• Title/Summary/Keyword: Rational curves

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IRREDUCIBILITY OF POLYNOMIALS AND DIOPHANTINE EQUATIONS

  • Woo, Sung-Sik
    • Journal of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.101-112
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    • 2010
  • In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coefficients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coefficients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over $\mathbb{Q}$ which are not of Eisenstein type.

Explicit Formulae for operations in Jacobian of hyperelliptic curves (종수 2의 초타원곡선에서의 구체적이고 효율적인 연산 방법)

  • Park, Young-Ju e;Lee, Eunjeong
    • Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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    • 2003.12a
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    • pp.634-642
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    • 2003
  • We give explicit formulae for composition of genus two. The previous work described in[4]only contains the formulae for common cases. In this paper, we give formulae for all cases of two divisors as input. Furthermore, the formulae contains the .form of rational functions such that related to the implementation of the Tate pairing.

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DOUBLE LINES IN THE QUINTIC DEL PEZZO FOURFOLD

  • Kiryong Chung
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.485-494
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    • 2023
  • Let Y be the quintic del Pezzo 4-fold defined by the linear section of Gr(2, 5) by ℙ7. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in Y. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree 2 in Y. We also compute the intersection Poincaré polynomial of the stable map space.

[ $C^1$ ] Continuous Piecewise Rational Re-parameterization

  • Liang, Xiuxia;Zhang, Caiming;Zhong, Li;Liu, Yi
    • International Journal of CAD/CAM
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    • v.6 no.1
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    • pp.59-64
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    • 2006
  • A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

Formulation of a rational dosage regimen of ceftiofur hydrochloride oily suspension by pharmacokinetic-pharmacodynamic (PK-PD) model for treatment of swine Streptococcus suis infection

  • Luo, Wanhe;Wang, Dehai;Qin, Hua;Chen, Dongmei;Pan, Yuanhu;Qu, Wei;Huang, Lingli;Xie, Shuyu
    • Journal of Veterinary Science
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    • v.22 no.6
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    • pp.41.1-41.14
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    • 2021
  • Background: Our previously prepared ceftiofur (CEF) hydrochloride oily suspension shows potential wide applications for controlling swine Streptococcus suis infections, while the irrational dose has not been formulated. Objectives: The rational dose regimens of CEF oily suspension against S. suis were systematically studied using a pharmacokinetic-pharmacodynamic model method. Methods: The healthy and infected pigs were intramuscularly administered CEF hydrochloride oily suspension at a single dose of 5 mg/kg, and then the plasma and pulmonary epithelial lining fluid (PELF) were collected at different times. The minimum inhibitory concentration (MIC), minimal bactericidal concentration, mutant prevention concentration (MPC), post-antibiotic effect (PAE), and time-killing curves were determined. Subsequently, the area under the curve by the MIC (AUC0-24h/MIC) values of desfuroylceftiofur (DFC) in the PELF was obtained by integrating in vivo pharmacokinetic data of the infected pigs and ex vivo pharmacodynamic data using the sigmoid Emax (Hill) equation. The dose was calculated based on the AUC0-24h/MIC values for bacteriostatic action, bactericidal action, and bacterial elimination. Results: The peak concentration, the area under the concentration-time curve, and the time to peak for PELF's DFC were 24.76 ± 0.92 ㎍/mL, 811.99 ± 54.70 ㎍·h/mL, and 8.00 h in healthy pigs, and 33.04 ± 0.99 ㎍/mL, 735.85 ± 26.20 ㎍·h/mL, and 8.00 h in infected pigs, respectively. The MIC of PELF's DFC against S. suis strain was 0.25 ㎍/mL. There was strong concentration-dependent activity as determined by MPC, PAE, and the time-killing curves. The AUC0-24h/MIC values of PELF's DFC for bacteriostatic activity, bactericidal activity, and virtual eradication of bacteria were 6.54 h, 9.69 h, and 11.49 h, respectively. Thus, a dosage regimen of 1.94 mg/kg every 72 h could be sufficient to reach bactericidal activity. Conclusions: A rational dosage regimen was recommended, and it could assist in increasing the treatment effectiveness of CEF hydrochloride oily suspension against S. Suis infections.

Epipolar Image Resampling from Kompsat-3 In-track Stereo Images (아리랑3호 스테레오 영상의 에피폴라 기하 분석 및 영상 리샘플링)

  • Oh, Jae Hong;Seo, Doo Chun;Lee, Chang No
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.31 no.6_1
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    • pp.455-461
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    • 2013
  • Kompsat-3 is an optical high-resolution earth observation satellite launched in May 2012. The AEISS sensor of the Korean satellite provides 0.7m panchromatic and 2.8m multi-spectral images with 16.8km swath width from the sun-synchronous near-circular orbit of 685km altitude. Kompsat-3 is more advanced than Kompsat-2 and the improvements include better agility such as in-track stereo acquisition capability. This study investigated the characteristic of the epipolar curves of in-track Kompsat-3 stereo images. To this end we used the RPCs(Rational Polynomial Coefficients) to derive the epipolar curves over the entire image area and found out that the third order polynomial equation is required to model the curves. In addition, we could observe two different groups of curve patterns due to the dual CCDs of AEISS sensor. From the experiment we concluded that the third order polynomial-based RPCs update is required to minimize the sample direction image distortion. Finally we carried out the experiment on the epipolar resampling and the result showed the third order polynomial image transformation produced less than 0.7 pixels level of y-parallax.

