• Communications of Mathematical Education
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• v.31 no.2
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• pp.139-152
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• 2017

In this paper, we examine how secondary school mathematics textbooks on calculus introduce the history of calculus. In order to identify the problem, we consider the Babylonian integration by trapezoidal rule, which was made to calculate the location of Jupiter in 350-50 B.C., and the integration by the method of the rotating plate of ibn al-Haytham in Egypt, about 1000 years. In conclusion, our secondary school mathematics textbooks describe Newton and Leibniz as inventing calculus and place their roots in ancient Greece. The origin of the calculus is in Babylonia and the Faṭimah Dynasty (909-1171) (Egypt) and it is desirable that the calculus is developed in Europe after the development of the power series in India, and that the value of Asia Africa is introduced in the textbooks.

• The Korean Journal of Nuclear Medicine
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• v.22 no.1
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• pp.39-45
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• 1988

To evaluate diagnostic accuracy of liver scintigraphy we analysed liver scans of 143 normal and 258 patients with various liver diseases. Three ROC curves for SOL, liver cirrhosis and diffuse liver disease were fitted using rating methods and areas under the ROC curves and their standard errors were calculated by the trapezoidal rule and the variance of the Wilcoxon statistic suggested by McNeil. We compared these results with that of National Institute of Radiological Science in Japan. 1) The sensitivity of liver scintigraphy was 74.2% in SOL, 71.8% in liver cirrhosis and 34.0% in diffuse liver disease. The specificity was 96.0% in SOL, 94.2% in liver cirrhosis and 87.6% in diffuse liver diasease. 2) ROC curves of SOL and liver cirrhosis approached the upper left-hand corner closer than that of diffuse liver disease. Area (${\pm}$ standard error). under the ROC curve was $0.868{\pm}0.024$ in SOL and $0.867{\pm}0.028$ in liver cirrhosis. These were significantly higher than $0.658{\pm}0.043$ in diffuse liver disease. 3) There was no interobserver difference in terms of ROC curves. But low sensitivty and high specificity of authors' SOL diagnosis suggested we used more strict decision threshold.

• Korean Journal of Clinical Pharmacy
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• v.15 no.1
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• pp.21-26
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• 2005

A bioequivalence study of CKD $Cefaclor^{(R)}$ capsule (Chong Kun Dang Pharm Co., Ltd) to $Ceclor^{(R)}$ capsule (Lilly Korea Co., Ltd.) was conducted according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty four healthy male Korean volunteers received each medicine at the cefaclor dose of 250 mg in a $2{\times}2$ crossover study. There was a one-week washout period between the doses. An improved high-performance liquid chromatorgraphy (HPLC) analytical method with UV detection was used to determine plasma cefaclor concentration in human volunteers for 8 hr after oral drug administration. The area under the plasma concentration-time curve from time zero to 8 hr ($AUC_{0-8hr}$) was calculated by the linear trapezoidal rule. the $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_{0-8hr}\;and\;C_{max}$. No significant sequence effect was found for all of the bioavailability parameters indicating that the cross-over design was properly performed. The $90{\%}$ confidence intervals of the $AUC_{0-8hr}$ ratio and the $C_{max}$ ratio for CKD $Cefaclor^{(R)}$ and $Ceclor^{(R)}$ were $0.9400{\leq}{\delta}{\leq}1.0345$ and $0.8858{\leq}{\delta}{\leq}1.1021$, respectively. These values were within the acceptable bioequivalence intervals of 0.80-1.25. Thus, our study demonstrated the of CKD $cefaclor^{(R)}$ capsule was bioequivalent to $Cefaclor^{(R)}$ capsule with respect to its bioavailability.

• Journal of Pharmaceutical Investigation
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• v.33 no.3
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• pp.215-221
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• 2003

A bioequivalence study of $Ambrect^{TM}$ tablets (Dong Wha Pharm. Ind. Co., Ltd.) to $Mucopect^{TM}$ tablets (Boehringer Ingelheim Korea, Ltd.) was conducted according to the guideline of Korea Food and Drug Administration (KFDA). Twenty four healthy male Korea volunteers received each medicine at the ambroxol hydrochloride dose of 30 mg in a $2{\times}2$ crossover study. There was a one-week wash out period between the doses. Plasma concentrations of ambroxol were monitored by a high-performance liquid chromatography for over a period of 24 hours after the administration. $AUC_t$ (the area under the plasma concentration-time curve from time zero to 24 hr) was calulated by the linear trapezoidal rule method. $C_{max}$ (maximum plasma drug concentration) and $T_{max}\;(time\;to\;reach\;C_{max})$ were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_t\;and\;C_{max}$. No significant sequence effect was found for all of the bioavailability parameters indicating that the crossover design was properly performed. The 90% confidence intervals of the $AUC_t$ ratio and the $C_{max}$ ratio for $Ambrect^{TM}/Mucopect^{TM}$ were 0.89-1.01 and 0.89-1.02, respectively. These values were within the acceptable bioequivalence intervals of 0.80-1.25. Thus, our study demonstrated the bioequivalence of $Ambrect^{TM}\;and\;Mucopect^{TM}$ with respect to the rate and extent of absorption.

