• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.659-662
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• 2000

다양한 보간 기법을 정리해 보고 이를 통해서 기존의 보간 기법의 한계를 고찰해 본다. 보간의 효율성과 보간 결과 영상의 화질과는 Trade off 관계가 있으며, 이를 적절한 수준에서 결정하는 것은 중요한 문제이다. 본 논문에서는 Quadratic B-spline을 기저 함수로 하는 윤곽보존형 보간 필터를 사용한 영상확대 알고리즘을 제안한다. Unser의 Cardinal Cubic spline함수에 비해 적은 하드웨어만으로도 이상적인 저역 통과 필터의 특성을 가지며, 입력영상의 윤곽의 방향성을 고려한 적응적인 보간 기법의 적용으로 화질이 우수한 영상확대 알고리즘을 제안한다.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.765-773
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• 2017

The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler-Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin's approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ($\bar{n}$).

• East Asian mathematical journal
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• v.29 no.5
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• pp.503-510
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• 2013

A quadratic B-spline finite element method for the spatial variable combined with a Newton method for the time variable is proposed to approximate a solution of Benjamin-Bona-Mahony-Burgers (BBMB) equation. Two examples were considered to show the efficiency of the proposed scheme. The numerical solutions obtained for various viscosity were compared with the exact solutions. The numerical results show that the scheme is efficient and feasible.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.349-363
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• 2020

Penalized spline is a suitable nonparametric approach in estimating mean model in small area. However, application of the approach in informative sampling in a published article is uncommon. We propose a semiparametric mixed-model using penalized spline under informative sampling to estimate mean of small area. The response variable is explained in terms of mean model, informative sample effect, area random effect and unit error. We approach the mean model by penalized spline and utilize a penalized spline function of the inclusion probability to account for the informative sample effect. We determine the best and unbiased estimators for coefficient model and derive the restricted maximum likelihood estimators for the variance components. A simulation study shows a decrease in the average absolute bias produced by the proposed model. A decrease in the root mean square error also occurred except in some quadratic cases. The use of linear and quadratic penalized spline to approach the function of the inclusion probability provides no significant difference distribution of root mean square error, except for few smaller samples.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.17-27
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• 2001

We discuss a finite difference preconditioner for the$C^1$ Lagrance quadratic spline collocation method for a uniformly elliptic operator with homogeneous Dirichlet boundary conditions. Using the generalized field of values argument, we analyzed eigenvalues of the matrix preconditioned by the matrix corresponding to a finite difference operator with zero boundary condition.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.10a
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• pp.246-249
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• 2007

In numerical analysis for phase change material, numerical values of thermodynamic properties such as temperature, pressure, specific volume, enthalpy and entropy are required. But the steam table or diagram itself cannot be used without modelling. In this study applicability of neural networks in modelling superheated vapor region of water was examined by comparing with the quadratic spline. neural network consists of an input layer with 2 nodes, two hidden layers and an output layer with 3 nodes. Quadratic spline interpoation method was also applied for comparison. Neural network model revealed smaller percentage error to quadratic spline interpolation. From these results, it is confirmed that the neural networks could be powerful method in modelling the superheated range of the steam table.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.269-277
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• 2014

A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.