spectrum and the first derivative of the phase spectrum, the third derivative of the phase spectrum has higher resolution in frequency domain and provides more accurate formant extraction.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.229-241
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• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.350-354
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• 1999

The problem of the computation of derivatives arises in various applications of rational Bezier curves. These applications sometimes require the computation of derivative on numerous points. Therefore, many researches have dealt with the representation for the computation of derivatives with the small computation error. This paper compares the performances of the representations for the derivative of rational Bezier curves in the performances. The performance is measured as computation requirements at the pre-processing stage and at the computation stage based on the theoretical derivation of computational bound as well as the experimental verification. Based on this measurement, this paper discusses which representation is preferable in different situations.

• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.7-21
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• 2015

We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.109-130
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• 2010

In this paper, a numerical method for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with the mixed type boundary conditions is presented. Parameter-uniform error bounds for the numerical solution and also to numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

• 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 Mechanical Engineers A
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• v.24 no.3 s.174
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• pp.543-549
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• 2000

Results of theoretical investigations of the stability characteristics of an actively controlled externally pressurized air journal bearing are presented. Proportional control and derivative control are used for the control algorithm of active air bearing. The stability characteristics of the actively controlled bearing operating at zero steady-state eccentricity is investigated with the step jump method. The speed at onset of instability is raised for both proportional control and derivative control of bearing. Proportional control increased the stability threshold without affecting the whirl ratio. But for derivative control of bearing, stability threshold increase is accompanied by a parallel reduction of the whirl ratio. Results show active control of bearing can be adopted for the stability improvement of air journal bearing.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1001-1015
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• 2009

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.