• Title/Summary/Keyword: Trapezoidal rule

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Meshfree consolidation analysis of saturated porous media with stabilized conforming nodal integration formulation

  • Wang, Dongdong;Xie, Pinkang;Lu, Hongsheng
    • Interaction and multiscale mechanics
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    • v.6 no.2
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    • pp.107-125
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    • 2013
  • A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

Romberg's Integration Using a Systolic Array (Romberg 적분법을 위한 Systolic Array)

  • 박덕원
    • Journal of the Korea Society of Computer and Information
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    • v.3 no.4
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    • pp.55-62
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    • 1998
  • This Paper proposed a systolic Arrays architecture for computing Romberg's integration method. It consists of systolic arrays of two stage, one for integration by Trapezoidal rule and the other for integration by using Richardson's extrapolation. the proposed its architecture is very high speed and regular. This paper illustrates how " mathematical hardware " package, as well as software library routines, may be part of the mathematical problem solver's tool kit in the future.he future.

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UNCONDITIONAL STABILITY AND CONVERGENCE OF FULLY DISCRETE FEM FOR THE VISCOELASTIC OLDROYD FLOW WITH AN INTRODUCED AUXILIARY VARIABLE

  • Huifang Zhang;Tong Zhang
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.273-302
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    • 2023
  • In this paper, a fully discrete numerical scheme for the viscoelastic Oldroyd flow is considered with an introduced auxiliary variable. Our scheme is based on the finite element approximation for the spatial discretization and the backward Euler scheme for the time discretization. The integral term is discretized by the right trapezoidal rule. Firstly, we present the corresponding equivalent form of the considered model, and show the relationship between the origin problem and its equivalent system in finite element discretization. Secondly, unconditional stability and optimal error estimates of fully discrete numerical solutions in various norms are established. Finally, some numerical results are provided to confirm the established theoretical analysis and show the performances of the considered numerical scheme.

A 45GHz $f_{T}\;and\;50GHz\;f_{max}$ SiGe BiCMOS Technology Development for Wireless Communication ICs (무선통신소자제작을 위한 45GHz $f_{T}$ 및 50GHZz $f_{max}$ SiGe BiCMOS 개발)

  • Hwang Seok-Hee;Cho Dae-Hyung;Park Kang-Wook;Yi Sang-Don;Kim Nam-Ju
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.42 no.9 s.339
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    • pp.1-8
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    • 2005
  • A $0.35\mu$m SiGe BiCMOS fabrication process has been timely developed, which is aiming at wireless RF ICs development and fast growing SiGe RF market. With non-selective SiGe epilayer, SiGe HBTs in this process used trapezoidal Ge base profile for the enhanced AC performance via Ge induced bandgap niuoin. The characteristics of hFE 100, $f_{T}\;45GHz,\;F_{max}\;50GHz,\;NF_{min}\;0.8dB$ have been obtained by optimizing not only SiGe base profile but also RTA condition after emitter polysilicon deposition, which enables the SiGe technology competition against the worldwide cutting edge SiGe BiCMOS technology. In addition, the process incorporates the CMOS logic, which is fully compatible with $0.35\mu$m pure logic technology. High Q passive elements are also provided for high precision analog circuit designs, and their quality factors of W(1pF) and inductor(2nH) are 80, 12.5, respectively.

Effects of Cyclosporine on Glucose Tolerance and Insulin Sensitivity in Sprague-Dawley Rats (Sprague-Dawley계 정상흰쥐에서 포도당 내성과 인슐린 감수성에 대한 Cyclosporine의 영향)

  • 강주섭;고현철;이창호;신인철;김동선;양석철;전용철
    • Biomolecules & Therapeutics
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    • v.7 no.4
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    • pp.342-346
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    • 1999
  • This study was performed to investigate the effect of cyclosporine (CsA) on glucose tolerance and peripheral insulin sensitivity in normal Sprague-Dawley rats. After daily treament of CsA (10 mg/kg, i.p.) for two weeks, glucose tolerance tests were carried out by the treatment of glucose (Glu, 2 g/kg, i.p.) alone or in conjunction with exogenous insulin (Ins; human regular insulin, 5 U/kg, s.c.) and measured the decrement of area under the time-plasma glucose concentration curve ($AUC_{o\longrightarrow120}$; g.min/ml) by the trapezoidal rule. The rats were divided into three groups (Glu- (Control), Ins+Glu- and CsA+Ins+Glu-, n=7 in each group). The $AUC_{o\longrightarrow120}$ of the CsA+Ins+Glu-group was significantly (p<0.01) lower than that of Glu-group (61.0% of control) and significantly (p<0.05) higher than that of Ins+Glu-group (197.4% of Ins+Glu-). The CsA+Ins+Glu- grou showed higher levels of maximal blood glucose concentration and higher $AUC_{o\longrightarrow120}$ than those of Ins+Glu-group in normal rats. Besides direct pancreatic toxicity of CsA previously reported (Hahn et al., 1972), these results suggest that CsA also make the possibility to induce peripheral insulin insensitivity and glucose intolerance in normal rats.

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The Characteristic of Control Response of BLDC using a Fuzzy PI Controller (퍼지 PI 제어기를 사용한 BLDC 제어 응답특성)

  • Yoon, Yong-Ho;Kim, Jae-Moon;Kim, Duk-Heon;Won, Chung-Yuen
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.10
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    • pp.1978-1983
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    • 2011
  • BLDC motor is used in a wide variety of industrial and servo applications. Its features and advantages mainly consist in high value of torque/inertia ratio, high efficiency with speed range and high dynamic performance. This paper deals with the speed control of a trapezoidal type brushless DC motor using Fuzzy PI controller. The conventional PI controller has been widely used in industrial applications. If we select a optimal PI control gain, the PI controller shows very good control performance. But it is very difficult to find the optimal PI control gain. Fuzzy control does not need any model of plant and is basically adaptive and gives robust performance for plant parameter variation. Therefore the combinations of conventional PI controller and fuzzy controller seem to be very effective. This paper deals with PI controller with 4-rule based fuzzy controller. The proposed fuzzy PI controller increases the control performance of the conventional PI controller. Simulation and experimental results show that fuzzy PI controller has a good robustness regarding the improper tuned PI controller.

On the Earthwork Volume Decision Using Spline Surfaces (스플라인 곡면을 이용한 토공량 결정에 관한 연구)

  • 류재칠;이승훈;문두열
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.20 no.1
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    • pp.85-92
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    • 2002
  • The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to advanced the accuracy of earthwork calculation. Current methods used for estimating the volume of pit excavation assumes that the ground profile between the grid points is linear(trapezoidal rule), or nonlinear(simpson's formulas). Generally speaking, the nonlinear profile formulas provide better accuracy than the linear profile formulas. However, all the formulas mentioned have a common drawback to ground profile, such as sharp corners or the grid points of any two straight lines. In this paper, we propose an algorithm of finding a spline surface which interpolates the given data and an appropriate method to calculate the earthwork. We present some computational results showing that our proposed method provides better accuracy than Chen and Lin's method.

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.

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.