• Journal of Pharmaceutical Investigation
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• v.35 no.2
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• pp.117-122
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• 2005

After establishing improved HPLC analytical method of cefaclor in human plasma samples, a bioavailability study of cefaclor capsules was conducted according to the guidelines of Korea Food and Drug Administration (KFDA). The standard calibration curve using an HPLC with UV detector was constructed in a range of $0.0324{\sim}16\;{\mu}g/ml$. The 6% perchloric acid instead of 6% trichloroacetic acid was used to precipitate plasma protein. The HPLC chromatograms were precisely and accurately resolved when spiked with human plasma spiked with cefaclor and cephalexin (internal standard). Twenty healthy male Korean volunteers received two commercial cefaclor capsules, $Neocef^{\circledR}$ capsule (Jinyang Pharm. Co., Ltd) or $Ceclor^{\circledR}$ capsule (Lilly Korea. Co., Ltd.) at the 250 mg cefaclor in a $2{\times}2$ crossover study. There was a one-week washout period between the doses. Plasma concentrations of cefaclor were monitored for 8 hours after oral drug administration. $AUC_t$ the area under the plasma concentration-time curve from time zero to 8 hr (13 points), was calculated by the linear trapezoidal rule method. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_t$ and $C_{max}$. No significant sequence effect was found for all of the bioavailability parameters indicating that the cross-over design was properly performed. The 90% confidence intervals of the $AUC_t$ ratio and the $C_{max}$ ratio for $Neocef^{\circledR}/Ceclor^{\circledR}$ were $0.9049{\leq}{\delta}{\leq}1.226$, respectively. These values were within the acceptable bioequivalence intervals of 0.80-1.25. Thus, our study demonstrated the bioequivalence of $Neocef^{\circledR}/Ceclor^{\circledR}$ with respect to the extent of absorption.

• Journal of Pharmaceutical Investigation
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• v.37 no.3
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• pp.197-203
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• 2007

A bioequivalence study of $Dilast^{TM}$ Capsule (Chong Kun Dang Pharma. Co., Ltd.) to $Ketas^{(R)}$ Capsule (Han Dok Pharma. Co., Ltd.) was conducted according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty eight healthy male Korean volunteers received each medicine at the ibudilast dose of 20 mg in a $2{\times}2$ crossover study. There was one week wash-out period between the doses. Plasma concentrations of ibudilast were monitored by a liquid chromatography-tandem mass spectrometry (LC-MS/MS) for over a period of 36 hours after drug administration. $AUC_t$ (the area under the plasma concentration-time curve from time zero to 36 hr) was calculated by the linear trapezoidal rule method. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_t\;and\;C_{max}$. No significant sequence effect was found for all of the bioavailability parameters indicating that the crossover design was properly performed. The 90% confidence intervals of the $AUC_t$ ratio and the $C_{max}$ ratio for $Dilast^{TM}$ $Capsule/Ketas^{(R)}$ Capsule were $log0.93{\sim}log1.06$ and $log0.93{\sim}log1.11$, respectively. These values were within the acceptable bioequivalence intervals of $log0.80{\sim}log1.25$. Thus, our study demonstrated the bioequivalence of $Dilast^{TM}$ Capsule and $Ketas^{(R)}$ Capsule with respect to the rate and extent of absorption.

• Journal of Pharmaceutical Investigation
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• v.39 no.1
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• pp.65-71
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• 2009

The aim of the present study was to evaluate the bioequivalence of two domperidone maleate tablets, Motilium-$M^{(R)}$ Tablet (Janssen Korea Ltd., reference product) and $Toriem^{(R)}$ Tablet (Daewon Pharm. Co., Ltd., test product). Domperidone was extracted by liquid-liquid extraction using tert-butyl methyl ether and separated in less than 3 min on $C_{18}$ reverse-phase column using an isocratic elution. A tandem mass spectrometer, as detector, was used for quantitative analysis in positive mode by a multiple reaction monitoring mode to monitor the m/z $426.1{\rightarrow}119.1$ and the m/z $837.4{\rightarrow}158.2$ transitions for domperidone and the internal standard (roxithromycin), respectively. Calibration curves, from $0.05{\sim}50$ ng/mL of domperidone, showed correlation coefficients (r) higher than 0.9941. Intra day and inter day precision (C.V. %) for quality control were ranged from 10.04 to 16.09% and from 10.87 to 18.69%, respectively. The lower limit of quantification (LLOQ) of domperidone was 0.05 ng/mL. The method described is precise and sensitive and has been successfully applied to the study of bioequivalence of domperidone in 24 healthy Korean volunteers. Twenty-four healthy male Korean volunteers received a single dose of each medicine ($2{\times}12.72\;mg$ domperidone maleate) in a $2{\times}2$ crossover study. There was a one-week washout period between the doses. Plasma concentrations of domperidone were monitored for over a period of 24 hr after the administration. $AUC_{0-t}$ (the area under the plasma concentration-time curve) was calculated by the linear trapezoidal rule. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. The 90% confidence intervals for the log transformed data were within acceptable range of log 0.8 to log 1.25 (e.g., $log\;0.92{\sim}log\;1.05$ for $AUC_{0-t}$, $log\;0.81{\sim}log\;1.05$ for $C_{max}$). The major parameters, $AUC_{0-t}$ and $C_{max}$ met the criteria of KFDA for bioequivalence indicating that $Toriem^{(R)}$ tablet is bioequivalent to Motilium-$M^{(R)}$ tablet.

