• Title/Summary/Keyword: trapezoidal rule method

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Free Vibrations of Arbitrary Tapered Beams with Static Deflections due to Arbitrary Distributed Dead Loads (임의분포 사하중에 정적변위를 갖는 변단면 보의 자유진동)

  • Lee, Byoung-Koo;Lee, Yong
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.38 no.3
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    • pp.50-57
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    • 1996
  • A numerical method is presented to obtain the natural frequencies and mode shapes of the arbitrary tapered beams with static deflection due to arbitrary distributed dead loads. The differential equation governing free vibration of such beams is derived and solved numerically. The double integration method using the trapezoidal rule is used to solve the static behaviour of beams loaded arbitrary distributed dead load. Also, the Improved Euler method and the determinant search method are used to integrate the differential equation subjected to the boundary conditions and to determine the natural frequencies of the beams, respectively. In the numerical examples, the various geometries of the beams are considered : (1) linearly tapered beams as the arbitrary variable cross-section, (2) the triangular, sinusoidal and uniform loads as the arbitrary distributed dead loads and (3) the hinged-hinged, clamped-clamped and hinged-clamped ends as the end constraints. All numerical results are shown as the non-dimensional forms of the system parameters. The lowest three natural frequencies versus load parameter, slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with and without the effects of static deflection are presented in the figure. According to the numerical results obtained in this analysis, the following conclusions may be drawn : (1) the natural frequencies increase when the effects of static deflections are included, (2) the effects are larger at the lower modes than the higher ones and (3) it should be betteF to include the effect of static deflection for calculating the frequencies when the beams are supported by both hinged ends or one hinged end.

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Bioequivalence of Mepiril Tablet to Amaryl Tablet (Glimepiride 2 mg) by Liquid Chromatography/Electrospray Tandem Mass Spectrometry

  • Lee, Heon-Woo;Cho, Sung-Hee;Park, Wan-Su;Im, Ho-Taek;Rew, Jae-Hwan;Lee, Kyung-Tae
    • Journal of Pharmaceutical Investigation
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    • v.35 no.4
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    • pp.287-293
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    • 2005
  • The purpose of the present study was to evaluate the bioequivalence of two glimepiride tablets, Amaryl tablet (Handok & Aventis Korea, reference drug) and Mepiril tablet (Myungmoon Pharm. Co., Ltd., Korea, test drug), according to the guidelines of Korea Food and Drug Administration (KFDA). After adding an internal standard (glibenclamide) to human plasma, plasma samples were extracted using 1mL of methyl tertiary butyl ether. Compounds extracted were analyzed by reverse-phase HPLC with multiple reaction monitoring (MRM) mode analyte detection. This method for determination glimepiride proved accurate and reproducible, with a limit of quantitation of 2 ng/mL in human plasma. Twenty-four healthy male Korean volunteers received each medicine at the glimepiride dose of 2 mg in a $2{\times}2$ crossover study. There was a one-week washout period between the doses. Plasma concentrations of glimepiride were monitored by a LC-MS/MS for over a period of 12 hr after the 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 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 Amaryl/Mepiril were log 0.9583-log 1.1357 and log 1.0570-log 1.2376, respectively. These values were within the acceptable bioequivalence intervals of log 0.80-log 1.25. Taken together, our study demonstrated the bioequivalence of Amaryl and Mepiril with respect to the rate and extent of absorption.

Bioequivalence Assessment of DM Tablet to Motilium-$M^{(R)}$ Tablet (모티리움엠정(말레인산 돔페리돈 12.72 mg)에 대한 디엠정의 생물학적동등성 평가)

