• Journal of the Korean Society of Visualization
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• v.20 no.3
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• pp.74-85
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• 2022

We propose a Cubic-Interpolated Pseudo-Particle Lattice Boltzmann method (CIP-LBM) for the convection-diffusion equation (CDE) based on the Bhatnagar-Gross-Krook (BGK) scheme equation. The CIP-LBM relies on an accurate numerical lattice equilibrium particle distribution function on the advection term and the use of a splitting technique to solve the Lattice Boltzmann equation. Different schemes of lattice spaces such as D1Q3, D2Q5, and D2Q9 have been used for simulating a variety of problems described by the CDE. All simulations were carried out using the BGK model, although another LB scheme based on a collision term like two-relation time or multi-relaxation time can be easily applied. To show quantitative agreement, the results of the proposed model are compared with an analytical solution.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.89-99
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• 2006

In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

• Journal of the Korea Society for Simulation
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• v.17 no.3
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• pp.19-26
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• 2008

In this paper, we propose a dynamic prediction algorithm to predict the bond price using actual data set of treasure note (T-Note). The proposed algorithm is based on term structure model of the interest rates, which takes place in various financial modelling, such as the standard Gaussian Wiener process. To obtain cumulative distribution functions (CDFs) of actual data for the interest rate measurement used, we use the natural cubic spline (NCS) method, which is generally used as numerical methods for interpolation. Then we also use the random number generation scheme (RNGS) to calculate the pricing of bond through the obtained CDF. In empirical computer simulations, we show that the lower values of precision in the proposed prediction algorithm corresponds to sharper estimates. It is very reasonable on prediction.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.89-112
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• 2017

In this study we have analyzed processes of generalization in which students have geometrically solved cubic equation $x^3+ax=b$, regarding geometrical solution of cubic equation $x^3+4x=32$ as examples. The result of this research indicate that students could especially re-interpret the geometric solution of the given cubic equation via dynamically understanding the variables in dynamic geometry environment. Furthermore, participants could simultaneously re-interpret the given geometric solution and then present a different geometric solutions of $x^3+ax=b$, so that the level of generalization could be improved. In conclusion, the study could provide useful pedagogical implications in school mathematics that the dynamic geometry environment performs significant function as a means of students-centered exploration when understanding variables and enhancing the level of generalization in problem solving.

• Journal of the Korea Society of Computer and Information
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• v.13 no.6
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• pp.163-171
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• 2008

In this paper, we present an adaptive parametric cubic convolution technique in order to enlarge the low resolution image to the high resolution image. The proposed method consists of two steps. During the first interpolation step, we acquire adaptive parameters in introducing a new cost-function to reflect frequency properties. And, the second interpolation step performs cubic convolution by applying the parameters obtained from the first step. The enhanced interpolation kernel using adaptive parameters produces output image better than the conventional one using a fixed parameter. Experimental results show that the proposed method can not only provides the performances of $0.5{\sim}4dB$ improvements in terms of PSNR, but also exhibit better edge preservation ability and original image similarity than conventional methods in the enlarged images.

• Journal of Electrical Engineering and Technology
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• v.10 no.2
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• Journal of the Korean Ceramic Society
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• v.54 no.1
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• pp.38-42
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• 2017

Vanadium nitride (VN) coatings were deposited using inductively coupled plasma (ICP) assisted sputtering at different ICP powers. Microstructural, crystallographic and mechanical characterizations were performed by FE-SEM, AFM, XRD and nanoindentation. The results show that ICP has significant effects on coating's microstructure, structural and mechanical properties of VN coatings. With an increase in ICP power, coating microstructure evolved from a porous columnar structure to a highly dense one. Single- phase cubic (FCC) VN coatings with different preferential orientations and residual stresses were obtained as a function of ICP power. Average crystal grain sizes of single phase cubic (FCC) VN coatings were decreased from 10.1 nm to 4.0 nm with an increase in ICP power. The maximum hardness of 28.2 GPa was obtained for the coatings deposited at ICP power of 200 W. The smoothest surface morphology with Ra roughness of 1.7 nm was obtained in the VN coating sputtered at ICP power of 200 W.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.17-29
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• 2018

We find modular equations of degree 3 to evaluate some new values of the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for $n={\frac{2{\cdot}4^m}{3}}$, ${\frac{1}{3{\cdot}4^m}}$, and ${\frac{2}{3{\cdot}4^m}}$, where m = 1, 2, 3, or 4.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.5
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• pp.463-470
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• 2005

This paper describes a method aimed at improving dead-reckoning accuracy with gyroscopes in mobile robots. The method is a precision calibration procedure for gyroscopes, which effectively reduces the ill effects of nonlinearity of the scale-factor and temperature dependency. This paper also describes the methods of gyro data collection fur all ambient temperature$(-40^{\circ}C{\~}+80^{\circ}C)$ using cubic spline interpolation and defining the error function. The sensor used was a vibrating gyroscope called the EWTS82NA21, which is low lost and commonly used in car navigation system, made by Panasonic. This angular rate sensor utilizes Coriolis force generated by a vibrating tuning fork. The paper also provides experimental results to check the performance and the effectiveness of the proposed method.