• Journal of applied mathematics & informatics
• /
• 제2권2호
• /
• pp.75-82
• /
• 1995

4대의 제어점에 의해 정의되는 3차 Bezier 곡선을 구간적 (piecewise) 2차 Bezier 곡선으로 근사 하는 기하적인 알고리듬을 제시한다. 또한 제시한알고리듬의 오차해석을 통하여 수정된 알 고리듬을 구성한다. 분확방법을 동시에 사용하여 주어진 허용오차 이내의 구간적 2차 근사 곡선을 구할수 있다. 제시한 알고리듬은 오차해석을 이용하여 필요한 분활의 수행회수를 미 리 결정할수있는장점을 가지고있다.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2001년도 추계학술대회 논문집
• /
• pp.58-61
• /
• 2001

An implicit finite element formulation for axisymmetric tube hydroforming is investigated. In order to describe normal anisotropy of the tube, Hill's non-quadratic yield function is employed. The frictional contact between die and tube and frictionless contact between tube and fluid are considered using the mesh-normal vector computed from finite element mesh of the tube. In order to verify the validity of the developed finite element formulation, the axisymmetric tube bulge test is simulated and simulation results are compared with experimental measurements. In the axisymmetric tube hydroforming process, an optimal hydraulic curve is pursued by performing the simulation with various internal pressures and axial forces.

• 대한수학회보
• /
• 제44권2호
• /
• pp.379-383
• /
• 2007

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

• Journal of Mechanical Science and Technology
• /
• 제15권2호
• /
• pp.192-198
• /
• 2001

We consider an interpolation problem with nonuniform rational B-spline curves given ordered data points. The existing approaches assume that weight for each point is available. But, it is not the case in practical applications. Schneider suggested a method which interpolates data points by automatically determining the weight of each control point. However, a drawback of Schneiders approach is that there is no guarantee of avoiding undesired poles; avoiding negative weights. Based on a quadratic programming technique, we use the weights of the control points for interpolating additional data. The weights are restricted to appropriate intervals; this guarantees the regularity of the interpolating curve. In a addition, a knot placement is proposed for pleasing interpolation. In comparison with integral B-spline interpolation, the proposed scheme leads to B-spline curves with fewer control points.

• 대한수학회지
• /
• 제60권5호
• /
• pp.1087-1107
• /
• 2023

Let E be an elliptic curve defined over ℚ of conductor N, c the Manin constant of E, and m the product of Tamagawa numbers of E at prime divisors of N. Let K be an imaginary quadratic field where all prime divisors of N split in K, P_K the Heegner point in E(K), and III(E/K) the Shafarevich-Tate group of E over K. Let 2u_K be the number of roots of unity contained in K. Gross and Zagier conjectured that if P_K has infinite order in E(K), then the integer c · m · u_K · |III(E/K)| $\frac{1}{2}$ is divisible by |E(ℚ)_tor|. In this paper, we prove that this conjecture is true if E(ℚ)_tor ≅ ℤ/2ℤ or ℤ/4ℤ except for two explicit families of curves. Further, we show these exceptions can be removed under Stein-Watkins conjecture.

• Journal of Ceramic Processing Research
• /
• 제13권spc2호
• /
• pp.241-245
• /
• 2012

The barrier rib on plasma display panel (PDP) is a typical 3D-patterned thick film with thickness of 120 ㎛ and it is hard to measure its dielectric constant in this state of the product. Because the porosity of ceramic thick film influenced the mechanical and dielectric characteristics, it was expected that there was the relationship between two properties. Therefore, the correlation analysis between porosity, hardness and dielectric constant of the barrier rib was studied and the exponential curve between porosity and hardness, and the quadratic curve between porosity and dielectric constant were drawn. The dielectric constant was well related to hardness by K400kHz = 0.5672 + 5.695 ln(Hv). The hardness was measured at five points on two real panels which sintered by two types of profiles and then dielectric constants and deviation were estimated by the above equation.

• International Journal of CAD/CAM
• /
• 제6권1호
• /
• pp.59-64
• /
• 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.

• 대한수의학회지
• /
• 제50권1호
• /
• pp.11-17
• /
• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• 천문학논총
• /
• 제30권2호
• /
• pp.593-594
• /
• 2015

We present our analysis results for an updated orbital ephemeris for the dipping low mass X-ray binary 4U 1624-49, using the light curve collected by the All Sky Monitor (ASM) on board the Rossi X-ray Timing Explorer (RXTE) and the Monitor of All-Sky X-ray Image (MAXI). To make clear dip profiles, the light curve from the ASM and the MAXI were divided into ten 500d segments and four 400d segments for ASM and MAXI light curves, respectively, and folded with the linear ephemeris proposed by Smale et al. (2001). The phases of dip centers were determined by the method adopted from Hu et al. (2008). The phase drift was then fitted with a linear function. We obtained an updated orbital period of 0.869896(1) d and a phase zero epoch of JD 2450088.6618(57). No clear orbital period derivative is detected with a 2-sigma upper limit of $1.4{\times}10^{-6}(yr)^{-1}$ from a quadratic curve fitting of the dip phase evolution.

• 통합자연과학논문집
• /
• 제9권2호
• /
• pp.144-151
• /
• 2016

The purpose of this study is to investigate the emotion effects on academic achievement for university students. The results are as follows. Resulting on the each emotions difference by the statistical variables, anxiety scores by gender showed a significant difference in the p<.01 level(F=7.685). The males anxiety(2.478, standard deviation: 0.180) had significantly lower scores than females(3.076, standard deviation: 0.168). But fear, anger, activity, and sociability scores were not significantly different respectively between male and female students. To see the emotions effect of academic achievement, the analysis method of the linear regression line was used. As the result, anxiety, fear, anger, activity, and sociability did not significantly influence academic achievement. And so unlike previous methods, the analysis method of the quadratic regression curve was used. As the result, anxiety, fear, anger, activity, and sociability showed did significantly influence academic achievement respectively within 5% of statistical significance level, to more than F=3.06. Therefore, the values on academic achievement of the each anxiety, fear, anger, activity, and sociability showed a quadratic regression curve. That is, [Academic achievement]=$-0.9685{\times}[Anxiety]^2+5.1342{\times}[Anxiety]+8.2679$,[Academic achievement]=$-1.0638{\times}[Fear]^2+5.5694{\times}[Fear]+7.5635$,[Academic achievement]=$-1.3497{\times}[Anger]^2+9.1284{\times}[Anger]+0.6720$,[Academic achievement]=$-1.0589{\times}[Activity]^2+7.4386{\times}[Activity]+1.8272$,[Academic achievement]=$-1.6830{\times}[Sociability]^2+11.2325{\times}[Sociability]-3.8258$. Therefore, we were able to determine the following conclusions. First, we were able to predict the degree of academic achievement by the each emotions scale. Second, when the each emotion scores of students was a moderate, the academic achievement was most excellent. So, in order for the students to become higher academic achievement, the maintenance of medium degree of the each emotions scores is required.