• Title/Summary/Keyword: Polynomial equation

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Numerical Analysis for Dynamic Characteristics of Next-Generation High-Speed Railway Bridge (차세대 고속철 통과 교량의 동적특성에 대한 수치해석)

  • Oh, Soon-Taek;Lee, Dong-Jun;Yi, Seong-Tae;Jeong, Byeong-Jun
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.26 no.2
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    • pp.9-17
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    • 2022
  • To take into account of the increasing speed of next generation high-speed trains, a new design code for the traffic safety of railway bridges is required. To solve dynamic responses of the bridge, this research offers a numerical analyses of PSC (Pre-stressed Concrete) box girder bridge, which is most representative of all the bridges on Gyungbu high-speed train line. This model takes into account of the inertial mass forces by the 38-degree-of-freedom and interaction forces as well as track irregularities. Our numerical analyses analyze the maximum vertical deflection and DAF (Dynamic Amplification Factor) between simple span and two-span continuous bridges to show the dynamic stability of the bridge. The third-order polynomial regression equations we use predict the maximum vertical deflections depending on varying running speeds of the train. We also compare the vertical deflections at several cross-sectional positions to check the influence of running speeds and the maximum irregularity at a longitudinal level. Moreover, our model analyzes the influence lines of vertical deflection accelerations of the bridge to evaluate traffic safety.

Motion Vector Based Overlay Metrology Algorithm for Wafer Alignment (웨이퍼 정렬을 위한 움직임 벡터 기반의 오버레이 계측 알고리즘 )

  • Lee Hyun Chul;Woo Ho Sung
    • KIPS Transactions on Software and Data Engineering
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    • v.12 no.3
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    • pp.141-148
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    • 2023
  • Accurate overlay metrology is essential to achieve high yields of semiconductor products. Overlay metrology performance is greatly affected by overlay target design and measurement method. Therefore, in order to improve the performance of the overlay target, measurement methods applicable to various targets are required. In this study, we propose a new algorithm that can measure image-based overlay. The proposed measurement algorithm can estimate the sub-pixel position by using a motion vector. The motion vector may estimate the position of the sub-pixel unit by applying a quadratic equation model through polynomial expansion using pixels in the selected region. The measurement method using the motion vector can calculate the stacking error in all directions at once, unlike the existing correlation coefficient-based measurement method that calculates the stacking error on the X-axis and the Y-axis, respectively. Therefore, more accurate overlay measurement is possible by reflecting the relationship between the X-axis and the Y-axis. However, since the amount of computation is increased compared to the existing correlation coefficient-based algorithm, more computation time may be required. The purpose of this study is not to present an algorithm improved over the existing method, but to suggest a direction for a new measurement method. Through the experimental results, it was confirmed that measurement results similar to those of the existing method could be obtained.

Optimal hot water extraction conditions of fermented Polygonum multiflorum root by Lentinula edodes pegler mycelials using response surface methodology (반응표면 분석법에 의한 표고균사체발효 적하수오 열수 추출조건의 최적화)

  • Oh, Junseok;Hong, Jae-Heoi;Park, Tae-Young;Shin, Ji-eun;Kim, Kyung-Je;Jin, Seong-Woo;Ban, Seung-Eon;Koh, Young-Woo;Im, Seung-Bin;Seo, Kyoung-Sun
    • Journal of Mushroom
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    • v.16 no.1
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    • pp.22-30
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    • 2018
  • This study was performed to determine optimal extraction conditions of fermented Polygonum multiflorum root by Lentinula edodes (JMI10079) Pegler mycelials using response surface methodology. The independent factors were extraction temperature (X1: $40-100^{\circ}C$), extraction time (X2: 2-10 hrs.), and the ratio of water to sample (X3: 33-100 mg/mL). Their effects were assessed on dependent variables of the extract properties, which included soluble solid contents (Y1), $^{\circ}Brix$ of sample extract (Y2), total polyphenol content (Y3), total flavonoid content (Y4), 2,2'-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) radical cation scavenging activity (Y5) and 2,2-diphenyl-1-picrylhydrazyl radical scavenging activity (Y6). The experimental data obtained were fit to a second-order polynomial equation. The optimal extraction conditions for fermented P. multiflorum root were: X1: $91.22^{\circ}C$, X2: 7.72 hrs, and X3: 39.71 mg/mL.

Optimization for Extraction of ${\beta}-Carotene$ from Carrot by Supercritical Carbon Dioxide (초임계 유체에 의한 당근의 ${\beta}-Carotene$ 추출의 최적화)

  • Kim, Young-Hoh;Chang, Kyu-Seob;Park, Young-Deuk
    • Korean Journal of Food Science and Technology
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    • v.28 no.3
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    • pp.411-416
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    • 1996
  • Supercritical fluid extraction of ${\beta}$-carotene from carrot was optimized to maximize ${\beta}$-carotene (Y) extraction yield. A central composite design involving extraction pressure ($X_1$ 200-,100 bar), temperature ($X_2,\;35-51^{\circ}C$) and time ($X_1$$ 60-200min) was used. Three independent factors ($X_1,\;X_2,\;X_3$) were chosen to determine their effects on the various responses and the function was expressed in terms of a quadratic polynomial equation,$Y={\beta}_0+{\beta}_1X_1+{\beta}_2X_2+{\beta}_3X_3+{\beta}_11X_12+{\beta}_22X_3^2+{\beta}_-12X_1X_2+{\beta}_12X_1X_2+{\beta}_13X_1X_3+{\beta}_23X_2X_3,$ which measures the linear, quadratic and interaction effects. Extraction yields of ${\beta}$-carotene were affected by pressure, time and temperature in the decreasing order, and linear effect of tenter point (${\beta}_11$) and pressure (${\beta}_1$) were significant at a level of 0.001(${\alpha}$). Based on the analysis of variance, the model fitted for ${\beta}_11$-carotene (Y) was significant at 5% confidence level and the coefficient of determination was 0.938. According to the response surface of ${\beta}$-carotene by cannoical analysis, the stationary point for quantitatively dependent variable (Y) was found to be the maximum point for extraction yield. Response area for ${\beta}$-carotene (Y) in terms of interesting region was estimated over $10,611{\mu}g$ Per 100 g raw carrot under extraction.

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