Cracking Analysis of Reinforced Concrete Tension Members with Concrete Fracture Mechanics (콘크리트 파괴역학을 이용한 철근콘크리트 인장부재의 균열성장 해석)

  • 홍창우;윤경구;양성철
    • Journal of the Korea Concrete Institute
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    • v.12 no.1
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    • pp.3-12
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    • 2000
  • A fracture energy concept proposed by Ouyang and Shah's fracture mechanics approach was used to predict cracking of reinforced concrete members subjected to tension. In this approach, fracture properties in plain concrete which incorporate the presence of the fracture process zone are first determined from the generalized size effect method, then fracture energy required for crack propagation with the same dimension and material properties are evaluated using an R-curve. Subsequently taking into account the material properties in Ouyang and Shah's approach, a theoretical analysis to predict the mechanical behavior of reinforced concrete members subjected to tension was performed and compared to observed experimental results. It is seen that the predicted average crack spacing curves agree well with the experimental results, whereas the analytical method seems to predict lower values for this study. The analytical approach predicts well responses of stress-strain curves before and after the first crack is formed. It is concluded from this study that a fracture energy concept based on the R-curve and the generalized size effect method is a rational approach to predict cracking of reinforced concrete members subjected to tension.

Estimation of mortality coefficients and survivorship curves for minke whales (Balaenoptera acutorostrata) in Korean waters

  • Zhang, Chang-Ik;Song, Kyung-Jun;Na, Jong-Hun
    • Animal cells and systems
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    • v.14 no.4
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    • pp.291-296
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    • 2010
  • Population ecological characteristics of growth and mortality play an important role in understanding the population dynamics of marine mammals. The instantaneous coefficients of natural and bycatch mortality were estimated for minke whales (Balaenoptera acutorostrata) in Korean waters using a population assessment model composed of bycatch and abundance data. The survivorship curve of this population was fitted to the data, and then the curve was revised using age-specific relative bycatchability coefficients ($q_t$). Instantaneous coefficients of natural and bycatch mortality of minke whales were estimated as 0.024/year and 0.076/year, respectively, and from this the survival rate was estimated as 0.905. This estimated survival rate was comparable to other cetaceans in other regions. The $q_t$ for this population ranged from 0.020 to 0.193. The revised survival rates were higher when the $q_t$ was taken into account. The mortality coefficient, survival rate, $q_t$ and survivorship curves had not previously been determined for minke whale in this area. This estimate could serve as fundamental information to assess the status of this population and for conservation and rational management.

Braking performance of working rail-mounted cranes under wind load

  • Jin, Hui;Chen, Da
    • Wind and Structures
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    • v.19 no.1
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    • pp.1-14
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    • 2014
  • Rail-mounted cranes can be easily damaged by a sudden gust of wind while working at a running speed, due to the large mass and high barycenter positions. In current designs, working rail-mounted cranes mainly depend on wheel braking torques to resist large wind load. Regular brakes, however, cannot satisfactorily stop the crane, which induces safety issues of cranes and hence leads to frequent crane accidents, especially in sudden gusts of wind. Therefore, it is necessary and important to study the braking performance of working rail mounted cranes under wind load. In this study, a simplified mechanical model was built to simulate the working rail mounted gantry crane, and dynamic analysis of the model was carried out to deduce braking performance equations that reflect the qualitative relations among braking time, braking distance, wind load, and braking torque. It was shown that, under constant braking torque, there existed inflection points on the curves of braking time and distance versus windforce. Both the braking time and the distance increased sharply when wind load exceeded the inflection point value, referred to as the threshold windforce. The braking performance of a 300 ton shipbuilding gantry crane was modeled and analyzed using multibody dynamics software ADAMS. The simulation results were fitted by quadratic curves to show the changes of braking time and distance versus windforce under various mount of braking torques. The threshold windforce could be obtained theoretically by taking derivative of fitted curves. Based on the fitted functional relationship between threshold windforce and braking torque, theoretical basis are provided to ensure a safe and rational design for crane wind-resistant braking systems.

FATIGUE STRENGTH OF FILLET WELDED STEEL STRUCTURE UNDER OUT-OF-PLANE BENDING LOAD

  • Kang, Sung-Won;Kim, Wha-Soo;Paik, Young-Min
    • Proceedings of the KWS Conference
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    • 2002.10a
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    • pp.113-120
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    • 2002
  • The effect of out-of-plane loads on the fatigue strength of welded steel structures is examined through fatigue tests with weldment of two fillet weld joint types. The results of the fatigue tests are compared with those under axial loads, on the basis of the hot spot stress range at the weld toe. From the result of the comparison, a method on how to incorporate the effect of the out-of-plane bending stress is proposed using design S-N curves derived from fatigue tests under the axial load. The proposed method is useful for rational assessment of the fatigue strength of fillet-welded structures, where combined stresses of the in-plane axial stress and the out-of-plane bending stress are induced simultaneously due to the complexity of applied loads and structural geometry.

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