  • Cho, Seong-Wan;Kim, Young-Il;Lee, Jong-Oh;Bang, Joon-Seok;Jeong, Ji-Hoon
    • Korean Journal of Clinical Pharmacy
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    • v.18 no.2
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    • pp.106-113
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    • 2008
  • The aim of this study was to evaluate the bioequivalence of two domperidone preparations. Bioequivalence assessment was conducted on 34 healthy volunteers who received two tablets (Domperidone Maleate, 12.72 mg/tablet) in the fasting state, in a randomized balanced $2{\times}2$ cross-over study design. This whole study was performed according to the implementation guidelines of the Korea Food Drug Administration. After dosing of two tablets, blood samples were collected serially for a period of 36 hours. Plasma was analyzed for domperidone by using LC/MS/MS assay method. The analysis system was validated in specificity, accuracy, precision, and linearity. $AUC_t$, (the area under the plasma concentration-time curve from the zero-time to 36 hr) was calculated through the trapezoidal rule. $C_{max}$ (maximum plasma drug concentration) and $T_{max}$ (time to reach $C_{max}$) were compiled from the plasma domperidone concentration-time data of each volunteer. No significant sequence effect was found for the bioavailability parameters indicating that the cross-over design was properly performed. The 90%-Confidence intervals of the $AUC_t$ ratio and the $C_{max}$ were from log 0.8007 to log 1.1240 and log 0.8645- log 1.2483, respectively. These values were within the acceptable bioequivalence intervals between 0.80 and 1.25. Therefore, this study demonstrated that two formulations have bioequivalence with respect to the rate and extent of absorption.

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Bioequivalence of Topamin Tablet to Topamax Tablet (Topiramate 100 mg) (토파맥스 정(토피라메이트 100mg)에 대한 토파민 정의 생물학적동등성)

  • Seo, Ji-Hyung;Lee, Myung-Jae;Choi, Sang-Jun;Kang, Jong-Min;Lee, Jin-Sung;Tak, Sung-Kwon;Lee, Kyung-Tae
    • Journal of Pharmaceutical Investigation
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    • v.38 no.4
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    • pp.277-282
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    • 2008
  • The purpose of the present study was to evaluate the bioequivalence of two topiramate tablets, Topamax tablet (Janssen Korea. Co., Ltd., Seoul, Korea, reference drug) and Topamin tablet (Myungmoon Pharm. Co., Ltd., Seoul, Korea, test drug), according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty-four healthy male Korean volunteers received one tablet at the dose of 100 mg topiramate in a $2{\times}2$ crossover study. There were two-weeks washout period between the doses. Plasma concentrations of topiramate were monitored by an LC-MS/MS for over a period of 96 hr after administration. $AUC_t$ (the area under the plasma concentration-time curve from time zero to 96 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 (ANOVA) was carried out using logarithmically transformed $AUC_t$ and $C_{max}$. The 90% confidence intervals of the $AUC_t$, ratio and the $C_{max}$ ratio for Topamin/Topamax were $\log0.88{\sim}\log1.02$ and $\log0.87{\sim}\log1.03$, respectively. These values were within the acceptable bioequivalence intervals of $\log0.80{\sim}\log1.25$. Taken together, our study demonstrated the bioequivalence of Topamax and Topamin with respect to the rate and extent of absorption.

Displacements, damage measures and response spectra obtained from a synthetic accelerogram processed by causal and acausal Butterworth filters

  • Gundes Bakir, Pelin;Richard, J. Vaccaro
    • Structural Engineering and Mechanics
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    • v.23 no.4
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    • pp.409-430
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    • 2006
  • The aim of this study is to investigate the reliability of strong motion records processed by causal and acausal Butterworth filters in comparison to the results obtained from a synthetic accelerogram. For this purpose, the fault parallel component of the Bolu record of the Duzce earthquake is modeled with a sum of exponentially damped sinusoidal components. Noise-free velocities and displacements are then obtained by analytically integrating the synthetic acceleration model. The analytical velocity and displacement signals are used as a standard with which to judge the validity of the signals obtained by filtering with causal and acausal filters and numerically integrating the acceleration model. The results show that the acausal filters are clearly preferable to the causal filters due to the fact that the response spectra obtained from the acausal filters match the spectra obtained from the simulated accelerogram better than that obtained by causal filters. The response spectra are independent from the order of the filters and from the method of integration (whether analytical integration after a spline fit to the synthetic accelerogram or the trapezoidal rule). The response spectra are sensitive to the chosen corner frequency of both the causal and the acausal filters and also to the inclusion of the pads. Accurate prediction of the static residual displacement (SRD) is very important for structures traversing faults in the near-fault regions. The greatest adverse effect of the high pass filters is their removal of the SRD. However, the noise-free displacements obtained by double integrating the synthetic accelerogram analytically preserve the SRD. It is thus apparent that conventional high pass filters should not be used for processing near-fault strong-motion records although they can be reliably used for far-fault records if applied acausally. The ground motion parameters such as ARIAS intensity, HUSID plots, Housner spectral intensity and the duration of strong-motion are found to be insensitive to the causality of filters.