• Journal of Pharmaceutical Investigation
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• v.35 no.4
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• pp.303-308
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• 2005

The purpose of the present study was to evaluate the bioequivalence of two talniflumate tablets, SOMALGEN tablet (Kun Wha Pharm. Co., Ltd., Seoul, Korea, reference drug) and FLUTAL tablet (Kukje Pharm. Co., Ltd., Korea, test drug), according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty-four healthy male Korean volunteers received two tablets at the talniflumate dose of 740 mg in a $2{\pm}2$ crossover study. There was a one-week washout period between the doses. Plasma concentrations of niflumic acid were monitored by an HPLC-UV for over a period of 14 hr after the administration. $AUC_t$(the area under the plasma concentration-time curve from time zero to 14 hr) was calculated by the linear trapezoidal rule method. $C_{max}$(maximum plasma drug concentration) and $T_{max}$(time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_t$, $C_{max}$ and untransformed $T_{max}$. No significant sequence effect was found for all of the bioavailability parameters indicating that the crossover design was properly performed. The 90% confidence intervals of the $AUC_t$, ratio and the $C_{max}$ ratio for SOMALGEN/FLUTAL were $log0.8510{\sim}log1.0318$ and $log0.9264{\sim}log1.0607$, respectively. These values were within the acceptable bioequivalence intervals of $log0.80{\sim}log1.25$. Taken together, our study demonstrated the bioequivalence of SOMALGEN and FLUTAL with respect to the rate and extent of absorption.

• Journal of Pharmaceutical Investigation
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• v.36 no.3
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• pp.193-199
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• 2006

A bioequivalence study of $Sudo^{TM}$ Ranitidine HCI tablet (Sudo Pharma. Ind. Co., Ltd.) to $Curan^{TM}$ tablet (Il Dong Pharma. Ind. Co., Ltd.) was conducted according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty four healthy male Korean volunteers received each medicine at the ranitidine hydrochloride dose of 150 mg in a 2x2 crossover study. There was a one week wash-out period between the doses. Plasma concentrations of ranitidine were monitored by a high-turbulent liquid chromatography (HTLC) for over a period of 12 hours after drug administration. $AUC_t$ (the area under the plasma concentration-time curve from time zero to 12 hr) was calculated by the linear trapezoidal rule method. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was carried out using logarithmically transformed $AUC_t$ and $C_{max}$. No significant sequence effect was found far all of the bioavailability parameters indicating that the crossover design was properly performed. The 90% confidence intervals of the $AUC_t$ ratio and the $C_{max}$ ratio for $Sudo^{TM}$ Ranitidine $HCl/Curan^{TM}$ were 0.92-1.00 and 0.90-1.03, respectively. These values were within the acceptable bioequivalence intervals of 0.80-1.25. Thus, our study demonstrated the bioequivalence of $Sudo^{TM}$ Ranitidine HCI and $Curan^{TM}$ with respect to the rate and extent of absorption.

• Journal of Pharmaceutical Investigation
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• v.34 no.5
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• pp.413-418
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• 2004

A bioequivalence of $Melax^{TM}$ capsules (Chong Kun Dang Pharm., Korea) and $Mobic^{TM}$ capsules (Boehringer Ingelheim Korea) was evaluated according to the guideline of Korea Food and Drug Administration (KFDA). Single 15 mg dose of meloxicam of each medicine was administered orally to 24 healthy male volunteers. This study was performed in a $2\;{\times}\;2$ crossover design. Concentrations of meloxicam in human plasma were monitored by a high-performance liquid chromatography. $AUC_t$ (the area under the plasma concentration-time curve from time zero to 72 hr) was calculated by the linear trapezoidal rule method. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma concentration-time data. Analysis of variance was performed using logarithmically transformed $AUC_t$ and $C_{max}$. No significant sequence effect was found for all of the bioavailability parameters. The 90% confidence intervals of the $AUC_t$ ratio and the $C_{max}$ ratio for $Melax^{TM}/Mobic^{TM}$ were 0.95 - 1.04 and 0.98 - 1.14, respectively. This study demonstrated a bioequivalence of $Melax^{TM}$ and $Mobic^{TM}$ with respect to the rate and extent of absorption.