• 대한수학회논문집
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• 제33권2호
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• pp.619-630
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• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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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.

• Computational Structural Engineering : An International Journal
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• 제2권1호
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• pp.43-50
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• 2002

This paper presents a method to predict dynamic responses of floating bodies in the time domain. Because of the frequency-dependence of the radiation wave forces, the memory effect must be taken into account when the responses are evaluated in the time domain. Although the formulations firstly developed by Cummins (1962) have been well-known for this purpose, the effective numerical procedure has not been established yet. This study employs FFT (Fast Fourier Transform) algorithm to evaluate the memory effect function, and the equations of motion of an integro-differential type are solved by Newmark-β method. Numerical examples for a truncated circular cylinder have indicated the effectiveness of the proposed numerical procedure.

• 호남수학학술지
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• 제45권2호
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• pp.184-197
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• 2023

For the numerous uses and significance of the Whittaker function in the diverse research areas of mathematical sciences and engineering sciences, This paper aims to introduce an extension of the Whittaker function by using a new extended confluent hypergeometric function of the first kind in terms of the Mittag-Leffler function. We also drive various valuable results like integral representation, integral transform and derivative formula. Further, we also analyze specific known results as a particular case of the main result.

• Journal of Ginseng Research
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• 제42권4호
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• pp.504-511
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• 2018

Background: The biological activities of ginseng saponins (ginsenosides) are associated with type, number, and position of sugar moieties linked to aglycone skeletons. Deglycosylated minor ginsenosides are known to be more biologically active than major ginsenosides. Accordingly, the deglycosylation of major ginsenosides can provide the multibioactive effects of ginsenosides. The purpose of this study was to transform ginsenoside Rb2, one of the protopanaxadiol-type major ginsenosides, into minor ginsenosides using ${\beta}$-glycosidase (BG-1) purified from Armillaria mellea mycelium. Methods: Ginsenoside Rb2 was hydrolyzed by using BG-1; the hydrolytic properties of Rb2 by BG-1 were also characterized. In addition, the influence of reaction conditions such as reaction time, pH, and temperature, and transformation pathways of Rb2, Rd, F2, compound O (C-O), and C-Y by treatment with BG-1 were investigated. Results: BG-1 first hydrolyzes 3-O-outer ${\beta}$-$\text\tiny{D}$-glucoside of Rb2, then 3-O-${\beta}$-$\text\tiny{D}$-glucoside of C-O into C-Y. C-Y was gradually converted into C-K with a prolonged reaction time, but the pathway of Rb2 ${\rightarrow}$ Rd ${\rightarrow}$ F2 ${\rightarrow}$ C-K was not observed. The optimum reaction conditions for C-Y and C-K formation from Rb2 by BG-1 were pH 4.0-4.5, temperature $45-60^{\circ}C$, and reaction time 72-96 h. Conclusion: ${\beta}$-Glycosidase purified from A. mellea mycelium can be efficiently used to transform Rb2 into C-Y and C-K. To our best knowledge, this is the first result of transformation from Rb2 into C-Y and C-K by basidiomycete mushroom enzyme.

• Journal of Microbiology and Biotechnology
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• 제19권12호
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• pp.1650-1655
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• 2009

The $\beta$-glucuronidase (GUS) gene from Lactobacillus brevis RO1 was cloned and expressed in Escherichia coli GMS407. The GUS gene was composed of 1,812 bp, encoding a 603-amino-acid protein belonging to glycosyl hydrolase family 2 with three conserved domains. The amino acid similarity was higher than 70% with the $\beta$-glucuronidases of various microorganisms, yet less than 58% with the $\beta$-glucuronidase of L. gasseri ADH. Overexpression and purification of the GUS was performed in $\beta$-glucuronidase-deficient E. coli GMS407. The purified GUS protein was 71 kDa and showed 1,284 U/mg of specific activity at optimum conditions of pH 5.0 and $37^{\circ}C$. At $37^{\circ}C$, the GUS remained stable for 80 min at pH values ranging from 5.0 to 8.0. The purified enzyme exhibited a half-life of 1 h at $60^{\circ}C$ and more than 2 h at $50^{\circ}C$. When the purified GUS was applied to transform baicalin and wogonoside into their corresponding aglycones, $150\;{\mu}M$ of baicalin and $125\;{\mu}M$ of wogonoside were completely transformed into baicalein and wogonin, respectively, within 3 h.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1997년도 춘계학술대회 논문집
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• pp.297-300
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• 1997

In this study, The PVDF thin film was fabricated on the one method of dry-process the physical vapor deposition method, applied electric field, and evaporation control in $\beta$-PVDF thin film preparation. A study on the electric-field-phase change of PVDF thin film in physical vapor deposition using the polymer deposition apparatus which are manufactured for oneself. In the analysis of Fourier-Transform Infrared spectra, according to increasing of electric field intensity, the 510$cm^{-1}$ / peak and 1273$cm^{-1}$ / peak which are showed in $\beta$-PVDF increase, on the contrary the 530$cm^{-1}$ / peak and 977$cm^{-1}$ / peak which are showed in $\alpha$-PVDF decrease.

• 대한의용생체공학회:의공학회지
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• 제8권2호
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• pp.223-230
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• 1987

In this paper the harmonic degrees between $\alpha$ wave and $\beta$ wave in visual evoked potential are analyzed by the bicoherence. The bicoherence analysis is based on an AR model which provides significantly better resolution than that of Fourier transform. The analysis results of visual evoked pope ntial are compared with the analysis results of background EEC. From the comparison results it is found that the harmonic degree of visual evoked potential is less than she harmonic degree of background EEG and the $\beta$ wave of visual evoke potential unlike the background EEC contains the non harmonic property of a wave more than the harmonic properity

• 동력기계공학회지
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• 제16권5호
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• pp.20-25
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• 2012

오늘날 고속 철도는 중요한 교통수단으로 사용되고 있다. 주행거리 단축을 위해 직선 선로를 만드는 것이 불가피해 졌고 그에 따라 터널과 교량의 구간이 늘어나게 되었다. 특히 터널 통과 시에 발생되는 실내 소음은 운행 속도, 운행 구간 레일의 종류 등 여러 가지 원인에 의해 야기되어 진다. 실내소음으로 인해 철도를 이용하는 승객의 쾌적한 환경에 많은 영향을 미치게 된다. 이에 본 연구에서는 KTX와 새마을호의 터널 통과 시 발생되는 소음이 피험자에게 미치는 영향을 EEG를 통해 살펴보았다. 먼저 터널 통과 시 KTX와 새마을호의 실내 소음을 실제로 측정하여 크기, 주파수별로 분석하였다. 측정된 실내 소음을 피험자에게 제시하였을 때 나타나는 EEG를 측정하였다. EEG의 분석에 대해서는 불안, 긴장 등 스트레스를 받을 때 강하게 나타나는 ${\beta}$파의 변화를 관찰한 결과를 제시하였다.

• 대한수학회논문집
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• 제32권2호
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• pp.321-332
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• 2017

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.