Bioequivalence Evaluation of Two brands of Cetirizine HCl 10 mg Tablets (Zyrix and Zyrtec) in Healthy Male Volunteers

  • Im, Ho-Taek;Won, Jong-Hoen;Cho, Sung-Hee;Lee, Heon-Woo;Park, Wan-Su;Rew, Jae-Hwan;Lee, Kyung-Tae
    • Journal of Pharmaceutical Investigation
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    • v.35 no.5
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    • pp.355-360
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    • 2005
  • The purpose of the present study was to evaluate the bioequivalence of two cetirizine HCl tablets, Zyrtec tablet (UCB Pharm. Co., Ltd. Korea, reference product) and Zyrix tablet (Kukje Pharm. Co., Ltd., Korea, test product), according to the guidelines of Korea Food and Drug Administration (KFDA). After adding an internal standard (diazepam), plasma samples were extracted using 1 mL of dichloromethane. Compounds extracted were analyzed by reverse-phase HPLC with ultra-violet detector. This method for determination cetirizine is proved accurate and reproducible with a limit of quantitation of 10 ng/mL in male plasma. Twenty-four healthy male Korean volunteers received each medicine at the cetirizine HCl dose of 10 mg in a $2{\times}2$ crossover study. There was a one-week wash out period between the doses. Plasma concentrations of cetirizine were monitored for over a period of 24 hr after the administration. AUC (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. Analysis of variance was carried out using logarithmically transformed AUC 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 for the log transformed data were acceptable range of log 0.8 to log 1.25 $(e.g.,\;log\;0.93-log\;1.08\;for\;AUC_{0-t},\;log\;0.91-log\;1.08\;for\;AUC_{0-{\infty}}\;and\;log\;1.01-log\;1.11\;for\;C_{max})$. The major parameters, AUC and $C_{max}$ met the criteria of KFDA for bioequivalence indicating that Zyrix tablet is bioequivalent to Zyrtec tablet.

Bioequivalence Assessment of Acephyll® Capsule to Surfolase® Capsule (Acebrophylline HCl 100 mg) by Liquid Chromatography Tandem Mass Spectrometry

  • Nam, Kyung-Don;Seo, Ji-Hyung;Yim, Sung-Vin;Lee, Kyung-Tae
    • Journal of Pharmaceutical Investigation
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    • v.41 no.5
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    • pp.309-315
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    • 2011
  • A sensitive and specific liquid chromatographic method coupled with tandem mass spectrometry (LC-MS/MS) was developed for the analysis of ambroxol (active moiety of acebrophylline). After acetonitrile precipitation of proteins from plasma samples, ambroxol and the domperidone (internal standard, IS) were eluted on a C18 column. The isocratic mobile phase was consisted of 10 mM ammonium acetate and methanol (10 : 90, v/v), with flow rate at 0.2 mL/min. 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 379.2${\rightarrow}$264.0 and the m/z 426.2${\rightarrow}$175.1 transitions for ambroxol and the IS, respectively. Twenty four healthy Korean male subjects received two capsules (100 mg ${\times}$ 2) of either the test or the reference formulation of acebrophylline HCl in a 2 ${\times}$ 2 crossover study, this was followed by a 1week washout period between either formulation. $AUC_{0-t}$ (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 acceptable range of log 0.8 to log 1.25 (e.g., log 0.8964 - log 0.9910 for $AUC_{0-t}$ log 0.8690 - log 1.0750 for $C_{max}$). The major parameters, $AUC_{0-t}$ and $C_{max}$ met the criteria of Korea Food and Drug Administration for bioequivalence indicating that Acephyll$^{(R)}$ capsule (test) is bioequivalent to Surfolase$^{(R)}$ capsule (reference).

