• 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.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.2
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• pp.104-109
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• 2011

I present a method of aspheric surface profile measurement using 2nd derivative of local area profile. This method is based on the principle of curvature sensor which measures the local 2nd derivative under test along a line. The profile is then reconstructed from the data on the each point. Unlike subaperture-stiching method and slope detection method, 2nd derivative method has strong points from a geometric point of view in measuring the aspheric surface profile. The second derivative terms of surface profile is an intrinsic property of the test piece, which is independent of its position and tip-tilt motion. The curvature is measured at every local area with high accuracy and high lateral resolution by using White-light scanning interferometry.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.191-198
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• 2012

Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2001.11a
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• pp.169-172
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• 2001

There are many people who suffer from simulation sickness when immersing in virtual reality. In this study, we analyzed two photoplethysmogram(PPG) parameters - a second derivative parameter and power spectral density ratios - in order to relate PPG parameters with simulation sickness. 36 young, healthy subjects were participated in the experiment, and each subject was equipped with a PPG electrode during his or her immersion. Simulation sickness section was defined as a 7 - second section which starts from the point where a subject reported simulation sickness, and normal section as a same-length section where no physical stimuli was presented to him or her. We compared the PPG parameters of the simulation sickness sections with the normal sections, - d/a ratio is believed to have lower value during vasodilation and higher value during vasoconstriction, however, we could not find much difference in the parameter between normal and simulation sickness sections. We also compared 1 to 10Hz power spectral density ratios in normal sections with in simulation sickness section, and found that 6 density ratios among them have different value. Therefore, the density ratios might be utilized as parameters to detect simulation sickness of subjects.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.5
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• pp.72-82
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• 1998

Power transformer protective relay should block the tripping during magnetizing imrush and rapidly operate the tripping during internal faults. But traditional approaches maloperate in the case of magnetizing inrush with low second harmonic component and internal faults with high second harmounic component. To enhance the fault detection sensitivities of conventional technuques, flux-differential current derivative curve by fuzzy theory approaches is used. This paper deals with fuzzy logic based protective relaying for power transformer. The proposed fuzzy based relaying algorithm consisits of flux-differential current derivative curve, harmonics restraint, and precentage differential characteristic curv. The proposed relaying was tested with relaying signals obtained from Salford EMTP simulation package and showed a fast and accurate trip operation.

• 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.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.11 no.10
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• pp.778-783
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• 1998

Film characteristics of thin ONO dielectric layers for MONOS(metal-oxide-nitride-oxide-semiconductor) EEPROM was investigated by TEM, AES and AFM. Seocnd derivative spectra of Auger Si LVV overlapping peak provide useful information fot chemical state analysis of superthin film. The ONO film with dimension of tunnel oxide 23$\AA$, nitride 33$\AA$, and blocking oxide 40$\AA$ was fabricated. During deposition of the LPCVD nitride film on tunnel oxide, this thin oxide was nitrized. When the blocking oxide was deposited on the nitride film, the oxygen not only oxidized the nitride surface, but diffused through the nitride. The results of ONO film analysis exhibits that it is made up of $SiO_2$ (blocking oxide)/O-rich SiON(interface)/N-rich SiON(nitride)/ O-rich SiON(tunnel oxide)

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• Journal of Acupuncture Research
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• v.19 no.3
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• pp.126-137
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• 2002

Objective : There is accumulating data that cardiovascular diseases, including hypertension, cerebro-vascular accident, coronary heart disease, relate to atherosclerotic changes. Increased serum levels of lipids could play a role in these circumstances. the SDPTG(the second derivative of photoplethysmogram waveform) is noninvasive methods for evaluating the pulse wave and is correlated with age and other risk factors for atherosclerosis. Methods : To study the effects of serum lipid levels on the SDPTG in the middle-age adults, data on serum lipid levels and the SDPTG were collected in 80 healthy middle age with varying serum lipid concentrations. Biological vascular age was assessed using the SDPTG. the SDPTG consists of an a, b, c, and d wave in systole and an e wave in diastole; an SDPTG aging index(Al) was calculated as (b-c-d-e)/a. Results : Serum triglyceride, total cholesterol, total lipid, phospholipid, HDL cholesterol levels were respectively and significantly correlated with SDPTG Al. Serum lipid levels and blood pressure are age-dependent and the SDPTG is blood pressure-dependent. Restricting analysis to age and blood pressure yield strong positive correlations between serum triglyceride, total lipid levels and SDPTG Al, but no correlations between serum total cholesterol, phospholipid levels and SDPTG Al. Conclusion : The results of this study suggest that preventive acupuncture programs or herbal medications for reducing serum lipid, especially triglyceride, levels in middle-age should include a evaluation of biological vascular aging with the second derivative of photoplethysmogram waveform.