• 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.

• Bulletin of the Korean Chemical Society
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• v.32 no.1
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• pp.109-112
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• 2011

A new derivative of tacrolimus was evaluated for its molecular weight, using LC-MS of the tacrolimus bulk active pharmaceutical ingredient (API) recovered through the purification of crude tacrolimus produced by Streptomyces clavuligerus CKD-1119. In addition, the molecular weight of the new derivative of tacrolimus was found to be at m/z 818 and was identified by $^{13}C$-NMR with peak assignments based on the differences in methyl group location resulting from the chemical structure. The structure of the new derivative, an unknown impurity of tacrolimus, was found to be 18-methyltacrolimus through comparison of the spectral data of the structural differences between ascomycin, tacrolimus, and the new derivative 18-methyltacrolimus.

• 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.

• Bulletin of the Korean Chemical Society
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• v.9 no.2
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• pp.84-87
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• 1988

The Photophysical and photochemical properties of Ruthenium bipyridine with two long hydrocarbon chains, $[Ru(bipy)_2(dhbipy)]^{2+}$ and transient phenothiazine derivative cation radical $(PTD^+)$ in the cationic vesicle were studied. Transient absorption spectra of cation radical of phenothiazine derivative in the vesicle system containing the $Ru^{2+}$ complex, $[Ru(bipy)_2(dhbipy)]^{2+}$, (1) as sensitizer and phenothiazine derivative as electron donor was observed by XeCl excimer laser photolysis system. Thus the excited ruthenium complex would be quenched by phenothiazine derivative(PTD) reductively in the vesicle system. The quenching rate constant($K_Q$) of $Ru^{2+}$ with two long hydrocarbon chains in the vesicle by PTD was $9.6{\times}10^8M^{-1}S^{-1}$. The absorption decay kinetics showed that lifetime of phenothiazine derivative cation radical is a value in the 4-8m sec range.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.629-640
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• 1998

The original work for representing derivative operators in the wavelet bases was done by Beylkin in [2]. In this paper we present an alternative and easier derivation.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.157-162
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• 1999

In this paper, we introduce approximate Perron-Stieltjes integral and approximate Roussel derivative and investigate the differentiability of indefinite approximate Perron-Stieltjes integral.

• The Journal of Internal Korean Medicine
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• v.23 no.2
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• pp.212-221
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• 2002

Objectives : Acording to the fact that Juakium has been frequently used in a lot of prescriptions to tonify bone marrow, We examined the hematopoietic effects of Juakium-derivative on aplastic anemia. Methods : After C57BL/6 mice were oral administrated with Juakium-derivative and injected with benzene, we counted the number of WBC, RBC, hemoglobin, platelet, nucleated cells and other erythroid parameters and weighed the spleen. Also we measured the expression of $CD34^+$ cell activity and analyzed the bone marrow tissue and spleen tissue histologically. Results : The results are summerized as follow: 1. The Juakium-derivative plus benzene group showed the improvement in the number of WBC, RBC, hemoglobin. platelet, nucleated cells and other erythroid parameters, compared with the benzene only group. 2. The spleen weight and the percent of $CD34^+$ cell of Juakium-derivative plus benzene group was higher, compared with the benzene only group. 3. The bone marrow tissue and spleen tissue of the Juakium-derivative plus benzene group showed the decrease of the infarcted area compared with the benzene only group. Conclusions : These results suggest that Juakium-derivative has hematopoietic effects on aplastic anemia induced by benzene through increasing the blood cells and stimulating the activity of $CD34^+$ cells. Therefore it is expected that Juakium-derivative can be used clinically to the patient with hematopoietic system disorder.

• Journal of Soil and Groundwater Environment
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• v.15 no.6
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• pp.46-52
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• 2010

Derivative analysis, based on the derivative of the drawdown as a function of time (i.e., rate of drawdown change), was applied to the evaluation of hydraulic parameters of the aquifer as an aid of the aquifer test interpretation based on the Theis solutions. Pumping tests were conducted at a coastal fractured aquifer in Muan county, Korea, of which the drawdown data, measured at the two observation wells, were used for derivative analysis. Wellbore storage and transition period were hard to identify at conventional log-log and semi long plots, but was easily recognized by distinctive curves of positive unit slope, hump and negative unit slope in the derivative plot. For the observation well of OW-2 at which wellbore storage and transition lasted over an hour, conventional aquifer analysis would suffer from the uniqueness problems and in further result in erroneous hydraulic parameters. Derivative analysis was found to be effective for distinguishing the drawdown data directly reflecting the aquifer property from those reflecting non aquifer effects such as wellbore storage and transition, which offers a unified methodology to yield correct hydraulic parameters from aquifer test data.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.4
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• pp.591-599
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• 2021

The increased risk in financial firms, due to Global Financial Crises and high international trade activities, has encouraged banks to use derivatives for both managing their financial risk and earning non-operating income simultaneously. The present study brings new evidence in the existing literature by determining the drivers behind financial derivative usage in Pakistani banks for 2011 till 2016. Moreover, the paper examines how risk plays a moderating role in determining the relationship between derivative usage and bank value. While assessing the determinants, a two-stage test has conducted, first, the logit regression was used to test the drivers behind the derivative usage in banks. Second, Tobit regression was run to analyze the factors leading to determine the extent of derivative usage. The findings demonstrate that Pakistani banks are using derivatives for both risk management and speculative motive as they are customers and users of derivatives at the same time. Empirical results, regarding moderating role of risk on the value implications of derivative usage, provide mixed findings as derivative usage gives value premium in case of non-systematic risk and foreign exchange risk. Whereas value discounts have been observed for cases where systematic risk is high and managers try to earn non-operating income from speculative activities.