Numerical Formulation for Flow Analysis of Dredged Soil (준설토 유동해석을 위한 유한요소 수식화)

  • Shin, Hosung
    • Journal of the Korean GEO-environmental Society
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    • v.15 no.3
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    • pp.41-48
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    • 2014
  • Experimental study of sedimentation and self-weight consolidation has been primary research area in dredged soil. However, good quality of the dredged soil and minimum water pollution caused by the pumping of reclaimed soil require intensive study of the flow characteristics of dredged material due to dumping. In this study, continuity and the equilibrium equations for mass flow assuming single phase was derived to simulate mass flow in dredged containment area. To optimize computation and modeling time for three dimensional geometry and boundary conditions, depth integration is applied to governing equations to consider three dimensional topography of the site. Petrov-Galerkin formulation is applied in spatial discretization of governing equations. Generalized trapezoidal rule is used for time integration, and Newton iteration process approximated the solution. DG and CDG technique were used for weighting matrix in discontinuous test function in dredged flow analysis, and numerical stability was evaluated by performed a square slump simulation. A comparative analysis for numerical methods showed that DG method applied to SU / PG formulation gives minimal pseudo oscillation and reliable numerical results.

Bioequivalence of DonpezilTM Tablet to AriceptTM Tablet (Donepezil Hydrochloride 10 mg) (아리셉트 정(염산도네페질 10 mg)에 대한 돈페질 정의 생물학적동등성)

  • Lee, Hyun-Su;Seo, Ji-Hyung;Kang, Il-Mo;Lee, Heon-Woo;Ryu, Ju-Hee;Lee, Kyung-Tae
    • Journal of Pharmaceutical Investigation
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    • v.37 no.1
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    • pp.57-62
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    • 2007
  • The purpose of the present study was to evaluate the bioequivalence of two donepezil tablets, $Aricept^{TM}$ tablet (Dae Woong Pharm. Co., Ltd., Korea, reference drug) and $Donpezil^{TM}$ tablet (Dong Wha Pharm. Ind. Co., Ltd., Korea, test drug), according to the guidelines of Korea Food and Drug Administration (KFDA). Twenty-four healthy male Korean volunteers received one tablet containing donepezil hydorchloride 10 mg in a $2{\times}2$ crossover study. There was a three-week washout period between the doses. Plasma concentrations of donepezil were monitored by an LC-MS/MS far over a period of 240 hr after the administration. $AUC_t$, (the area under the plasma concentration-time curve from time zero to 240 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 effects were found for all of the bioavailability parameters indicating that the crossover design was properly performed. The 90% confidence intervals of the $AUC_t$ and $C_{max}$ were log 0.95${\sim}$log 1.03 and log 0.94${\sim}$log 1.08, respectively. These values were within the acceptable bioequivalence intervals of log 0.80${\sim}$log 1.25. Taken together, our study demonstrated the bioequivalence of $Aricept^{TM}$ and $Donpezil^{TM}$ with respect to the rate and extent of absorption.

Pharmacokinetic Comparison of Actonel and Risenel Tablet Containing Risedronate sodium in Healthy Volunteers (건강한 지원자에 있어서 리세드로네이트 35 mg 함유 악토넬정과 리세넬정의 약물 동력학적 비교)

  • Choi, Sung-Up;Kim, Young-Il;Park, Young-Joon;Lee, Jong-Oh;Song, Jin-Ho;Cho, Seong-Wan
    • Korean Journal of Clinical Pharmacy
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    • v.19 no.1
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    • pp.23-31
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    • 2009
  • The aim of this study was to evaluate the pharmacokinetic parameters of two risedronate preparations. The clinical assessment was conducted on 46 healthy volunteers who received one tablet (Risedronate sodium 35 mg/tablet) in the fasting state, in a randomized balanced $2{\times}2$ cross-over study design. After dosing of one tablet containing 35 mg risedronate sodium, blood samples were collected serially for a period of 48 hours. Plasma was analyzed for risedronate by using LC/MS/MS assay method. The analysis system was validated in specificity, accuracy, precision, and linearity. $AUC_t$, (the area under the plasma concentration-time curve from the zero-time to 48 hr) was calculated through the trapezoidal rule. $C_{max}$ (maximum plasma drug concentration) were compiled from the plasma risedronate concentration-time data of each volunteer. No significant sequence effect was found for the pharmacokinetic parameters indicating that the cross-over design was properly performed. The 90 % - Confidence intervals of the $AUC_t$ ratio and the $C_{max}$ were from log 0.8752 to log 1.1888 and log 0.8457 to log 1.1478, respectively. These values were within the acceptable intervals between 0.80 and 1.25. Therefore, this study demonstrated that no statistically significant difference was identified with respect to the rate and extent of absorption.

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